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Plane wave representing a particle passing through two slits, resulting in an interference pattern on a screen some distance away from the slits. [1] .

The double-slit experiment is an experiment in quantum mechanics and optics demonstrating the wave-particle duality of electrons , photons , and other fundamental objects in physics. When streams of particles such as electrons or photons pass through two narrow adjacent slits to hit a detector screen on the other side, they don't form clusters based on whether they passed through one slit or the other. Instead, they interfere: simultaneously passing through both slits, and producing a pattern of interference bands on the screen. This phenomenon occurs even if the particles are fired one at a time, showing that the particles demonstrate some wave behavior by interfering with themselves as if they were a wave passing through both slits.

Niels Bohr proposed the idea of wave-particle duality to explain the results of the double-slit experiment. The idea is that all fundamental particles behave in some ways like waves and in other ways like particles, depending on what properties are being observed. These insights led to the development of quantum mechanics and quantum field theory , the current basis behind the Standard Model of particle physics , which is our most accurate understanding of how particles work.

The original double-slit experiment was performed using light/photons around the turn of the nineteenth century by Thomas Young, so the original experiment is often called Young's double-slit experiment. The idea of using particles other than photons in the experiment did not come until after the ideas of de Broglie and the advent of quantum mechanics, when it was proposed that fundamental particles might also behave as waves with characteristic wavelengths depending on their momenta. The single-electron version of the experiment was in fact not performed until 1974. A more recent version of the experiment successfully demonstrating wave-particle duality used buckminsterfullerene or buckyballs , the \(C_{60}\) allotrope of carbon.

Waves vs. Particles

Double-slit experiment with electrons, modeling the double-slit experiment.

To understand why the double-slit experiment is important, it is useful to understand the strong distinctions between wave and particles that make wave-particle duality so intriguing.

Waves describe oscillating values of a physical quantity that obey the wave equation . They are usually described by sums of sine and cosine functions, since any periodic (oscillating) function may be decomposed into a Fourier series . When two waves pass through each other, the resulting wave is the sum of the two original waves. This is called a superposition since the waves are placed ("-position") on top of each other ("super-"). Superposition is one of the most fundamental principles of quantum mechanics. A general quantum system need not be in one state or another but can reside in a superposition of two where there is some probability of measuring the quantum wavefunction in one state or another.

Left: example of superposed waves constructively interfering. Right: superposed waves destructively interfering. [2]

If one wave is \(A(x) = \sin (2x)\) and the other is \(B(x) = \sin (2x)\), then they add together to make \(A + B = 2 \sin (2x)\). The addition of two waves to form a wave of larger amplitude is in general known as constructive interference since the interference results in a larger wave.

If one wave is \(A(x) = \sin (2x)\) and the other is \(B(x) = \sin (2x + \pi)\), then they add together to make \(A + B = 0\) \(\big(\)since \(\sin (2x + \pi) = - \sin (2x)\big).\) This is known as destructive interference in general, when adding two waves results in a wave of smaller amplitude. See the figure above for examples of both constructive and destructive interference.

Two speakers are generating sounds with the same phase, amplitude, and wavelength. The two sound waves can make constructive interference, as above left. Or they can make destructive interference, as above right. If we want to find out the exact position where the two sounds make destructive interference, which of the following do we need to know?

a) the wavelength of the sound waves b) the distances from the two speakers c) the speed of sound generated by the two speakers

This wave behavior is quite unlike the behavior of particles. Classically, particles are objects with a single definite position and a single definite momentum. Particles do not make interference patterns with other particles in detectors whether or not they pass through slits. They only interact by colliding elastically , i.e., via electromagnetic forces at short distances. Before the discovery of quantum mechanics, it was assumed that waves and particles were two distinct models for objects, and that any real physical thing could only be described as a particle or as a wave, but not both.

In the more modern version of the double slit experiment using electrons, electrons with the same momentum are shot from an "electron gun" like the ones inside CRT televisions towards a screen with two slits in it. After each electron goes through one of the slits, it is observed hitting a single point on a detecting screen at an apparently random location. As more and more electrons pass through, one at a time, they form an overall pattern of light and dark interference bands. If each electron was truly just a point particle, then there would only be two clusters of observations: one for the electrons passing through the left slit, and one for the right. However, if electrons are made of waves, they interfere with themselves and pass through both slits simultaneously. Indeed, this is what is observed when the double-slit experiment is performed using electrons. It must therefore be true that the electron is interfering with itself since each electron was only sent through one at a time—there were no other electrons to interfere with it!

When the double-slit experiment is performed using electrons instead of photons, the relevant wavelength is the de Broglie wavelength \(\lambda:\)

\[\lambda = \frac{h}{p},\]

where \(h\) is Planck's constant and \(p\) is the electron's momentum.

Calculate the de Broglie wavelength of an electron moving with velocity \(1.0 \times 10^{7} \text{ m/s}.\)

Usain Bolt, the world champion sprinter, hit a top speed of 27.79 miles per hour at the Olympics. If he has a mass of 94 kg, what was his de Broglie wavelength?

Express your answer as an order of magnitude in units of the Bohr radius \(r_{B} = 5.29 \times 10^{-11} \text{m}\). For instance, if your answer was \(4 \times 10^{-5} r_{B}\), your should give \(-5.\)

Image Credit: Flickr drcliffordchoi.

While the de Broglie relation was postulated for massive matter, the equation applies equally well to light. Given light of a certain wavelength, the momentum and energy of that light can be found using de Broglie's formula. This generalizes the naive formula \(p = m v\), which can't be applied to light since light has no mass and always moves at a constant velocity of \(c\) regardless of wavelength.

The below is reproduced from the Amplitude, Frequency, Wave Number, Phase Shift wiki.

In Young's double-slit experiment, photons corresponding to light of wavelength \(\lambda\) are fired at a barrier with two thin slits separated by a distance \(d,\) as shown in the diagram below. After passing through the slits, they hit a screen at a distance of \(D\) away with \(D \gg d,\) and the point of impact is measured. Remarkably, both the experiment and theory of quantum mechanics predict that the number of photons measured at each point along the screen follows a complicated series of peaks and troughs called an interference pattern as below. The photons must exhibit the wave behavior of a relative phase shift somehow to be responsible for this phenomenon. Below, the condition for which maxima of the interference pattern occur on the screen is derived.

Left: actual experimental two-slit interference pattern of photons, exhibiting many small peaks and troughs. Right: schematic diagram of the experiment as described above. [3]

Since \(D \gg d\), the angle from each of the slits is approximately the same and equal to \(\theta\). If \(y\) is the vertical displacement to an interference peak from the midpoint between the slits, it is therefore true that

\[D\tan \theta \approx D\sin \theta \approx D\theta = y.\]

Furthermore, there is a path difference \(\Delta L\) between the two slits and the interference peak. Light from the lower slit must travel \(\Delta L\) further to reach any particular spot on the screen, as in the diagram below:

Light from the lower slit must travel further to reach the screen at any given point above the midpoint, causing the interference pattern.

The condition for constructive interference is that the path difference \(\Delta L\) is exactly equal to an integer number of wavelengths. The phase shift of light traveling over an integer \(n\) number of wavelengths is exactly \(2\pi n\), which is the same as no phase shift and therefore constructive interference. From the above diagram and basic trigonometry, one can write

\[\Delta L = d\sin \theta \approx d\theta = n\lambda.\]

The first equality is always true; the second is the condition for constructive interference.

Now using \(\theta = \frac{y}{D}\), one can see that the condition for maxima of the interference pattern, corresponding to constructive interference, is

\[n\lambda = \frac{dy}{D},\]

i.e. the maxima occur at the vertical displacements of

\[y = \frac{n\lambda D}{d}.\]

The analogous experimental setup and mathematical modeling using electrons instead of photons is identical except that the de Broglie wavelength of the electrons \(\lambda = \frac{h}{p}\) is used instead of the literal wavelength of light.

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Wave Optics

Young’s double slit experiment, learning objectives.

By the end of this section, you will be able to:

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 1).

Figure 1. Young’s double slit experiment. Here pure-wavelength light sent through a pair of vertical slits is diffracted into a pattern on the screen of numerous vertical lines spread out horizontally. Without diffraction and interference, the light would simply make two lines on the screen.

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single λ ) light to clarify the effect. Figure 2 shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

Figure 2. The amplitudes of waves add. (a) Pure constructive interference is obtained when identical waves are in phase. (b) Pure destructive interference occurs when identical waves are exactly out of phase, or shifted by half a wavelength.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 3a. Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 3b. Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

Figure 3. Double slits produce two coherent sources of waves that interfere. (a) Light spreads out (diffracts) from each slit, because the slits are narrow. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). We can only see this if the light falls onto a screen and is scattered into our eyes. (b) Double slit interference pattern for water waves are nearly identical to that for light. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this. (credit: PASCO)

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 4. Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 4a. If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in Figure 4b. More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [(1/2) λ , (3/2) λ , (5/2) λ , etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ( λ , 2 λ , 3 λ , etc.), then constructive interference occurs.

Figure 4. Waves follow different paths from the slits to a common point on a screen. (a) Destructive interference occurs here, because one path is a half wavelength longer than the other. The waves start in phase but arrive out of phase. (b) Constructive interference occurs here because one path is a whole wavelength longer than the other. The waves start out and arrive in phase.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Figure 5. The paths from each slit to a common point on the screen differ by an amount dsinθ, assuming the distance to the screen is much greater than the distance between slits (not to scale here).

Figure 5 shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle θ between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be d sin  θ , where d is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or  d sin  θ = mλ, for   m = 0, 1, −1, 2, −2, . . . (constructive).

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

[latex]d\sin\theta=\left(m+\frac{1}{2}\right)\lambda\text{, for }m=0,1,-1,2,-2,\dots\text{ (destructive)}\\[/latex],

where λ is the wavelength of the light, d is the distance between slits, and θ is the angle from the original direction of the beam as discussed above. We call m the order of the interference. For example, m  = 4 is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 6. The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation  d sin  θ = mλ, for   m = 0, 1, −1, 2, −2, . . . .

For fixed λ and m , the smaller d is, the larger θ must be, since [latex]\sin\theta=\frac{m\lambda}{d}\\[/latex]. This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance d apart) is small. Small d gives large θ , hence a large effect.

Figure 6. The interference pattern for a double slit has an intensity that falls off with angle. The photograph shows multiple bright and dark lines, or fringes, formed by light passing through a double slit.

Example 1. Finding a Wavelength from an Interference Pattern

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that m  = 3. We are given d = 0.0100 mm and θ  = 10.95º. The wavelength can thus be found using the equation  d sin  θ = mλ  for constructive interference.

The equation is d sin  θ = mλ . Solving for the wavelength λ gives [latex]\lambda=\frac{d\sin\theta}{m}\\[/latex].

Substituting known values yields

[latex]\begin{array}{lll}\lambda&=&\frac{\left(0.0100\text{ nm}\right)\left(\sin10.95^{\circ}\right)}{3}\\\text{ }&=&6.33\times10^{-4}\text{ nm}=633\text{ nm}\end{array}\\[/latex]

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with λ , so that spectra (measurements of intensity versus wavelength) can be obtained.

Example 2. Calculating Highest Order Possible

Interference patterns do not have an infinite number of lines, since there is a limit to how big m can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation  d sin  θ = mλ ( for   m = 0, 1, −1, 2, −2, . . . ) describes constructive interference. For fixed values of d and λ , the larger m is, the larger sin  θ  is. However, the maximum value that sin  θ  can have is 1, for an angle of 90º. (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which m corresponds to this maximum diffraction angle.

Solving the equation  d sin  θ = mλ  for m gives [latex]\lambda=\frac{d\sin\theta}{m}\\[/latex].

Taking sin  θ = 1 and substituting the values of d and λ from the preceding example gives

[latex]\displaystyle{m}=\frac{\left(0.0100\text{ mm}\right)\left(1\right)}{633\text{ nm}}\approx15.8\\[/latex]

Therefore, the largest integer m can be is 15, or  m  = 15.

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

Section Summary

• Young’s double slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.
• There is constructive interference when  d sin  θ = mλ ( for   m = 0, 1, −1, 2, −2, . . . ), where d  is the distance between the slits, θ is the angle relative to the incident direction, and m  is the order of the interference.
• There is destructive interference when  d sin  θ = mλ ( for   m = 0, 1, −1, 2, −2, . . . ).

Conceptual Questions

• Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.
• Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.
• Is it possible to create a situation in which there is only destructive interference? Explain.
• Figure 7 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Figure 7. This double slit interference pattern also shows signs of single slit interference. (credit: PASCO)

Problems & Exercises

• At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?
• Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.
• What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of 30.0º?
• Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of 45.0º.
• Calculate the wavelength of light that has its third minimum at an angle of 30.0º when falling on double slits separated by 3.00 μm.
• What is the wavelength of light falling on double slits separated by 2.00 μm if the third-order maximum is at an angle of 60.0º?
• At what angle is the fourth-order maximum for the situation in Question 1?
• What is the highest-order maximum for 400-nm light falling on double slits separated by 25.0 μm?
• Find the largest wavelength of light falling on double slits separated by 1.20 μm for which there is a first-order maximum. Is this in the visible part of the spectrum?
• What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?
• (a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?
• (a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of 10.0º, at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?

Figure 8. The distance between adjacent fringes is [latex]\Delta{y}=\frac{x\lambda}{d}\\[/latex], assuming the slit separation d  is large compared with λ .

• Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 8.
• Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 8).

coherent:  waves are in phase or have a definite phase relationship

constructive interference for a double slit:  the path length difference must be an integral multiple of the wavelength

destructive interference for a double slit:  the path length difference must be a half-integral multiple of the wavelength

incoherent:  waves have random phase relationships

order:  the integer m  used in the equations for constructive and destructive interference for a double slit

Selected Solutions to Problems & Exercises

3. 1.22 × 10 −6 m

9. 1200 nm (not visible)

11. (a) 760 nm; (b) 1520 nm

13. For small angles sin θ − tan θ  ≈ θ  (in radians).

For two adjacent fringes we have,  d  sin θ m = mλ  and  d sin θ m + 1 = ( m  + 1) λ

Subtracting these equations gives

[latex]\begin{array}{}d\left(\sin{\theta }_{\text{m}+1}-\sin{\theta }_{\text{m}}\right)=\left[\left(m+1\right)-m\right]\lambda \\ d\left({\theta }_{\text{m}+1}-{\theta }_{\text{m}}\right)=\lambda \\ \text{tan}{\theta }_{\text{m}}=\frac{{y}_{\text{m}}}{x}\approx {\theta }_{\text{m}}\Rightarrow d\left(\frac{{y}_{\text{m}+1}}{x}-\frac{{y}_{\text{m}}}{x}\right)=\lambda \\ d\frac{\Delta y}{x}=\lambda \Rightarrow \Delta y=\frac{\mathrm{x\lambda }}{d}\end{array}\\[/latex]

• College Physics. Authored by : OpenStax College. Located at : http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics . License : CC BY: Attribution . License Terms : Located at License

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The observation of interference effects definitively indicates the presence of overlapping waves. Thomas Young postulated that light is a wave and is subject to the superposition principle; his great experimental achievement was to demonstrate the constructive and destructive interference of light (c. 1801). In a modern version of Young’s experiment, differing in its essentials only in the source of light, a laser equally illuminates two parallel slits in an otherwise opaque surface. The light passing through the two slits is observed on a distant screen. When the widths of the slits are significantly greater than the wavelength of the light, the rules of geometrical optics hold—the light casts two shadows, and there are two illuminated regions on the screen. However, as the slits are narrowed in width, the light diffracts into the geometrical shadow, and the light waves overlap on the screen. (Diffraction is itself caused by the wave nature of light, being another example of an interference effect—it is discussed in more detail below.)

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The superposition principle determines the resulting intensity pattern on the illuminated screen. Constructive interference occurs whenever the difference in paths from the two slits to a point on the screen equals an integral number of wavelengths (0, λ, 2λ,…). This path difference guarantees that crests from the two waves arrive simultaneously. Destructive interference arises from path differences that equal a half-integral number of wavelengths (λ/2, 3λ/2,…). Young used geometrical arguments to show that the superposition of the two waves results in a series of equally spaced bands, or fringes, of high intensity, corresponding to regions of constructive interference, separated by dark regions of complete destructive interference.

An important parameter in the double-slit geometry is the ratio of the wavelength of the light λ to the spacing of the slits d . If λ/ d is much smaller than 1, the spacing between consecutive interference fringes will be small, and the interference effects may not be observable. Using narrowly separated slits, Young was able to separate the interference fringes. In this way he determined the wavelengths of the colours of visible light. The very short wavelengths of visible light explain why interference effects are observed only in special circumstances—the spacing between the sources of the interfering light waves must be very small to separate regions of constructive and destructive interference.

Observing interference effects is challenging because of two other difficulties. Most light sources emit a continuous range of wavelengths, which result in many overlapping interference patterns, each with a different fringe spacing. The multiple interference patterns wash out the most pronounced interference effects, such as the regions of complete darkness. Second, for an interference pattern to be observable over any extended period of time, the two sources of light must be coherent with respect to each other. This means that the light sources must maintain a constant phase relationship. For example, two harmonic waves of the same frequency always have a fixed phase relationship at every point in space, being either in phase, out of phase, or in some intermediate relationship. However, most light sources do not emit true harmonic waves; instead, they emit waves that undergo random phase changes millions of times per second. Such light is called incoherent . Interference still occurs when light waves from two incoherent sources overlap in space, but the interference pattern fluctuates randomly as the phases of the waves shift randomly. Detectors of light, including the eye, cannot register the quickly shifting interference patterns, and only a time-averaged intensity is observed. Laser light is approximately monochromatic (consisting of a single wavelength) and is highly coherent; it is thus an ideal source for revealing interference effects.

After 1802, Young’s measurements of the wavelengths of visible light could be combined with the relatively crude determinations of the speed of light available at the time in order to calculate the approximate frequencies of light. For example, the frequency of green light is about 6 × 10 14 Hz ( hertz , or cycles per second). This frequency is many orders of magnitude larger than the frequencies of common mechanical waves. For comparison, humans can hear sound waves with frequencies up to about 2 × 10 4 Hz. Exactly what was oscillating at such a high rate remained a mystery for another 60 years.

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Young's Experiment

• Anatomy of a Two-Point Source Interference Pattern
• The Path Difference
• Young's Equation
• Young's Experiment
• Other Applications of Two-Point Source Interference

Today's classroom version of the same experiment is typically performed using a laser beam as the source. Rather than using a note card to split the single beam into two coherent beams, a carbon-coated glass slide with two closely spaced etched slits is used. The slide with its slits is most commonly purchased from a manufacturer who provides a measured value for the slit separation distance - the d value in Young's equation. Light from the laser beam diffracts through the slits and emerges as two separate coherent waves. The interference pattern is then projected onto a screen where reliable measurements can be made of L and y for a given bright spot with order value m . Knowing these four values allows a student to determine the value of the wavelength of the original light source.

To illustrate some typical results from this experiment and the subsequent analysis, consider the sample data provided below for d, y, L and m.

(Note: AN 0 = central antinode and AN 4 = fourth antinode)  

The determination of the wavelength demands that the above values for d, y, L and m be substituted into Young's equation.

Careful inspection of the units of measurement is always advisable. The sample data here reveal that each measured quantity is recorded with a different unit. Before substituting these measured values into the above equation, it is important to give some thought to the treatment of units. One means of resolving the issue of nonuniform units is to simply pick a unit of length and to convert all quantities to that unit. If doing so, one might want to pick a unit that one of the data values already has so that there is one less conversion. A wise choice is to choose the meter as the unit to which all other measured values are converted. Since there are 1000 millimeters in 1 meter, the 0.250 mm is equivalent to 0.000250 meter. And since there are 100 centimeters in 1 meter, the 10.2 cm is equivalent to 0.102 m. Thus, the new values of d, y and L are:

While the conversion of all the data to the same unit is not the only means of treating such measured values, it might be the most advisable - particularly for those students who are less at ease with such conversions.

Now that the issue regarding the units of measurement has been resolved, substitution of the measured values into Young's equation can be performed.

λ  = 6.52 x 10 -7 m

As is evident here, the wavelength of visible light is rather small. For this reason wavelength is often expressed using the unit nanometer, where 1 meter is equivalent to 10 9 nanometers. Multiplying by 10 9 will convert the wavelength from meters to nanometers (abbreviated nm).

We Would Like to Suggest ...

Check Your Understanding

1. The diagram below depicts the results of Young's Experiment. The appropriate measurements are listed on the diagram. Use these measurements to determine the wavelength of light in nanometers. (GIVEN: 1 meter = 10 9 nanometers)

Answer: 657 nm

First, identify known values in terms of their corresponding variable symbol:

L = 10.2 m = 1020 cm y = 22.5 cm m = 10 d = 0.298 mm = 0.0298 cm

(Note: m was chosen as 10 since the y distance corresponds to the distance from the 5th bright band on one side of the central band and the 5th bright band on the other side of the central band.)

Then convert all known values to an identical unit. In this case, cm has been chosen as the unit to use. The converted values are listed in the table above.

Substitute all values into Young's equation and perform calculation of the wavelength. The unit of wavelength is cm.

λ = y • d / ( m • L) λ = ( 22.5 cm ) • ( 0.0298 cm ) / [ ( 10 ) • ( 1020 cm ) ] λ = 6.57 x 10 -5 cm

Finally convert to nanometers using a conversion factor. If there are 10 9 nm in 1 meter, then there must be 10 7 nm in the smaller centimeter.

λ = ( 6.57 x 10 -5 cm ) • ( 10 7 nm / 1 cm ) = 657 nm

2. A student uses a laser and a double-slit apparatus to project a two-point source light interference pattern onto a whiteboard located 5.87 meters away. The distance measured between the central bright band and the fourth bright band is 8.21 cm. The slits are separated by a distance of 0.150 mm. What would be the measured wavelength of light?

Answer: 524 nm

L = 5.87 m = 587 cm y = 8.21 cm m = 4 d = 0.150 mm = 0.0150 cm

λ = y • d / ( m • L) λ = ( 8.21 cm ) • ( 0.0150 cm ) / [ ( 4 ) • ( 587 cm ) ] λ = 5.24 x 10 -5 cm

λ = ( 5.24 x 10 -5 cm ) • ( 10 7 nm / 1 cm ) = 524 nm

3. The analysis of any two-point source interference pattern and a successful determination of wavelength demands an ability to sort through the measured information and equating the values with the symbols in Young's equation. Apply your understanding by interpreting the following statements and identifying the values of y, d, m and L. Finally, perform some conversions of the given information such that all information share the same unit.

This question simply asks to equate the stated information with the variables of Young's equation and to perform conversions such that all information is in the same unit.

(Note that m = 4.5 represents the fifth nodal position or dark band from the central bright band. Also note that the given values have been converted to cm.)

b. An interference pattern is produced when light is incident upon two slits that are 50.0 micrometers apart. The perpendicular distance from the midpoint between the slits to the screen is 7.65 m. The distance between the two third-order antinodes on opposite sides of the pattern is 32.9 cm.

This question simply asks to equate the stated information with the variables of Young's equation and to perform conversions such that all information is in the same unit. 

(Note that m = 6 corresponds to six spacings. There are three spacings between the central antinode and the third antinode. The stated distance is twice as far so the m value must be doubled. Also note that the given values have been converted to cm. There are 10 6 µm in one meter; so there are 10 4 µm in one centimeter.)

c. The fourth nodal line on an interference pattern is 8.4 cm from the first antinodal line when the screen is placed 235 cm from the slits. The slits are separated by 0.25 mm.

 ( Note that the fourth nodal line is assigned the order value of 3.5. Also note that the given values have been converted to cm.)

d. Two sources separated by 0.500 mm produce an interference pattern 525 cm away. The fifth and the second antinodal line on the same side of the pattern are separated by 98 mm.

  ( Note that there are three spacings between the second and the fifth bright bands. Since all spacings are the same distance apart, the distance between the second and the fifth bright bands would be the same as the distance between the central and the third bright bands. Thus, m = 3. Also note that the given values have been converted to cm.)

e. Two slits that are 0.200 mm apart produce an interference pattern on a screen such that the central maximum and the 10th bright band are distanced by an amount equal to one-tenth the distance from the slits to the screen.

 ( Note that there are 10 spacings between the central anti-node and the tenth bright band or tenth anti-node. And observe that they do not state the actual values of L and y; the value of y is expressed in terms of L. )

f. The fifth antinodal line and the second nodal line on the opposite side of an interference pattern are separated by a distance of 32.1 cm when the slits are 6.5 m from the screen. The slits are separated by 25.0 micrometers.

 ( Note that there are five spacings between the central anti-node and the fifth anti-node. And there are 1.5 spacings from the central anti-node in the opposite direction out to the second nodal line. Thus, m = 6.5. Also note that the given values have been converted to cm. There are 10 6 µm in one meter; so there are 10 4 µm in one centimeter.)

g. If two slits 0.100 mm apart are separated from a screen by a distance of 300 mm, then the first-order minimum will be 1 cm from the central maximum.

  ( Note that a the first-order minimum is a point of minimum brightness or a nodal position. The first-order minimum is the first nodal position and is thus the m = 0.5 node. Also note that the given values have been converted to cm. )

h. Consecutive bright bands on an interference pattern are 3.5 cm apart when the slide containing the slits is 10.0 m from the screen. The slit separation distance is 0.050 mm.

   ( Note that the spacing between adjacent bands is given. This distance is equivalent with the distance from the central bright band to the first antinode. Thus, m = 1. Also note that the given values have been converted to cm. )

Chapter 27 Wave Optics

27.3 Young’s Double Slit Experiment

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 1 ).

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 3 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 3 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 6 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

Example 1: Finding a Wavelength from an Interference Pattern

Substituting known values yields

Example 2: Calculating Highest Order Possible

Strategy and Concept

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

Section Summary

• Young’s double slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.

Conceptual Questions

1: Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

2: Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

3: Is it possible to create a situation in which there is only destructive interference? Explain.

4:   Figure 7 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Problems & Exercises

2: Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

7: At what angle is the fourth-order maximum for the situation in Problems & Exercises 1 ?

10: What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

11: (a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

14: Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 8 .

15: Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 8 ).

9: 1200 nm (not visible)

11: (a) 760 nm

(b) 1520 nm

For two adjacent fringes we have,

Subtracting these equations gives

College Physics Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• He placed a screen that had two slits cut into it in front of a monochromatic ( single color ) light.
• The results of Young's Double Slit Experiment should be very different if light is a wave or a particle.
• Let’s look at what the results would be in both situations, and then see how this experiment supports the wave model.

If light is a particle…

We set up our screen and shine a bunch of monochromatic light onto it.

• Imagine it as being almost as though we are spraying paint from a spray can through the openings.
• Since they are little particles they will make a pattern of two exact lines on the viewing screen ( Figure 1 ).

If light is a wave…

If light is a wave, everything starts the same way, but results we get are very different.

• Remember, diffraction is when light passes through a small opening and starts to spread out. This will happen from both openings ( Figure 2 ).
• Where crest meets crest , there will be constructive interference and the waves will make it to the viewing screen as a bright spot .
• Where crest meets trough there will be destructive interference that cancel each other out… a black spot will appear on the screen.
• When this experiment is performed we actually see this, as shown in Figure 3 .

We must conclude that light is made up of waves, since particles can not diffract.

Calculations

When you set up this sort of an apparatus, there is actually a way for you to calculate where the bright lines (called fringes ) will appear.

• There is always a middle line, which is the brightest. We call it the central fringe .
• The central fringe is n = 0 .
• The fringe to either side of the central fringe has an order of n = 1 (the first order fringe ).
• The order of the next fringe out on either side is n = 2 (the second order fringe ).
• And so on, as shown in Figure 4 .

The formula that we will use to figure out problems involving double slit experiments is easy to mix up, so make sure you study it carefully.

λ = wavelength of light used (m) x = distance from central fringe (m) d = distance between the slits (m) n = the order of the fringe L = length from the screen with slits to the viewing screen (m)

It is very easy to mix up the measurements of x, d, and L.

• Make sure to look at Figure 5 and see the different things each is measuring.
• If you mix up x and d it's not so bad, since they are both on top in the formula. If you were to mix them up with L, you would get the wrong answer.
• Almost all questions that you will see for this formula just involve sorting out what each variable is... you might find it helpful to write out a list of givens.

Example 1 : A pair of screens are placed 13.7m apart. A third order fringe is seen on the screen 2.50cm from the central fringe. If the slits were cut 0.0960 cm apart, determine the wavelength of this light. Roughly what colour is it?

Just to make sure you’ve got all the numbers from the question matched with the correct variables… L = 13.7 m n = 3 x = 2.50cm = 0.0250 m d = 0.0960cm = 9.60e-4 m It’s probably a yellow light being used given the wavelength we've measured.

If a white light is used in the double slit experiment, the different colours will be split up on the viewing screen according to their wavelengths.

• The violet end of the spectrum (with the shortest wavelengths) is closer to the central fringe, with the other colours being further away in order.

There is also a version of the formula where you measure the angle between the central fringe and whatever fringe you are measuring.

• The formula works the same way, with the only difference being that we measure the angle instead of x and L.
• Make sure that your calculator is in degree mode before using this version of the formula.

Example 2 : If a yellow light with a wavelength of 540 nm shines on a double slit with the slits cut 0.0100 mm apart, determine what angle you should look away from the central fringe to see the second order fringe?

Do not forget to: Change the wavelength into metres. Change the slit separation into metres. "Second order" is a perfect number and has an infinite number of sig digs.

The Single Slit

A surprising experiment is that you can get the same effect from using a single slit instead of a double slit.

• In Figure 7 , the blue path has to travel further than the red path... if this difference is equal to half a wavelength, they will meet each other out of sync .
• If they meet crest to crest or trough to trough they will be in sync , but if they meet crest to trough they will be out of sync .
• Being in sync will result in constructive interference , while meeting out of sync will result in destructive interference .
• After the first couple of fringes (n = 1 and 2), the edges start getting really fuzzy, so you have a hard time measuring anything.
• The only real difference in calculations is that "d" is now the width of the single opening.
• If two slits work better than one, would more than two slits work better? This is a question that we will answer in the next section.

Example 3 : For a single slit experiment apparatus like the one described above, determine how far from the central fringe the first order violet (λ = 350nm) and red (λ = 700nm) colours will appear if the screen is 10 m away and the slit is 0.050 cm wide.

We need to solve the formula for “x”, the distance from the central fringe. For the violet light… For the red light…

Diffraction of Light and Young's Double Slit Experiment

Hsc physics syllabus.

conduct investigations to analyse qualitatively the diffraction of light

conduct investigations to analyse quantitatively the interference of light using double slit apparatus and diffraction gratings dsinθ=mλ (ACSPH116, ACSPH117, ACSPH140)

Diffraction & Young's Double Slit Experiment

How to Do Diffraction related Calculation Questions

What is Diffraction?

Diffraction is the scattering behaviour a wave exhibits when it travels through a small opening or around the end of an object.

When light passes through an aperture, slit or around a bend/edge of an object, it also experiences this scattering effect, causing it to propagate outward. 

The scattering process bends light’s direction of propagation. The degree of bend is dependent on the relative difference between its wavelength and size of the slit.

• If the slit size is smaller than or equal to light’s wavelength, considerable diffraction occurs. Smaller the slit, greater the degree of diffraction.
• If the slit size is larger than light’s wavelength, diffraction still occurs but is unnoticeable to the naked eye. 

• Diffraction of light creates a unique repeating pattern

Diffraction of light creates a repeating pattern where a white band is observed centrally and bands of rainbow are dispersed away from the centre, each separated by dark space.

Huygens' Wave Model of Light

In the 17 th century, Christiaan Huygens proposed that when a wave reaches an opening, its wavefront can be perceived as individual points emitting spherical secondary wavelets.

When light travels through a slit, some of these wavelets are obstructed and can no longer propagate. As a result, the new wavefront is formed from the interference between wavelets that managed to pass through the opening. The absence of wavelets on the periphery causes the wavefront to scatter and propagate outward.

Huygens' wave model of light also provides a plausible explanation to why waves diffract around an edge of an opaque material. This is due to the propagation of some wavelets being obstructed by the object.

Diffraction Pattern through a Double Slit

In 1818, Fresnel improved Huygens’s theory by adding his theory of interference. Together, their theories could explain both the effect of diffraction and presence of dark fringes. Fresnel proposed that the diffraction pattern obtained from white light is a result of constructive and destructive interference between secondary ‘wavelets’ emitted from the original wavefront.

• When waves are out of phase, they undergo destructive interference . This results in dark fringes or ‘ minima ’ of diffraction.
• When waves are in phase, they undergo constructive interference . This results in spectral bands or ‘ maxima ’ of diffraction.

The intensity of each spectral band decreases away from the centre. This is because the diffracted ray of light is lower in intensity the greater the angle of diffraction from the midline (θ).

Young's Double-slit Experiment

In 1801, Thomas Young conducted an experiment using a double-slit apparatus. A monochromatic light source was shone through two narrow slits separated by a very small distance. A viewing screen was set-up directly behind the double-slit apparatus.

Newton's corpuscular (particle) model of light and Huygens' wave model of light made different predictions regarding the pattern of light formed on the screen.

Young's observations supported the wave model of light.

If light was a particle or consisted of particles, only light particles which pass through the slits would be observed on the viewing screen 

However, Young instead observed multiple bright bands/spots on the viewing screen rather than just two. These spots spanned a larger distance than that between the slits and had alternating dark and bright spots (minima and maxima).

Young’s qualitative observations showed that light cannot be particle in nature as this would otherwise produce only two bright bands directly behind the two slits.

Analysis of Diffraction Pattern

In addition, the bright spots showed varying intensity and their position can be calculated for a given wavelength of light.

Constructive interference produce maxima

When the difference in phase between two waves are exactly one wavelength apart, they will undergo constructive interference.

$$d\sin{\theta} = m\lambda$$ 

Where d is the distance between two slits and m is the ‘order’ of interference. 

m = 0, ±1, ±2... 

The order of interference begins with 0 which corresponds to the central band on the viewing board. The intensity of band decreases with higher orders of interference.

Destructive interference produce minima

$$d\sin{\theta} = (m+\frac{1}{2})\lambda$$ 

Where d is the distance between two slits and m is the ‘order’ of interference. m = 0, 1, 2, 3...

Number of Maxima

For a particular wavelength of light and distance ( d ) between slits, the number of orders ( m ) of bright spots (maxima) is finite. A maximum cannot form more than 90 degrees from the midline between the two slits. Thus, the angle at which the furthest maximum is formed must be smaller than 90º. 

Substitute an angle of 90º into the diffraction equation, the greatest order is given by

$$m = \frac{d}{\lambda}$$

This equation will often produce a number with decimal places. The greatest order is the largest integer  lower than the calculated value. 

How can we change the number of bright spots present?

• For a given wavelength, we can increase the separation distance between slits. However, this does not always work as when separation distance becomes too large, the interference between waves becomes negligible. This results in two bright spots being formed for a double slit experiment.
• For a given separation distance, we can decrease the wavelength of light to increase the number of maxima present.
• Both slit separation distance and wavelength can be manipulated to produce varying number of bright spots and dark fringes.

Diffraction Grating

Diffraction of light produces a similar array of bright and black spots when more than 2 slits are used.

Increased number of slits produces diffraction bands with greater resolution.

This is because as the number of slits increases, so does the number of waves being directed at the same angle (or same position on the viewing board). This increases the intensity of bright spots as more waves experience constructive interference which leads to a greater amplitude.

In contrast, when waves do not exactly overlap at their crests or troughs, they will undergo destructive interference. The extent of destructive interference again increases with the number of slits. Greater the extent, more defined the black fringes are.

Diffraction of White Light

Diffraction of white light produces repeating rainbow-like spectra.  Within each spectrum, longer wavelength of visible light (red) is further away from the centre. This is because the angle of diffraction increases for light of longer wavelengths.

Previous section:  Applications of Spectroscopy

Next section:  Particle and Wave Models of Light

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Physics in a minute: The double slit experiment

One of the most famous experiments in physics is the double slit experiment. It demonstrates, with unparalleled strangeness, that little particles of matter have something of a wave about them, and suggests that the very act of observing a particle has a dramatic effect on its behaviour.

To start off, imagine a wall with two slits in it. Imagine throwing tennis balls at the wall. Some will bounce off the wall, but some will travel through the slits. If there's another wall behind the first, the tennis balls that have travelled through the slits will hit it. If you mark all the spots where a ball has hit the second wall, what do you expect to see? That's right. Two strips of marks roughly the same shape as the slits.

In the image below, the first wall is shown from the top, and the second wall is shown from the front.

The pattern you get from particles.

Now imagine shining a light (of a single colour, that is, of a single wavelength) at a wall with two slits (where the distance between the slits is roughly the same as the light's wavelength). In the image below, we show the light wave and the wall from the top. The blue lines represent the peaks of the wave. As the wave passes though both slits, it essentially splits into two new waves, each spreading out from one of the slits. These two waves then interfere with each other. At some points, where a peak meets a trough, they will cancel each other out. And at others, where peak meets peak (that's where the blue curves cross in the diagram), they will reinforce each other. Places where the waves reinforce each other give the brightest light. When the light meets a second wall placed behind the first, you will see a stripy pattern, called an interference pattern . The bright stripes come from the waves reinforcing each other.

An interference pattern.

Here is a picture of a real interference pattern. There are more stripes because the picture captures more detail than our diagram. (For the sake of correctness, we should say that the image also shows a diffraction pattern , which you would get from a single slit, but we won't go into this here, and you don't need to think about it.)

Image: Jordgette , CC BY-SA 3.0 .

Now let's go into the quantum realm. Imagine firing electrons at our wall with the two slits, but block one of those slits off for the moment. You'll find that some of the electrons will pass through the open slit and strike the second wall just as tennis balls would: the spots they arrive at form a strip roughly the same shape as the slit.

Now open the second slit. You'd expect two rectangular strips on the second wall, as with the tennis balls, but what you actually see is very different: the spots where electrons hit build up to replicate the interference pattern from a wave.

Here is an image of a real double slit experiment with electrons. The individual pictures show the pattern you get on the second wall as more and more electrons are fired. The result is a stripy interference pattern.

Image: Dr. Tonomura and Belsazar , CC BY-SA 3.0

How can this be?

One possibility might be that the electrons somehow interfere with each other, so they don't arrive in the same places they would if they were alone. However, the interference pattern remains even when you fire the electrons one by one, so that they have no chance of interfering. Strangely, each individual electron contributes one dot to an overall pattern that looks like the interference pattern of a wave.

Could it be that each electrons somehow splits, passes through both slits at once, interferes with itself, and then recombines to meet the second screen as a single, localised particle?

To find out, you might place a detector by the slits, to see which slit an electron passes through. And that's the really weird bit. If you do that, then the pattern on the detector screen turns into the particle pattern of two strips, as seen in the first picture above! The interference pattern disappears. Somehow, the very act of looking makes sure that the electrons travel like well-behaved little tennis balls. It's as if they knew they were being spied on and decided not to be caught in the act of performing weird quantum shenanigans.

What does the experiment tell us? It suggests that what we call "particles", such as electrons, somehow combine characteristics of particles and characteristics of waves. That's the famous wave particle duality of quantum mechanics. It also suggests that the act of observing, of measuring, a quantum system has a profound effect on the system. The question of exactly how that happens constitutes the measurement problem of quantum mechanics.

Further reading

• For an extremely gentle introduction to some of the strange aspects of quantum mechanics, read Watch and learn .
• For a gentle introduction to quantum mechanics, read A ridiculously short introduction to some very basic quantum mechanics .
• For a more detailed, but still reasonably gentle, introduction to quantum mechanics, read Schrödinger's equation — what is it?

Originally published on 05/02/2017.

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Double slit experiment

The scientist at Washington University found that quasimeasurements cause the zeno effect possibly explaining why the particles do not form a interference pattern if one detects which slit they pass through.

double slit experiment

Seem to be leaving out the fact that the difference occurs when being actively observed.

Heisenberg uncertainty principle

Everything we see is our brain "interpreting" the photons of light reflected off a object. Just like our brains turns 30 FPS and up into a smooth video image. Any experiment that has the word "Observation" in it is flawed. A human used as test equipment for the observation part of a experiment can never be accurate.

It has nothing to do with a human observing anything. It has to do with how one observes things at the atomic and quantum scale. We make these observations by bouncing other particles off of the particles we're interested in examining. At the macro-scale this is not a problem as the particles were bounce off of things are much smaller and have little no affects at the macro.

But at the atomic and smaller scales, the particles we bounce off of things to observe them are similar in "size" (this is a stand in for mass, charge, etc.) to the particles we are trying to observe.

You can think of it like trying to figure out where a billiard ball is by bouncing a golf ball it. That will change the position, spin, etc. of the billiard ball.

I agree with you. Yet, seemingly, the rest of the world either believes - when they do not believe what you've just said - humans have a psychic grip on subatomic particles, or this proves a God exists.

Why not both?

I believe both, and agree with both of you. The two dont have to be mutually exclusive... It actually makes for a more narrow view that way.

Leave room for more

I agree. What we don't know is much greater than what we do and much of what we think we know will change. I think it's best to leave room for many possibilities. Magic is just science undiscovered. If we keep placing boundaries on what's possible and teach others to ignore something for lack of explanations, scientific discovery suffers.

The two slit experiment

The duality of the particle has nothing to do with proving a god exists, just that science is indeterminate and is a duality of possible existences dependent on the observation of a consciousness. Seems like its human consciousness that determines the outcome not any god.

This isn't actually true either. Experiments have shown that even if the photon used to make an observation is of low enough energy that it doesn't alter a large molecules trajectory much, the interference pattern still disappears.

Also, null interaction experiments have been done in which there is no contact between particles at all. But if info about which slit can be found, the interference pattern disappears.

Source for that?

Hey, do you have a source on finding information about which slit with out active observation causing the interference pattern to not appear?

Information on the Double Split experiment

Try QED: The Strange Theory of Light and Matter by Richard P. Feynman. It's been a while since I've enjoyed this book, but my recollection is that it covered the topic well.

Thank you! I didn’t think that explanation made sense, since any effect upon the particle being observed would surely be taken into account in these experiments…and because the detection unit (which “catches” the electrons passing through either slit) doesn’t work by shooting particles at them, as far as I know…even if it did, that wouldn’t be ignored as a variable or whatever…right? I assume such interaction isn’t the method of detection anyway; how the materials used in the experiment could potentially influence the subject being measured is exactly what they control for, among other things- the environment itself, the actions taken as it is conducted and how conditions change…etc. I just don’t think what the commenter described is true since, well, I’d assume the researchers would know that sort of thing could skew the results & therefore lead to an incorrect conclusion. Scientists aren’t just straight up missing the impact of what would be such an obvious flaw in these experiments. I mean, in general they either eliminate the possibility of their tools affecting what they’re measuring OR they take that into account as a variable. Usually the second one is only possible if it’s something that like…as long as it’s known, it won’t render their data useless…if that makes sense (so being aware that it is a factor is key) Anyway…

yet this works at the molecular level too

Molecules are much larger than photons, yet you get the same result.

Quantum Games

If a player has two attached low emission lasers either side of head, beamed through a double slit screen at, say, a home movie or scenario created by the player, bounces back as photons via player's retina to the player's neurons, will player perceive or believe he/she is part of the home movie?

Are you Sure?

Placing only 1 detector in front of one of the double slits ALSO collapses the wave function of both slits. This unequivocally proves that it isn’t the measurement method, but the ACT of measurement itself.

For example, we get the wave pattern. We place a detector in front of both holes we then get 2 bands. ..now, if it were the detector interfering as you mentioned, we will take 1 detector away and leave the other. This way only 1 slit has a detector that interacts with the electron as it passes through.

This would mean the slit with the detector produces a band while the slit without the detector produces a partial striped pattern of the wave.

This is not what we observe however. Measuring just 1 slit still causes 2 bands.

This is because even measuring just 1 slit gives us information on the other. It’s the information that is seemingly the cause of the collapse of the wave function.

Process of Elimination

Hello, I like your idea of removing one detector to see if there is a tangible difference. Given how complex the science behind this is, it doesn't seem ethical to have a biased conclusion with such conviction after just 1 adjustment.

Why has no one tried 3,4,5 slits? With those slits, why haven't we tried removing one detector at a time, and swapping out different ones for each slit? Speeding up or slowing down the particle beam? There are so many variables that could lead to comprehensible evidence if the results are as consistent to previous attempts.

However, it just seems this experiment was done 60 years ago and then we just left it as is with no additional input or further experimentation; just copy paste imitations doing the same thing for educational purposes of the original experiment. That just becomes a history lesson, not a science one.

I come here after watching a conspiracy theory and they referenced this experiment as the leading evidence that we live in a simulation, that the universe is just a projection controlled by a program that detects when its being observed like when a video game detects the players position and renders in whats necessary around them. Suggesting that the light particles can bend the rules of physics and time as soon as someone attempts to measure them.

My initial reaction is not to believe this, however I fully appreciate a rebuttal to come armed with objective, comprehensible evidence like any good debate where possible.

I think this experiment needs a make over and we need to breathe new life into it with far more variables to play with, leaving no stone unturned to draw a general trend and any potential outliers to help solve this once and for all. Or at least, as close as our minds will allow us.

We are our own limitations.

Re: Process of Elimination

I agree with you, the whole furore around this experiment has made it more of a history lesson. It's become almost like the Galileo stone/feather thing; i've had people tell me that in normal every-day circumstances, if i dropped a pen and a pebble at exactly the same moment, they would hit the floor at the same time. Even, when i demonstrate this live, people are still adamant in their stance; after-all, i'm no better than Galileo.

This represents a great discrepancy to the original format of experiment by Galileo. I think some of these experiments have been so popularised in pop-culture and pop-science that people have ruled out the possibility of questioning them. Just like the Galileo stone and feather thing, Everyone is still quoting the same concept from decades ago without any iota of desire to question it. This means that some of these science-cum-history concepts are left to grow into "unquestionables" filled with errors.

I think its about time we re-visit the whole premise of this experiment. Let's introduce 3,4, or even 10 slits! Let's do it today with more control over the variables. We can't let this become another one of the "unquestionables". We can't adopt beliefs and never question them. That would be disastrously dogmatic. The opposite of what it means to do real science!

Also, what was the youtube video you watched? thanks

Uh...no. That is definitely not what happens. If so, there would be no conceptual problem. But don't take my word for it. Here's what Richard Feynman said: “I think I can safely say that nobody really understands quantum mechanics." That's because QM seems to suggest that there's a real connection between the mind of the observer and the results obtained. Also, you're not taking into account the results of the quantum eraser phenomenon, which is another aspect of this experiment that suggests the trajectory of an electron in the past can be altered by an experimenter's actions in the present. You'll have to look it up as it's rather lengthy.

Impact of measuring

Thank you so much for this explanation! We have been fretting about this for quite a while. I wish this physical interaction were more clearly included in other explanations of the slit experiment or just quantum mechanics and general

Question for you

You’re saying to observe a particle we’re bouncing particles off of that observed particle? I don’t think that’s the case. What exactly is bouncing off the particle being observed? How is it being directed toward the target particle? With the way they design these experiments, as far as I know, there should be no overt effect like that- certainly not the actual impact of matter as you’re describing. I don’t think anything is being expelled from the detection materials. Or if it were, that would be taken into account- so precise calculations would be made about how it should impact the results. Basically, if something physical was being intentionally shot at the particles and that somehow was the way we detected them, then the scientists performing the research would do that math using specific measurements (including the mass of that projectile matter). I mean if there was anything being directed toward the electrons or whatever, they’d surely have an idea of what forces it would exert and the interaction it should have, etc… Now you could say the electron being observed has some effect upon the detection unit itself (the “quantum observer”) because logically, in order to even register the electron’s presence/position, it must. But I believe that by all known science, there shouldn’t be any effect upon the particle being observed- other than the fact that it’s being observed. That’s kind of the whole point and is exactly what makes this discovery so mind-blowing…right? So I would assume that in these experiments, they’re controlling for those conditions (the observation device having any physical effect or exerting force upon the observed electron, and all possible variables). Do you disagree? I am genuinely curious about what you’re asserting!

What if there are smaller units than photons, which are presently invisible to our instruments? We'll call them units of consciousness (or thought) that we as conscious beings emanate without knowing it, and it is these very tiny units of consciousness (relative to the photon) that influence the photons to behave as they do. In other words the invisible is influencing the visible like the soul influences the body. These same units could explain the placebo effect.

curtesy call

I agree to your theory. Just want to point it out there as a suggestion to proof read your work before submitting it. I have I found a couple of mistakes where a word had been left out.

Curtesy call

I thought it was well thought out and written. Has it been edited since your comment? If we're being semantic you may wish to check your spelling of courtesy.

Objective observation, unlike subjective observation, is very much allowed in conducting data in experiments.

Plus, unless you have robots conducting the experiment ans/or collecting the data, humans are going to be involved.

observer does not need to be human!

A houseplant would work too. Humans cannot see at this level in any case. Machinery is used, and humans don't have to be in the room for the effects to continue. Observation just means measurement, and Wheeler's Delayed Choice and the Quantum Eraser experiments showed the measurement can occur after the photon, electron, or molecule has hit the wall...and it will still change.

This word is used for convenience, but no conscious observer is required. You can also say “detected”. And by detected what is meant is that information exists that is, in principal, detectable even if not yet technically feasible. Look up “The World’s Smallest Double-Slit Experiment” (2007) and you will find that a single low-energy electron can be an “observer” and collapse the quantum interference pattern of a high-energy electron exiting a single hydrogen molecule.

This is BS. When being observed by a sensor, electrons behave as particles. You lack sufficient understanding of the double slit experiment.

A summarily dismissal of a complex phenomenon that has world class physicists, accompanied by a " You don't understand" line illustrates a simple mind

Deeper understanding is to look at our process of observation.

Everything we recieve through our sences gets interpreted in our brains as being solid, founded by rules/laws/logic & most importantly being OUTSIDE our bodies, ie, being real. Reality is though, that these words you now read, are IN your head as is ALL experiences. Point being, WHY are we being TRICKED to think we are experiencing life OUTSIDE our heads when in fact, we are experiencing life IN our heads, just a observation.

Slit Experiment

The only reason a human may not be good test equipment for observation would be because the person lacks awareness. Human observation can be as accurate as any mechanical scientific devise. It just depends on the awareness of the individual.

by detector , they mean, not human but mechanical

Double Split Experiment

"Seem to be leaving out the fact that the difference occurs when being actively observed" EXACTLY!! This experiment shows that matter is not what we think it is. Scientists have known this for a century yet scientific materialism for some reason still prevails. Matter is a product of Mind. NOT the other way around. For more information read "Ontological Mathematics"

That is not what comes out

That is not what comes out this. "Observer" is a misleading term. It does not specifically refer to humans, nor even conscious creatures, although they can be.

About what you wrote

I do agree with you

double slit Hijinx

Ive noticed this trend everywhere. I chock it up to the materialists clinging to their dead ideology

What happens as the distance between the slits becomes greater ? Is there a relationship between the distance between the slits, and the distance of the source from the slits??

Double slit

What if the light is reacting to the material the slits were cut out from. Maybe electromagnetism causing the light particles to bend and change their direction just like how planets and comets change their orbits when passing near something with mass.

The double slits, are on the

The double slits, are on the both sides of the direction of the flow of light. Also, the slit will be more massive on the two outer edges of the double slits. If it were to be hindered due to presence of slits, wouldn't the effect be more on the outer edges and not on the inner edges, i.e. in the middle.

Double Slit

Such is the problem. Particles don't bend when acted upon by electromagnetic fields. They simply form a trajectory. Bending or warping is the property of a wave. Their trajectory could be altered but I'm sure the material is neutral in all aspects to avoid interference.

Electrons have almost no mass and therefore almost no gravity. Atoms of the slit have a huge mass compared to the electrons. As the electrons passes the slit the gravity of the atoms cause some of the closest electrons to start to spin, the same way water spins when shot through a slit. This spin then sends some of the electrons out of their normal straight line trajectory which causes the apparent wave effect.

If that were the case it would happen if there was only one slit. But it doesn't.

Doesn't bend when "observed".

Electrons spin.

Electrons always have a spin of 1/2. This is a fundemental property of electrons and all fermions. Even if electrons were pushed off their trajectory, how do electrons shot one at a time form an interference pattern?

Because it behaves like wave regardless by itself or by groups

When you say wave, do you mean as in bye bye?

Running paint

If light passes through two slits and it reflects off a object that photon leaves some of itself behind and continues on as if you put paint on your hand and slap a wall then run, how many walls you slap depends on how much paint you got, when light reflects off the object or the slit where does it go is it passing through itself or is it colliding with itself in that direction and handing itself some extra light to continue like say you been running with paint on your hand and you have a train of people that follow you and you are the leader. What if you grab just a finger swap of paint for that extra inch foot mile etc. so when the rays reflects off the rectangle will that rectangle of photons continue colliding into each other and handing itself more photons or snatching some to create a another rectangle and so on till it fades away.

agree with Chris Isaacson

I also thought the materials used may have properties that interfere, and the detector might too.

How does the detector itself work? Does it not rely on an intrinsic property of electrons to function? Connecting the detector to that property then necessarily interferes with the experiment. That interference is then to be expected and can be explained rationally rather than through a spooky effect, quantum effect.

Light/Photon/Electron/Particle interacting with slit material

Agree with you. Details of double/single slit experiments should give more information on the slits material, their dimensions (gap width and distance between slits) and the probability of these materials influencing the path/direction of WAVICLES (waves-cum-particles!). This topic needs to discussed and debated.

Young's Double Slit Experiment

The Original Experiment

• Physics Laws, Concepts, and Principles
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Throughout the nineteenth century, physicists had a consensus that light behaved like a wave, in large part thanks to the famous double slit experiment performed by Thomas Young. Driven by the insights from the experiment, and the wave properties it demonstrated, a century of physicists sought out the medium through which light was waving, the luminous ether . Though the experiment is most notable with light, the fact is that this sort of experiment can be performed with any type of wave, such as water. For the moment, however, we'll focus on the behavior of light.

What Was the Experiment?

In the early 1800s (1801 to 1805, depending on the source), Thomas Young conducted his experiment. He allowed light to pass through a slit in a barrier so it expanded out in wave fronts from that slit as a light source (under Huygens' Principle ). That light, in turn, passed through the pair of slits in another barrier (carefully placed the right distance from the original slit). Each slit, in turn, diffracted the light as if they were also individual sources of light. The light impacted an observation screen. This is shown to the right.

When a single slit was open, it merely impacted the observation screen with greater intensity at the center and then faded as you moved away from the center. There are two possible results of this experiment:

Particle interpretation: If light exists as particles, the intensity of both slits will be the sum of the intensity from the individual slits.

Wave interpretation: If light exists as waves, the light waves will have interference under the principle of superposition , creating bands of light (constructive interference) and dark (destructive interference).

When the experiment was conducted, the light waves did indeed show these interference patterns. A third image that you can view is a graph of the intensity in terms of position, which matches with the predictions from interference.

Impact of Young's Experiment

At the time, this seemed to conclusively prove that light traveled in waves, causing a revitalization in Huygen's wave theory of light, which included an invisible medium, ether , through which the waves propagated. Several experiments throughout the 1800s, most notably the famed Michelson-Morley experiment , attempted to detect the ether or its effects directly.

They all failed and a century later, Einstein's work in the photoelectric effect and relativity resulted in the ether no longer being necessary to explain the behavior of light. Again a particle theory of light took dominance.

Expanding the Double Slit Experiment

Still, once the photon theory of light came about, saying the light moved only in discrete quanta, the question became how these results were possible. Over the years, physicists have taken this basic experiment and explored it in a number of ways.

In the early 1900s, the question remained how light — which was now recognized to travel in particle-like "bundles" of quantized energy, called photons, thanks to Einstein's explanation of the photoelectric effect — could also exhibit the behavior of waves. Certainly, a bunch of water atoms (particles) when acting together form waves. Maybe this was something similar.

One Photon at a Time

It became possible to have a light source that was set up so that it emitted one photon at a time. This would be, literally, like hurling microscopic ball bearings through the slits. By setting up a screen that was sensitive enough to detect a single photon, you could determine whether there were or were not interference patterns in this case.

One way to do this is to have a sensitive film set up and run the experiment over a period of time, then look at the film to see what the pattern of light on the screen is. Just such an experiment was performed and, in fact, it matched Young's version identically — alternating light and dark bands, seemingly resulting from wave interference.

This result both confirms and bewilders the wave theory. In this case, photons are being emitted individually. There is literally no way for wave interference to take place because each photon can only go through a single slit at a time. But the wave interference is observed. How is this possible? Well, the attempt to answer that question has spawned many intriguing interpretations of  quantum physics , from the Copenhagen interpretation to the many-worlds interpretation.

It Gets Even Stranger

Now assume that you conduct the same experiment, with one change. You place a detector that can tell whether or not the photon passes through a given slit. If we know the photon passes through one slit, then it cannot pass through the other slit to interfere with itself.

It turns out that when you add the detector, the bands disappear. You perform the exact same experiment, but only add a simple measurement at an earlier phase, and the result of the experiment changes drastically.

Something about the act of measuring which slit is used removed the wave element completely. At this point, the photons acted exactly as we'd expect a particle to behave. The very uncertainty in position is related, somehow, to the manifestation of wave effects.

More Particles

Over the years, the experiment has been conducted in a number of different ways. In 1961, Claus Jonsson performed the experiment with electrons, and it conformed with Young's behavior, creating interference patterns on the observation screen. Jonsson's version of the experiment was voted "the most beautiful experiment" by  Physics World  readers in 2002.

In 1974, technology became able to perform the experiment by releasing a single electron at a time. Again, the interference patterns showed up. But when a detector is placed at the slit, the interference once again disappears. The experiment was again performed in 1989 by a Japanese team that was able to use much more refined equipment.

The experiment has been performed with photons, electrons, and atoms, and each time the same result becomes obvious — something about measuring the position of the particle at the slit removes the wave behavior. Many theories exist to explain why, but so far much of it is still conjecture.

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The double-slit experiment: Is light a wave or a particle?

The double-slit experiment is universally weird.

How does the double-slit experiment work?

Interference patterns from waves, particle patterns, double-slit experiment: quantum mechanics, history of the double-slit experiment, additional resources.

The double-slit experiment is one of the most famous experiments in physics and definitely one of the weirdest. It demonstrates that matter and energy (such as light) can exhibit both wave and particle characteristics — known as the particle-wave duality of matter — depending on the scenario, according to the scientific communication site Interesting Engineering .

According to the University of Sussex , American physicist Richard Feynman referred to this paradox as the central mystery of quantum mechanics. 

We know the quantum world is strange, but the two-slit experiment takes things to a whole new level. The experiment has perplexed scientists for over 200 years, ever since the first version was first performed by British scientist Thomas Young in 1801.

Related: 10 mind-boggling things you should know about quantum physics  

Christian Huygens was the first to describe light as traveling in waves whilst Isaac Newton thought light was composed of tiny particles according to Las Cumbres Observatory . But who is right? British polymath Thomas Young designed the double-slit experiment to put these theories to the test. 

To appreciate the truly bizarre nature of the double-split experiment we first need to understand how waves and particles act when passing through two slits. 

When Young first carried out the double-split experiment in 1801 he found that light behaved like a wave. 

Firstly, if we were to shine a light on a wall with two parallel slits — and for the sake of simplicity, let's say this light has only one wavelength. 

As the light passes through the slits, each, in turn, becomes almost like a new source of light. On the far side of the divider, the light from each slit diffracts and overlaps with the light from the other slit, interfering with each other. 

According to Stony Brook University , any wave can create an interference pattern, whether it be a sound wave, light wave or waves across a body of water. When a wave crest hits a wave trough they cancel each other out — known as destructive interference — and appear as a dark band. When a crest hits a crest they amplify each other — known as constructive interference — and appear as a bright band. The combination of dark and bright bands is known as an interference pattern and can be seen on the sensor screen opposite the slits. 

This interference pattern was the evidence Young needed to determine that light was a wave and not a particle as Newton had suggested. 

But that is not the whole story. Light is a little more complicated than that, and to see how strange it really is we also need to understand what pattern a particle would make on a sensor field. 

If you were to carry out the same experiment and fire grains of sand or other particles through the slits, you would end up with a different pattern on the sensor screen. Each particle would go through a slit end up in a line in roughly the same place (with a little bit of spread depending on the angle the particle passed through the slit).  

Clearly, waves and particles produce a very different pattern, so it should be easy to distinguish between the two right? Well, this is where the double-slit experiment gets a little strange when we try and carry out the same experiment but with tiny particles of light called photons. Enter the realm of quantum mechanics. 

The smallest constituent of light is subatomic particles called photons. By using photons instead of grains of sand we can carry out the double-slit experiment on an atomic scale. 

If you block off one of the slits, so it is just a single-slit experiment, and fire photons through to the sensor screen, the photons will appear as pinprick points on the sensor screen, mimicking the particle patterns produced by sand in the previous example. From this evidence, we could suggest that photons are particles. 

Now, this is where things start to get weird. 

If you unblock the slit and fire photons through both slits, you start to see something very similar to the interference pattern produced by waves in the light example. The photons appear to have gone through the pair of slits acting like waves. 

But what if you launch photons one by one, leaving enough time between them that they don't have a chance of interfering with each other, will they behave like particles or waves? 

At first, the photons appear on the sensor screen in a random scattered manner, but as you fire more and more of them, an interference pattern begins to emerge. Each photon by itself appears to be contributing to the overall wave-like behavior that manifests as an interference pattern on the screen — even though they were launched one at a time so that no interference between them was possible.

It's almost as though each photon is "aware" that there are two slits available. How? Does it split into two and then rejoin after the slit and then hit the sensor? To investigate this, scientists set up a detector that can tell which slit the photon passes through. 

Again, we fire photons one at a time at the slits, as we did in the previous example. The detector finds that about 50% of the photons have passed through the top slit and about 50% through the bottom, and confirms that each photon goes through one slit or the other. Nothing too unusual there. 

But when we look at the sensor screen on this experiment, a different pattern emerges. 

This pattern matches the one we saw when we fired particles through the slits. It appears that monitoring the photons triggers them to switch from the interference pattern produced by waves to that produced by particles. 

If the detection of photons through the slits is apparently affecting the pattern on the sensor screen, what happens if we leave the detector in place but switch it off? (Shh, don't tell the photons we're no longer spying on them!) 

This is where things get really, really weird. 

Same slits, same photons, same detector, just turned off. Will we see the same particle-like pattern? 

No. The particles again make a wave-like interference pattern on the sensor screen. 

The atoms appear to act like waves when you're not watching them, but as particles when you are. How? Well, if you can answer that, a Nobel Prize is waiting for you. 

In the 1930s, scientists proposed that human consciousness might affect quantum mechanics. Mathematician John Von Neumann first postulated this in 1932 in his book " The Mathematical Foundations of Quantum Mechanics ." In the 1960s, theoretical physicist, Eugene Wigner conceived a thought experiment called Wigner's friend — a paradox in quantum physics that describes the states of two people, one conducting the experiment and the observer of the first person, according to science magazine Popular Mechanics . The idea that the consciousness of a person carrying out the experiment can affect the result is knowns as the Von Neumann–Wigner interpretation.

Though a spiritual explanation for quantum mechanic behavior is still believed by a few individuals, including author and alternative medicine advocate Deepak Chopra , a majority of the science community has long disregarded it. 

As for a more plausible theory, scientists are stumped. 

Furthermore —and perhaps even more astonishingly — if you set up the double-slit experiment to detect which slit the photon went through after the photon has already hit the sensor screen, you still end up with a particle-type pattern on the sensor screen, even though the photon hadn't yet been detected when it hit the screen. This result suggests that detecting a photon in the future affects the pattern produced by the photon on the sensor screen in the past. This experiment is known as the quantum eraser experiment and is explained in more detail in this informative video from Fermilab . 

We still don't fully understand how exactly the particle-wave duality of matter works, which is why it is regarded as one of the greatest mysteries of quantum mechanics. 

The first version of the double-slit experiment was carried out in 1801 by British polymath Thomas Young, according to the American Physical Society (APS). His experiment demonstrated the interference of light waves and provided evidence that light was a wave, not a particle. 

Young also used data from his experiments to calculate the wavelengths of different colors of light and came very close to modern values.

Despite his convincing experiment that light was a wave, those who did not want to accept that Isaac Newton could have been wrong about something criticized Young. (Newton had proposed the corpuscular theory, which posited that light was composed of a stream of tiny particles he called corpuscles.) 

According to APS, Young wrote in response to one of the critics, "Much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible."

Since the development of quantum mechanics, physicists now acknowledge light to be both a particle and a wave. 

Explore the double-slit experiment in more detail with this article from the University of Cambridge, which includes images of electron patterns in a double-slit experiment. Discover the true nature of light with Canon Science Lab . Read about fragments of energy that are not waves or particles — but could be the fundamental building blocks of the universe — in this article from The Conversation . Dive deeper into the two-slit experiment in this article published in the journal Nature . 

Bibliography

Grangier, Philippe, Gerard Roger, and Alain Aspect. " Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. " EPL (Europhysics Letters) 1.4 (1986): 173.

Thorn, J. J., et al. "Observing the quantum behavior of light in an undergraduate laboratory. " American Journal of Physics 72.9 (2004): 1210-1219.

Ghose, Partha. " The central mystery of quantum mechanics. " arXiv preprint arXiv:0906.0898 (2009).

Aharonov, Yakir, et al. " Finally making sense of the double-slit experiment. " Proceedings of the National Academy of Sciences 114.25 (2017): 6480-6485.

Peng, Hui. " Observations of Cross-Double-Slit Experiments. " International Journal of Physics 8.2 (2020): 39-41. 

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4.3 Double-Slit Diffraction

Learning objectives.

By the end of this section, you will be able to:

• Describe the combined effect of interference and diffraction with two slits, each with finite width
• Determine the relative intensities of interference fringes within a diffraction pattern
• Identify missing orders, if any

When we studied interference in Young’s double-slit experiment, we ignored the diffraction effect in each slit. We assumed that the slits were so narrow that on the screen you saw only the interference of light from just two point sources. If the slit is smaller than the wavelength, then Figure 4.10 (a) shows that there is just a spreading of light and no peaks or troughs on the screen. Therefore, it was reasonable to leave out the diffraction effect in that chapter. However, if you make the slit wider, Figure 4.10 (b) and (c) show that you cannot ignore diffraction. In this section, we study the complications to the double-slit experiment that arise when you also need to take into account the diffraction effect of each slit.

To calculate the diffraction pattern for two (or any number of) slits, we need to generalize the method we just used for a single slit. That is, across each slit, we place a uniform distribution of point sources that radiate Huygens wavelets, and then we sum the wavelets from all the slits. This gives the intensity at any point on the screen. Although the details of that calculation can be complicated, the final result is quite simple:

Two-Slit Diffraction Pattern

The diffraction pattern of two slits of width a that are separated by a distance d is the interference pattern of two point sources separated by d multiplied by the diffraction pattern of a slit of width a .

In other words, the locations of the interference fringes are given by the equation d sin θ = m λ d sin θ = m λ , the same as when we considered the slits to be point sources, but the intensities of the fringes are now reduced by diffraction effects, according to Equation 4.4 . [Note that in the chapter on interference, we wrote d sin θ = m λ d sin θ = m λ and used the integer m to refer to interference fringes. Equation 4.1 also uses m , but this time to refer to diffraction minima. If both equations are used simultaneously, it is good practice to use a different variable (such as n ) for one of these integers in order to keep them distinct.]

Interference and diffraction effects operate simultaneously and generally produce minima at different angles. This gives rise to a complicated pattern on the screen, in which some of the maxima of interference from the two slits are missing if the maximum of the interference is in the same direction as the minimum of the diffraction. We refer to such a missing peak as a missing order . One example of a diffraction pattern on the screen is shown in Figure 4.11 . The solid line with multiple peaks of various heights is the intensity observed on the screen. It is a product of the interference pattern of waves from separate slits and the diffraction of waves from within one slit.

Example 4.3

Intensity of the fringes.

From Equation 4.4 ,

Substituting from above,

For a = 2 λ a = 2 λ , d = 6 λ d = 6 λ , and m = 1 m = 1 ,

Then, the intensity is

Significance

Example 4.4, two-slit diffraction.

Using d sin θ = m λ d sin θ = m λ for θ = 2.5 × 10 −2 rad θ = 2.5 × 10 −2 rad , we find

which is the maximum interference order that fits inside the central peak. We note that m = ± 10 m = ± 10 are missing orders as θ θ matches exactly. Accordingly, we observe bright fringes for

for a total of 19 bright fringes.

Check Your Understanding 4.3

For the experiment in Example 4.4 , show that m = 20 m = 20 is also a missing order.

Interactive

Explore the effects of double-slit diffraction. In this simulation written by Fu-Kwun Hwang, select N = 2 N = 2 using the slider and see what happens when you control the slit width, slit separation and the wavelength. Can you make an order go “missing?”

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• Youngs Double Slit Experiment

Young's Double Slit Experiment

What is young’s double slit experiment.

Young’s double slit experiment uses two coherent sources of light placed at a small distance apart. Usually, only a few orders of magnitude greater than the wavelength of light are used. Young’s double slit experiment helped in understanding the wave theory of light , which is explained with the help of a diagram. As shown, a screen or photodetector is placed at a large distance, ‘D’, away from the slits.

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JEE Main 2021 LIVE Physics Paper Solutions 24 Feb Shift-1 Memory-based

The original Young’s double slit experiment used diffracted light from a single source passed into two more slits to be used as coherent sources. Lasers are commonly used as coherent sources in modern-day experiments.

Table of Contents

• Position of Fringes
• Shape of Fringes
• Intensity of Fringes

Special Cases

• Displacement of Fringes

Each source can be considered a source of coherent light waves . At any point on the screen at a distance ‘y’ from the centre, the waves travel distances  l 1  and  l 2 to create a path difference of Δl at the point. The point approximately subtends an angle of θ at the sources (since the distance D is large, there is only a very small difference between the angles subtended at sources).

Derivation of Young’s Double Slit Experiment

Consider a monochromatic light source ‘S’ kept at a considerable distance from two slits: s 1 and s 2 . S is equidistant from s 1 and s 2 . s 1 and s 2 behave as two coherent sources as both are derived from S.

The light passes through these slits and falls on a screen which is at a distance ‘D’ from the position of slits s 1 and s 2 . ‘d’ is the separation between two slits.

If s 1 is open and s 2 is closed, the screen opposite to s 1 is closed, and only the screen opposite to s 2 is illuminated. The interference patterns appear only when both slits s 1 and s 2 are open.

When the slit separation (d) and the screen distance (D) are kept unchanged, to reach P, the light waves from s 1 and s 2 must travel different distances. It implies that there is a path difference in Young’s double slit experiment between the two light waves from s 1 and s 2 .

Approximations in Young’s double slit experiment 

• Approximation  1: D > > d: Since D > > d, the two light rays are assumed to be parallel.
• Approximation  2:   d/λ >> 1:  Often, d is a fraction of a millimetre, and λ is a fraction of a micrometre for visible light.

Under these conditions, θ is small. Thus, we can use the approximation sin θ = tan θ ≈ θ = λ/d.

∴ path difference, Δz = λ/d

This is the path difference between two waves meeting at a point on the screen. Due to this path difference in Young’s double slit experiment, some points on the screen are bright, and some points are dark.

Now, we will discuss the position of these light and dark fringes and fringe width.

Position of Fringes in Young’s Double Slit Experiment

Position of bright fringes.

For maximum intensity or bright fringe to be formed at P,

Path difference, Δz = nλ (n = 0, ±1, ±2, . . . .)

i.e., xd/D = nλ

The distance of the n th   bright fringe from the centre is

x n = nλD/d

Similarly, the distance of the (n-1) th  bright fringe from the centre is

x (n-1) = (n -1)λD/d

Fringe width,  β =  x n   – x (n-1)  = nλD/d – (n -1)λD/d = λD/d

(n = 0, ±1, ±2, . . . .)

Position of Dark Fringes

For minimum intensity or dark fringe to be formed at P,

Path difference, Δz = (2n + 1) (λ/2) (n = 0, ±1, ±2, . . . .)

i.e., x = (2n +1)λD/2d

The distance of the n th   dark fringe from the centre is

x n = (2n+1)λD/2d

x (n-1) = (2(n-1) +1)λD/2d

Fringe width, β = x n   – x (n-1)  = (2n + 1) λD/2d – (2(n -1) + 1)λD/2d = λD/d

Fringe Width

The distance between two adjacent bright (or dark) fringes is called the fringe width.

If the apparatus of Young’s double slit experiment is immersed in a liquid of refractive index  (μ), then the wavelength of light and fringe width decreases ‘μ’ times.

If white light is used in place of monochromatic light, then coloured fringes are obtained on the screen, with red fringes larger in size than violet.

Angular Width of Fringes

Let the angular position of n th bright fringe is θ n, and because of its small value, tan θ n   ≈ θ n

Similarly, the angular position of (n+1) th bright fringe is θ n+1,  then

∴ The angular width of a fringe in Young’s double slit experiment is given by,

Angular width is independent of ‘n’, i.e., the angular width of all fringes is the same.

Maximum Order of Interference Fringes

But ‘n’ values cannot take infinitely large values as it would violate the 2 nd approximation.

i.e., θ is small (or) y < < D

When the ‘n’ value becomes comparable to d/ λ, path difference can no longer be given by d γ/D.

Hence for maxima, path difference = nλ

The above represents the box function or greatest integer function.

Similarly, the highest order of interference minima

The Shape of Interference Fringes in YDSE

From the given YDSE diagram, the path difference between the two slits is given by

The above equation represents a hyperbola with its two foci as, s 1 and s 2 .

The interference pattern we get on the screen is a section of a hyperbola when we revolve the hyperbola about the axis s 1 s 2 .

If the screen is a yz plane, fringes are hyperbolic with a straight central section.

If the screen is xy plane , the fringes are hyperbolic with a straight central section.

The Intensity of Fringes in Young’s Double Slit Experiment

For two coherent sources, s 1 and s 2 , the resultant intensity at point p is given by

I = I 1 + I 2 + 2 √(I 1 . I 2 ) cos φ

Putting I 1 = I 2 = I 0  (Since, d<<<D)

I = I 0 + I 0 + 2 √(I 0 .I 0 ) cos φ

I = 2I 0 + 2 (I 0 ) cos φ

I = 2I 0 (1 +  cos φ)

For maximum intensity

phase difference   φ = 2nπ

Then, path difference \(\begin{array}{l}\Delta x=\frac{\lambda }{{2}{\pi }}\left( {2}n{\pi } \right)\end{array} \) = nλ

The intensity of bright points is maximum and given by

I max = 4I 0

For minimum intensity

φ = (2n – 1) π

Phase difference φ = (2n – 1)π

Thus, the intensity of minima is given by

If I 1 ≠ I 2 , I min ≠ 0.

Rays Not Parallel to Principal Axis:

From the above diagram,

Using this, we can calculate different positions of maxima and minima.

Source Placed beyond the Central Line:

If the source is placed a little above or below this centre line, the wave interaction with S 1 and S 2 has a path difference at point P on the screen.

Δ x= (distance of ray 2) – (distance of ray 1)

= bd/a + yd/D → (*)

We know Δx = nλ for maximum

Δx = (2n – 1) λ/2 for minimum

By knowing the value of Δx from (*), we can calculate different positions of maxima and minima .

Displacement of Fringes in YDSE

When a thin transparent plate of thickness ‘t’ is introduced in front of one of the slits in Young’s double slit experiment, the fringe pattern shifts toward the side where the plate is present.

The dotted lines denote the path of the light before introducing the transparent plate. The solid lines denote the path of the light after introducing a transparent plate.

Where μt is the optical path.

Then, we get,

Term (1) defines the position of a bright or dark fringe; term (2) defines the shift that occurred in the particular fringe due to the introduction of a transparent plate.

Constructive and Destructive Interference

For constructive interference, the path difference must be an integral multiple of the wavelength.

Thus, for a bright fringe to be at ‘y’,

Or, y = nλD/d

Where n = ±0,1,2,3…..

The 0th fringe represents the central bright fringe.

Similarly, the expression for a dark fringe in Young’s double slit experiment can be found by setting the path difference as

Δl = (2n+1)λ/2

This simplifies to

(2n+1)λ/2 = y d/D

y = (2n+1)λD/2d

Young’s double slit experiment was a watershed moment in scientific history because it firmly established that light behaved like a wave.

The double slit experiment was later conducted using electrons , and to everyone’s surprise, the pattern generated was similar as expected with light. This would forever change our understanding of matter and particles, forcing us to accept that matter, like light, also behaves like a wave.

Wave Optics

Young’s double slit experiment.

Frequently Asked Questions on Young’s Double Slit Experiment

What was the concept explained by young’s double slit experiment.

Young’s double slit experiment helps in understanding the wave theory of light.

What are the formulas derived from Young’s double slit experiment?

For constructive interference, dsinθ = mλ , for m = 0,1,-1,2,-2

For destructive interference, dsinθ = (m+½)λ, for m = 0,1,-1,2,-2 Here, d is the distance between the slits. λ is the wavelength of the light waves.

What is called a fringe width?

The distance between consecutive bright or dark fringe is called the fringe width.

What kind of source is used in Young’s double slit experiment?

A coherent source is used in Young’s double slit experiment.

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Interference of Light Waves - Young's Double-slit Experiment

Wave nature of light, parameters and equations, effects of varying certain variables.

Early physicists such as Issac Newton and Christiann Huygens thought tt was a steady stream of particles and had a wave motion. Indeed, such theories were correct but were unproven because light does indeed consists of moving quantas of photons which are packets of particles of pure energy. It was not until 1802, that Thomas Young proved that light does have a wave motion. In his experiment, he hypothesized that parallel beams of light should produce a brighter area where they overlapped if light were a steady stream. Instead, they produced bright bands separated by dark bands, the result of two sets of waves coinciding or canceling each other out. Thus, light is a form of wave.

• Interference is the phenomenon that arises when two or more waves meet at the same place and their amplitudes add in a way that they are either constructive or destructive depending on their relative phases.
• Intereference occurs any time two waves interact, but in order to get a reliable pattern of intereference, coherent or zmonochromatic light sources are needed. This is because coherent light means that the waves emitted are in-phase, whereas monochromatic light emit a single color which means the waves are in-phase for sure. (This is why light bulbs are not used in light waves experiments because they are incoherent.)
• In his experiment, Young allowed sunlight to pass through a small hole, that in turn pass through a pair of closely spaced slits, which then illuminated a screen. Waves diffract at each slit and then interfere in the region between the slits and the screen thus causing a pattern of alternating dark and bright regions on the screen. These regions are called fringes .
• Dark fringes are the result of destructive interference when the waves are out of phase, whereas bright fringes are formed by constructive interence when the waves are in-phase.

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• Published: 03 September 2024

Quantum double slit experiment with reversible detection of photons

• Vipin Devrari 1 &
• Mandip Singh 1  

Scientific Reports volume  14 , Article number:  20438 ( 2024 ) Cite this article

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• Quantum mechanics
• Single photons and quantum effects

Principle of quantum superposition permits a photon to interfere with itself. As per the principle of causality, a photon must pass through the double-slit prior to its detection on the screen to exhibit interference. In this paper, a double-slit quantum interference experiment with reversible detection of Einstein–Podolsky–Rosen quantum entangled photons is presented. Where a photon is first detected on a screen without passing through a double-slit, while the second photon is propagating towards the double-slit. A detection event on the screen cannot affect the second photon with any signal propagating at the speed of light, even after its passage through the double-slit. After the detection of the first photon on the screen, the second photon is either passed through the double-slit or diverted towards a stationary photon detector. Therefore, the question of whether the first photon carries the which-path information of the second photon in the double-slit is eliminated. No single photon interference is exhibited by the second photon, even if another screen is placed after the double-slit.

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Introduction.

In 1801, Young’s double-slit interference experiment proved that light behaves as a wave 1 , 2 . A first experimental observation of interference with very low intensity of light was reported by Taylor 3 . However, quantum mechanically, light consists of discrete energy packets known as photons, which can exhibit particle- or wave-like behaviour. According to the principle of quantum superposition, a single particle can exist at different locations simultaneously 4 , 5 . This counter-intuitive law of nature gives wave nature to a particle, and by its consequence, a particle can interfere with itself, i.e. all quantum superimposed states of a particle interfere with each other. In a single particle quantum double-slit experiment, a single particle is passed through a double-slit, and an interference pattern gradually emerges on the screen by accumulating particle detections by repeating the experiment. Each detection of a particle on the screen determines its position on the screen, whereas this measurement cannot determine the path of a particle in the double-slit. However, the interference pattern cannot be formed, when the which-path information of a particle is measured or stored by modifying the experiment. The casual temporal order of this experiment signifies a detection on the screen after the passage of a particle through the double-slit. This casual self interference was demonstrated experimentally with electrons 6 , 7 , 8 , 9 , neutrons 10 , 11 , photons 12 , 13 and positrons 14 . Quantum mechanics exerts no restriction on the self interference of macromolecules, which is experimentally demonstrated 15 , 16 , 17 , 18 , 19 , 20 . An experiment demonstrating self interference of two-photon amplitudes in a double-double-slit is performed with momentum entangled photons 21 , 22 . Another version of a double-slit experiment is realised by placing a double-slit in the path of one photon, where the interference pattern is formed only when both photons are measured 23 , 24 , 25 , 26 , 27 , 28 , 29 . However, in these experiments, both photons are measured after one of them is passed through the double-slit.

In this paper, a quantum double-slit experiment with reversible detection of photons is presented, which is carried out with continuous variable Einstein–Podolsy–Rosen (EPR) 30 quantum entangled photon pairs. A reversible detection implies that a photon of a quantum entangled pair is first detected on a screen while the other photon is propagating towards a double-slit, and later it can pass either through the double-slit or it can be diverted towards a stationary single photon detector. The experiment is configured such that the detection of a first photon on the screen cannot affect the second photon through any local communication, even after its interaction with the double-slit. This is because the second photon is separated from the detection event by a lightlike interval. Since the second photon passes through the double-slit after the detection of the first photon therefore, the first photon carried no which-path information of the second photon in the double-slit. The second photon is detected by stationary single photon detectors, which are placed at fixed locations throughout the interference experiment. The interference pattern is produced on the screen by repeating the experiment each time with a new EPR entangled pair, provided those photon detections on the screen are considered when the second photon is detected by a stationary detector positioned after the double-slit. However, position measurements of individual photons do not produce any interference pattern, even if the detector placed after the double-slit is displaced gradually to count photons at different locations. The experiment is performed with continuous variable EPR entangled photon pairs produced simultaneously in a Beta Barium Borate (BBO) nonlinear crystal by Type-I spontaneous parametric down conversion (SPDC) in a noncollinear configuration 31 , 32 , 33 , 34 , 35 , 36 , 37 . A real double-slit is used in this experiment, whereas the quantum entangled pair production rate is intentionally reduced to keep one entangled photon pair in the experiment until its detection. The second EPR entangled pair of photons is produced considerably later than the detection of the first entangled pair of photons. In addition, this paper presents a theoretical analysis of the experiment.

Concept and analysis

The EPR state is a continuous variable entangled quantum state of two particles, where both particles are equally likely to exist at all position and momentum locations. A one-dimensional EPR state in position basis is written as \(|\alpha \rangle =\int ^{\infty }_{-\infty }|x\rangle _{1}|x+{\textbf {x}}_{o}\rangle _{2} \textrm{d}x\) , where subscripts 1 and 2 represent particle-1 and particle-2, respectively. A constant \({\textbf {x}}_{o}\) corresponds to the position difference of particles. The same EPR state is expressed in momentum basis as \(|\alpha \rangle =\int ^{\infty }_{-\infty }e^{i \frac{p x_{o}}{\hslash }}|p\rangle _{1}|-p\rangle _{2}\textrm{d}p\) , where particles have opposite momenta, and \(\hslash =h/2\pi\) is the reduced Planck’s constant. Therefore, both position and momentum of each particle are completely unknown. If the position of any one particle is measured, then the EPR state is randomly collapsed onto \(|x'\rangle _{1}|x'+{\textbf {x}}_{o}\rangle _{2}\) where a prime on x indicates a single measured position value from the integral range. Therefore, the measured positions of particles are correlated, i.e. they are separated by \({\textbf {x}}_{o}\) irrespective of \(x'\) . Instead of position, if momentum, which is a complementary observable to the position, of a particle is measured, then the EPR state is randomly collapsed onto \(| p'\rangle _{1}|-p'\rangle _{2}\) , where both the particles exhibit opposite momenta irrespective of \(p'\) thus, their measured momenta are correlated.

A schematic diagram of the experiment, where a screen corresponds to a single photon detector capable of detecting locations of photon detection events. A screen is placed considerably closer to the source than a beam splitter and a double-slit.

In this paper, the EPR state of two photons in three-dimensions, propagated away from a finite size of source, is evaluated as follows: Consider a schematic of the experiment shown in Fig.  1 , where EPR entangled photons are produced by a finite source size. Photon-1 is detected on a screen, which can record the position of a detected photon as a point on the screen. This measurement corresponds to a position measurement of photon-1 while photon-2 is propagating towards a double-slit, and later it passes through a 50:50 beam splitter. The reflected probability amplitude of photon-2 is incident on a single photon detector-3, which is placed at the focal point of a convex lens. Whereas the transmitted probability amplitude is passed through a double-slit and incident on a single photon detector-2. The detector-2 is stationary, and it measures the position of photon-2 behind the double-slit. Each single photon detector is equipped with a very narrow aperture in order to measure the position of a photon around a location.

To evaluate the EPR state of two photons emanating from a three-dimensional source of finite extension, consider a source placed around the origin of a right-handed Cartesian coordinate system, as shown in Fig.  1 . Two photons are produced simultaneously from each point in the source as a consequence of the EPR constraint. Corresponding to an arbitrary point \(\mathbf {r'}\) within the source, a two-photon probability amplitude to find photon-1 at a point \(o_{a}\) in region- a left to the source and photon-2 at a point \(o_{b}\) in region- b right to the source is written as \(\frac{e^{ip_{1}|\textbf{r}_{a}-\textbf{r}'|/\hslash }}{|\textbf{r}_{a}-\textbf{r}'|}\frac{e^{ip_{2}|\textbf{r}_{b}-\textbf{r}'|/\hslash }}{|\textbf{r}_{b}-\textbf{r}'|}\) 38 , 39 , where \(p_{1}\) and \(p_{2}\) are magnitudes of momentum of photon-1 and of photon-2, respectively, and \(\textbf{r}_{a}\) and \(\textbf{r}_{b}\) are the position vectors of points \(o_{a}\) and \(o_{b}\) from the origin. Since the source size is finite, the total finite amplitude to find a photon at \(o_{a}\) and a photon at \(o_{b}\) is a linear quantum superposition of amplitudes originating from all points located in the source, which is written as

where both photons have the same linear polarisation state. A case for different polarisation states of photons leads to a hyper-entangled state, which is reported in Refs. 40 , 41 . However, for this experiment, an EPR entanglement is sufficient. Therefore, both photons are assumed to have the same linear polarisation state along the y -axis, which is omitted in this analysis. In Eq. ( 1 ), \(A_{o}\) is a constant, and \(\psi (x',y',z')\) is the probability amplitude of a pair production at a position \(r'(x',y',z')\) in the source. This amplitude is constant for an infinitely extended EPR state at any arbitrary position vector \(\textbf{r}'\) in the source. This integral represents the amplitude of two photons emanating from a three-dimensional photon pair source of finite size. It leads to a two-photon amplitude, which corresponds to the probability amplitude to find two photons together at different locations. Further, the magnitudes of momenta of photons are considered to be equal \(p_{1}=p_{2}=p\) , for the degenerate photon pair production. The amplitude of pair production \(\psi (x',y',z')\) is considered to be a three-dimensional Gaussian function such that, \(\psi (x',y',z')= a e^{-(x'^2+y'^2)/\sigma ^2}e^{-z'^2/w^2}\) , where a is a constant, \(\sigma\) and w are the widths of the Gaussian.

To evaluate the integral, consider two planes oriented perpendicular to the z -axis such that a plane-1 is located at a distance \(s_{1}\) and a plane-2 is located at a distance \(s_{2}\) from the origin. These planes are not shown in Fig.  1 however, a screen can be placed in a plane-1 and a double-slit can be placed in a plane-2. The amplitude to find photon-1 on plane-1 and photon-2 on plane-2 is evaluated as follows: Consider the distances of planes from the origin are such that, \(\sigma ^{2}p/h s_{1}\ge 1\) and \(\sigma ^{2}p/h s_{2} \ge 1\) , where the magnitudes of \(s_{1}\) and \(s_{2}\) are considerably larger than \(\sigma\) and w . This approximation is valid for the experimental considerations of this paper. Since the double-slit and the detectors are placed close to the z -axis therefore, Eq. ( 1 ) can be written as

where \(\Phi (x_{1},y_{1}; x_{2}, y_{2})\) is a two-photon position amplitude with variables of its argument separated by a semicolon denoting a position of photon-1 on plane-1 and of photon-2 on plane-2. After solving the integral, \(\Phi (x_{1},y_{1}; x_{2}, y_{2})\) is written as

where \(c_{n}\) is a constant and tan( \(\Phi\) )=–p(s 1 +s 2 )σ 2 /2 ℏ s 1 s 2 . It is evident from Eq. ( 3 ) that both photons can be found at arbitrary positions. Once a photon is detected at a well-defined location ( \(x'_{i}, y'_{i}\) ), where a label \(i\in \{1,2\}\) corresponds to any single measured photon, then its position is determined. This measurement collapses the total wavefunction of both photons. Note that when a photon is detected at a well-defined position, even then the amplitude to find the other photon in the position space is delocalised, i.e. the projected position wavefunction has a nonzero spread. This wavefunction projection happens immediately once a photon is detected.

The second order quantum interference is exhibited if photon-1 detections are retained on the screen with the condition that photon-2 is detected after the double-slit by a stationary detector-2 as shown in Fig.  1 . However, this stationary detector will not always detect photon-2 since, photon has a nonzero amplitude to exist at different positions even after passing through the double-slit. The conditional detection corresponds to a joint measurement of photons. If all photon-1 detections on the screen are considered, then the interference pattern does not appear. Single photon interference is suppressed on the screen as well as after the double-slit, since photons are EPR entangled. To evaluate the second order interference pattern, consider a screen placed at \(z=-s_{1}\) and a double-slit placed at \(z=s_{2}\) with their planes oriented perpendicular to the z -axis. If the transmission function of the double-slit is \(A_{T}(x_{2},y_{2})\) then the joint amplitude to detect photon-1 on the screen at a position \((x_{1}, y_{1})\) and photon-2 by a stationary detector-2 is written as

where an integration represents a projection onto a quantum superposition of position states of the photon-2 in the plane of the double-slit. A phase multiplier \(B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }\) represents a phase acquired by a photon to reach detector-2 from the double-slit plane. The distance between detector-2 location ( \(x_{o}, y_{o}, z_{o}\) ) and an arbitrary point location ( \(x_{2}, y_{2}, s_{2}\) ) in the double-slit plane is \(r_{d}=(D^{2}+(x_{2}-x_{o})^{2}+ (y_{2}-y_{o})^{2})^{1/2}\) , where \(D=z_{o}-s_{2}\) is the distance of detector-2 from the double-slit. Note that \(x_{o}\) is different than the symbol \({\textbf {x}}_{o}\) which is denoting separation of particles in the one-dimensional EPR state. Thus, the second order interference pattern depends on the position of detector-2. For a double-slit with slit separation d along the x -axis and infinite extension along the y -axis, the transmission function is given by \(A_{T}(x_{2},y_{2})= [\delta (x_{2}-d/2)+\delta (x_{2}+d/2)]/\sqrt{2}\) . In the following experiment, each slit of the double-slit is largely extended along the y -axis as compared to its width. The effect of slit width and position resolution of single photon detectors is considered in the analysis of the following experiment. It is also evident that the two-photon interference pattern exhibits a shift when the position of the stationary detector-2 is shifted.

Experimental results

An experiment is performed with continuous variable EPR entangled photons of equal wavelength 810 nm, which are produced by the Type-I SPDC in a negative-uniaxial BBO nonlinear crystal. An experimental diagram of the setup is shown in Fig.  2 , where the x -axis is perpendicular to the optical table passing through the crystal. This experimental setup is a folded version of a diagram shown in Fig.  1 , where folding is along the x -axis such that photons propagate close to the angle of the conical emission pattern in a horizontal plane parallel to the optical table. Furthermore, photons propagating at a small inclination w.r.t. a horizontal plane pass through the double-slit. A vertical linearly polarised laser beam, along the x -axis, of wavelength 405 nm is expanded ten times to obtain a beam diameter of 8 mm at the full-width-half-maximum. The expanded laser beam is passed through the BBO crystal, whose optic-axis can be precisely tilted in a vertical plane passing through the crystal. This configuration results in noncollinear spontaneous down-converted photon pair emission in a broad conical pattern, where both the photons of each pair have the same linear polarisation state perpendicular to the polarisation state of the pump photons. The down-converted photons are EPR entangled in a plane perpendicular to the symmetry axis of the cone. The pump laser beam, after passing through the nonlinear crystal, is absorbed by a beam dumper to minimise unwanted background light.

An experimental diagram, where EPR entangled pairs of photons are emanated in a conical emission pattern. The paths of entangled photons are represented by red lines. The pump laser beam, after passing through the crystal, is represented by a narrow white line for clarity. The x -axis is perpendicular to the optical table and passing though the nonlinear crystal.

A screen is represented by a movable single photon detector-1 ( \(D_{1}\) ), which is placed close to the crystal at a distance of 26.4 cm to detect photon-1 at about 5.68 ns prior to the detection of photon-2. The aperture of a single photon detector \(D_{1}\) is an elongated single-slit of width 0.1 mm along the x -axis, which represents an effective detector width. It also corresponds to the resolution of the position measurements along the x -axis. This detector can be displaced parallel to the x -axis in steps of 0.1 mm to detect photons at different positions. Photon-1 is passed through a band-pass filter of band-width 10 nm at the centre wavelength 810 nm prior to its detection. Photon-2 is incident on a 50:50 polarisation independent beam splitter, which is placed at a distance of 93.8 cm from the crystal. A double-slit with an orientation of single slits perpendicular to the x -axis is placed after the beam splitter at a distance of 3 cm. Another elongated single-slit aperture of width 0.1 mm along the x -axis is placed after the double-slit at a distance of 23 cm from the double-slit in front of an optical fibre coupler. After passing through the double-slit, photon-2 is filtered by a band-pass filter of band-width 10 nm at the centre wavelength 810 nm. It is then passed through the aperture and directed towards a single photon detector-2 ( \(D_{2}\) ) with a multimode optical fibre of length 0.5 m. This single-slit aperture can be displaced along the x -axis with a resolution of 0.1 mm. However, it is positioned at a predetermined location during one complete interference pattern data collection. In this experimental configuration, photon-1 is detected much earlier while photon-2 is propagating towards the beam splitter. Detection of photon-1 cannot affect photon-2 through any signalling limited by the speed of light until it reaches at an optical fibre coupler placed after the double-slit. Photon-2 arrives at the beam splitter 2.26 ns after the detection of photon-1, and from the beam splitter, its transmitted amplitude takes about 0.1 ns to arrive at the double-slit. The reflected amplitude of photon-2 is detected after passing through a band-pass filter by another optical fibre coupled single photon detector-3 ( \(D_{3}\) ) without any aperture. Photons are focused on an optical fibre input with a convex lens, which projects the incident quantum state of photon-2 onto an eigen-state of the transverse momentum, provided photon-2 is detected by a single photon detector \(D_{3}\) . Distance of the lens from the beam splitter is 25 cm, where this lens and the single photon detector \(D_{3}\) are positioned at predetermined fixed locations throughout the experiment.

( a ) Quantum interference pattern obtained by measuring the coincidence detection of photons by a variable position single photon detector \(D_{1}\) and a stationary single photon detector \(D_{2}\) , where a solid line represents the theoretically evaluated interference pattern. ( b ) Coincidence detection of photons results in no interference, when photon-2 is detected by a stationary single photon detector \(D_{3}\) and photon-1 is detected by \(D_{1}\) . Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The shift in the two-photon quantum interference pattern when, ( a ) single photon detector \(D_{2}\) position is \(x_{o} = +0.11\) mm, ( b ) \(D_{2}\) position is \(x_{o} = -0.11\) mm. Single photons do not interfere in this experiment. Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The experiment is performed with 19 mW power of the pump laser beam, which is incident on the crystal. Each single photon detector output is connected to an electronic time correlated single photon counter (TCSPC), which measures the single and coincidence photon counts with 81 ps temporal resolution. A selected width of time window for the coincidence detection of photons is 81 ns. Single photon counts of each detector and coincidence photon counts of \(D_{1}\) and \(D_{2}\) , \(D_{1}\) and \(D_{3}\) are measured for 60 s. These measurements are repeated ten times to obtain an average of photon counts. A two-photon quantum interference pattern with a reversible detection of photons is shown in Fig.  3 a, where open circles represent the measured coincidence photon counts of single photon detectors \(D_{1}\) and \(D_{2}\) and the single photon counts of \(D_{1}\) . Whereas, a solid line corresponds to the theoretical calculation of two-photon quantum interference using Eq. ( 4 ) by considering the finite width of each slit of the double-slit and position resolution of \(D_{2}\) . A position of \(D_{2}\) relative to the double slit is \((x_{o}, D)\) in a vertical plane with \(D=23\) cm. The two-photon quantum interference pattern exhibits a shift as the position \(x_{o}\) of \(D_{2}\) is displaced, which is due to the phase-shift multiplier term \(B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }\) in Eq. ( 4 ). The slit separation of the double-slit is 0.75 mm and the width of each slit is 0.15 mm. A fixed position of a single photon detector \(D_{2}\) is taken to be the reference point with \(x_{o}=0\) . There is no single photon interference pattern produced in this experiment by scanning the detector \(D_{1}\) or \(D_{2}\) . When photon-1 is detected, photon-2 is still propagating towards the beam splitter, and later its transmitted amplitude is detected by a fixed position single photon detector \(D_{2}\) at a time lapse of 5.68 ns after the detection of a photon-1. On the other hand, if the reflected amplitude of photon-2 is detected by a single photon detector \(D_{3}\) then \(D_{2}\) will not measure any photon. In this case, photon-2 is not passed through the double-slit, and therefore, no two-photon quantum interference results as shown in Fig.  3 b, which shows coincidence counts of single photon detectors \(D_{1}\) and \(D_{3}\) and the single counts of \(D_{1}\) . A choice of whether to detect a photon after the double-slit or not is naturally and randomly occurring due to the presence of a beam splitter in the path of photon-2 after its detection. A path superposition quantum state of photon-2 after the beam splitter is projected either onto the transmitted or the reflected path due to a single photon detection by a detector \(D_{2}\) or \(D_{3}\) , respectively. The main characteristic of two-photon quantum interference is that it exhibits a shift of the entire pattern as the single photon detector \(D_{2}\) is displaced to another fixed position. This shift in the pattern is shown in Fig.  4 when, (a) \(D_{2}\) is placed at a position \(x_{o}= 0.11\) mm, (b) \(D_{2}\) is placed at a position \(x_{o}=-0.11\) mm with same D . This shift is also observed experimentally in the quantum ghost interference experiment by Strekalov et al. 23 . As a consequence of the EPR entanglement, there is no single photon interference. Therefore, the experiment in this paper presents a quantum two-photon interference with a reversible detection of photons, which has no classical counterpart.

This paper presents a two-photon double-slit experiment with the reversible detection of photons. Continuous variable EPR entangled photons are produced by the Type-I SPDC process, where photon-1 is detected on a screen while photon-2 is propagating towards a beam splitter. At a later time, photon-2 is produced in a quantum superposition of reflected and transmitted path amplitudes at the beam splitter. The transmitted amplitude is passed through the double-slit, and if this amplitude is detected by a detector-2 then the path quantum superposition state of photon-2 is collapsed onto the transmitted path. Then detector-3 does not detect this photon. Since photon-2 interacted with the double-slit considerably later than the detection of photon-1 therefore, it is ruled out that photon-1 has carried the path information of photon-2 in the double-slit to suppress the single photon interference. In addition, a position measurement of photon-1 cannot affect photon-2 through any signal propagating with speed, which is limited by the speed of light. If photon-2 is detected by a detector-3 then the quantum superposition state is collapsed onto the reflected path. Therefore, detector-2 does not detect photon-2, which results in no interference in single photon and two-photon measurements.

It is very important to expand the beam diameter of the pump laser beam to produce a continuous variable EPR quantum entangled state. It also leads to a broader envelope of the interference pattern. To achieve low background counts limited by the dark counts of the single photon detectors, the pump laser beam should have minimal scattering from optical components, and it should be properly dumped after passing through the crystal. A source of EPR entangled photons consists of a thin crystal in Type-1 SPDC configuration, where down-converted photons have the same linear polarisation. The nonlinear crystal is anti-reflection coated for wavelengths of pump and down-converted photons to reduce scattering and back reflection. The nonlinear crystal is kept at room temperature without any temperature control. Its optical-axis is precisely aligned w.r.t. the polarisation vector of the pump laser beam to obtain a broad conical emission pattern of down-converted photons with a full cone angle of  9.5°. The optical power of the pump laser beam is 19 mW, which is x -polarised. Single-slit apertures, which are placed in front of \(D_{1}\) and an input coupler of an optical fibre of \(D_{2}\) , are attached to translational stages to displace them precisely to collect photons corresponding to different positions of apertures. To increase the number of photons passing through the double slit, a double slit consists of two elongated single slits separated by a distance of 0.75 mm along the x -axis, where the width of each slit is 0.15 mm. In the experimental configuration, photons are EPR entangled in a plane perpendicular to the direction of propagation of the pump laser beam. The efficiency of each single photon detector is about 65 %. The single photon detector \(D_{1}\) equipped with a convex lens is directly collecting photons and it is placed close to the crystal. Whereas, the single photon detectors \(D_{2}\) and \(D_{3}\) are coupled to multimode optical fibres of length 0.5 m. The input of each optical fibre is attached to respective optical fibre couplers, each consisting of a convex lens of diameter  1 cm. Photons are collected by the lenses after passing through the single-slit apertures to measure the position of photons by \(D_{1}\) and \(D_{2}\) . However, a coupler of a single photon detector \(D_{3}\) is not equipped with any aperture. A band-pass optical filter of band-width 10 nm at centre wavelength  810 nm is placed at the input of each single photon detector to filter the unwanted scattered photons of the pump laser and background light.

Data availability

All data generated or analysed during this study are included in this article.

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Acknowledgements

Mandip Singh acknowledges research funding by the Department of Science and Technology, Quantum Enabled Science and Technology grant for project No. Q.101 of theme title “Quantum Information Technologies with Photonic Devices”, DST/ICPS/QuST/Theme-1/2019 (General).

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Vipin Devrari & Mandip Singh

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MS setup the experiment and made its theoretical model, VD took data and analysed data, MS wrote this manuscript. Both authors discussed the experiment.

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Devrari, V., Singh, M. Quantum double slit experiment with reversible detection of photons. Sci Rep 14 , 20438 (2024). https://doi.org/10.1038/s41598-024-71091-1

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Two-Slit Experiment

Recreate one of the most important experiments in the history of physics–the two-slit experiment–by shining a laser pointer through two narrow slits and observing the interference pattern on a distant screen.

• Laser pointer
• Lice comb (or, not quite as good, an eyelash comb with narrowly spaced metal teeth)
• White screen or 5 x 7-inch index card
• Two large binder clips, 1 inch (2.5 cm) wide, 2 inches (5 cm) long
• Two medium binder clips, 1/2 in (1 cm) wide, 1 inch (2.5 cm) long
• A single-edge razor blade or straight-edge knife (not shown)

• Use the black tape to cover the teeth on the lice comb, leaving exposed only two slits between adjacent teeth.
• Insert the handle of the comb into a large binder clip and set the clip on its side on a table or other flat surface so the teeth of the comb are vertical (click to enlarge photo)
• .Clip the two medium binder clips to the barrel of the laser pointer and position them so the laser pointer rests horizontally.
• Attach the remaining large binder clip to the index card so that it creates a stand for the card.
• Set up the laser pointer and comb so that the laser beam shines through the two open slits on the comb onto the white screen. Position the screen so it is at least 4 feet (1.5 meters) from the two slits.

Look at the pattern produced when the light goes through the two slits and shines on the distant screen. Notice there are alternating dark and light regions.

Use the razor blade or knife to block the light from going through one of the slits. Notice that some of the dark bands vanish. Try blocking the light from going through the other slit.

Remove the razor blade and notice that when you allow light from both slits to shine on the screen, the dark bands re-appear.

When light goes through a slit, diffraction causes it to bend and spread across the screen, making a predictable banded pattern. When light goes through two slits, new dark regions appear. The dark and light regions are produced by interference of the light passing through the slits.

As light coming through one slit reaches the screen, it overlaps with light coming through the other slit. When the crest of one wave of light overlaps with the crest of another wave, the two waves combine to make a bigger wave and you see a bright blob of light. When the trough of one wave overlaps with the crest of another wave, the waves cancel each other out and you see a dark band. The appearance of dark bands when two light sources strike a screen shows that light is a wave phenomenon.

This experiment was first performed in 1801 by Thomas Young, and it provided support for a wave theory of light.

The angle,  T , between two adjacent dark bands in the interference pattern and the slits depends on the distance between the centers of the slits,  d , and the wavelength of light,  L . For small angles, the angle is inversely proportional to the distance between the slits and proportional to the wavelength of the light:

$$T = \frac{L}{d}$$

If light of multiple wavelengths is shone through two or more slits, each wavelength will be bent at a different angle. This spreads light out into a spectrum, with red light bent at a larger angle than blue light. This is the principle behind a diffraction grating.

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Concerning the dark bands in the light "wave" interference pattern

I'll begin with a with a brief and familiar example to frame the question:

|_>EXAMPLE

|_> QUESTION

I have many other questions and of course, more to read. But I think this is the most important start.

The question has been slightly addressed here, but I welcome more complicated answers: Are double-slit patterns really due to wave-like interference?

• interference
• double-slit-experiment

3 Answers 3

There's an important difference between water waves and light waves. Water waves require a medium to travel through (i.e. water). Light waves require no medium. In fact, even postulating they do contradicts special relativity.

So when the waves in the water cancel out, the water is left behind, but when the light waves cancel out, nothing is left behind.

• $\begingroup$ A wave is just energy transfer. If we can agree on that, then we can say that both water waves and light waves can exist in space because they are not just waves, the water and the light are both particles as well. Sound for example is just a pressure wave with no associated "sound particle (phonon)", therefore pressure waves cannot travel without a particle to interact with. Alright, now that I have told you everything you already know I will ask the same question I asked creillyucla: $\endgroup$ –  Aerros Commented Jul 26, 2015 at 16:56
• $\begingroup$ when two waves of water are "shot" at each other exactly out of phase, the result is flat water....the water doesn't disappear. When two waves of polarized, out of phase laser beams are faced against each other, is the result then darkness at the meeting point or something else to expand on your answer? Also, if a rope is tied on one end and held in hand on the other in space and "shaken" to attempt to make a transverse wave, does the wave happen? (the last question is actually important to me as well) $\endgroup$ –  Aerros Commented Jul 26, 2015 at 16:56

For water waves, the quantity that is subject to interference is the amplitude of the surface disturbance (i.e. the water's height above its undisturbed value). So as you correctly stated at regions of destructive interference the water's height remains at its undisturbed value for all times.

For light waves, the quantity that is subject to interference is the total amplitude of the light, so at regions of destructive interference the amplitude of the light is zero for all times, and so we observe no light emitted from these regions.

It is not true that two water waves shot at each other will produce a flat surface for all times. In fact, if you superimpose two traveling waves moving in opposite directions, you will get what is referred to as a standing wave. This is the case no matter what type of wave we consider (water or light or sound, etc.) The most familiar example of a standing wave, for visualization purposes, is a vibrating string. Just like a simple oscillator, energy in a standing wave is continuously converted from kinetic energy to potential energy as the wave's amplitude grows, and vice versa as its amplitude diminishes. There are, then, instants in time during the standing wave's evolution where its amplitude is zero at all points along the wave. These instants are what you refer to when you say the surface of the water is flat. But these are just instants, and moments before or after these instants the wave will be shrinking and growing, respectively. So if you shoot two lasers beams at each other you will get a standing wave. This is in fact exactly what you get in a laser cavity, where light traveling in one direction reflects off the cavity mirrors and superimposes its leading portion on top of its trailing portion, producing a standing wave.

• $\begingroup$ Amplitude is half the distance between crest and trough. If both light and water are considered transverse waves then, as stated both will exhibit combinations of crest and trough patterns. When two waves of water are "shot" at each other exactly out of phase, the result is flat water....the water doesn't disappear. When two waves of polarized, out of phase laser beams are faced against each other, is the result then darkness at the meeting point or something else to expand on your answer? $\endgroup$ –  Aerros Commented Jul 26, 2015 at 16:40
• $\begingroup$ A transverse wave with one source which is reflected accordingly will produce a standing wave: [link](bit.ly/1JLaVRP) A transverse wave with two sources, out of phase as I indicated) will yield a flat line: [link](bit.ly/1MsuFif) I was referring to the second example because the double slit experiment technically involves two source waves. When the double slit experiment is done with a transverse wave (water), the resulting alternating pattern of amplified-flat-amplified-flat is seen: [link](bit.ly/1SJLYv2) When done with light it should be similar: [link](bit.ly/1eu3e9P) $\endgroup$ –  Aerros Commented Jul 28, 2015 at 15:56
• $\begingroup$ But the amplified-flat alternating pattern is not observed as expected with light seen as a transverse wave. Instead we observe a pattern only exhibited by longitudinal waves of amplified-dark alternating patterns as seen here: (wrd.cm/1VJiOjS) I'm reading this right now that I just found entitled "The Illusion of Light as Transverse Electromagnetic Waves" : (bit.ly/1etSb0n) $\endgroup$ –  Aerros Commented Jul 28, 2015 at 15:56

Since no one else has contributed, and the most satisfactory answer was the pdf I found, I will state that that is the answer to my question:

"The Illusion of Light as Transverse Electromagnetic Waves" (bit.ly/1etSb0n)

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Emergency Import Restrictions Imposed on Categories of Archaeological and Ethnological Material of Ukraine

A Rule by the U.S. Customs and Border Protection and the Treasury Department on 09/10/2024

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Final rule.

This document amends the U.S. Customs and Border Protection (CBP) regulations to reflect the imposition of emergency import restrictions on categories of archaeological and ethnological material of Ukraine, pursuant to a determination made by the United States Department of State under the terms of the Convention on Cultural Property Implementation Act. The emergency import restrictions will be in effect until March 5, 2029, unless extended. This document contains the Designated List of Archaeological and Ethnological Material of Ukraine that describes the types of objects or categories of ( print page 73281) archaeological and ethnological material to which the import restrictions apply.

Effective on September 10, 2024.

For legal aspects, W. Richmond Beevers, Chief, Cargo Security, Carriers and Restricted Merchandise Branch, Regulations and Rulings, Office of Trade, (202) 325-0084, [email protected] . For operational aspects, Julie L. Stoeber, Chief, 1USG Branch, Trade Policy and Programs, Office of Trade, (202) 945-7064, [email protected] .

The Convention on Cultural Property Implementation Act (Pub. L. 97-446, 19 U.S.C. 2601 et seq. ) (CPIA), which implements the 1970 United Nations Educational, Scientific and Cultural Organization (UNESCO) Convention on the Means of Prohibiting and Preventing the Illicit Import, Export and Transfer of Ownership of Cultural Property (823 U.N.T.S. 231 (1972)) (Convention), allows for the conclusion of an agreement between the United States and another party to the Convention to impose import restrictions on eligible archaeological and ethnological material. In certain limited circumstances, the CPIA authorizes the imposition of restrictions on an emergency basis ( 19 U.S.C. 2603 ). The emergency restrictions are effective for no more than five years from the date of the State Party's request and may be extended for three years where it is determined that the emergency condition continues to apply with respect to the covered material ( 19 U.S.C. 2603(c)(3) ). These restrictions may also be continued, in whole or in part, pursuant to an agreement concluded within the meaning of the CPIA ( 19 U.S.C. 2603(c)(4) ).

Pursuant to 19 U.S.C. 2602(a) , the government of Ukraine, a State Party to the Convention, requested on March 5, 2024, that import restrictions be imposed on certain archaeological and ethnological material, the pillage of which jeopardizes the cultural heritage of Ukraine. The CPIA authorizes the President (or designee) to apply import restrictions on an emergency basis if the President determines that an emergency condition applies with respect to any archaeological or ethnological material of any requesting State Party ( 19 U.S.C. 2603 ).

On July 26, 2024, the Assistant Secretary for Educational and Cultural Affairs, United States Department of State, after consultation with and recommendation by the Cultural Property Advisory Committee, made the determinations necessary under the CPIA for the emergency imposition of import restrictions on categories of archaeological material and ethnological material of the cultural heritage of Ukraine. The Designated List below sets forth the categories of material to which the import restrictions apply. Thus, U.S. Customs and Border Protection (CBP) is amending § 12.104g(b) of title 19 of the Code of Federal Regulations ( 19 CFR 12.104g(b) ) accordingly.

Importation of covered material from Ukraine will be restricted until March 5, 2029, unless the conditions set forth in 19 U.S.C. 2606 and 19 CFR 12.104c are met.

The Designated List includes, but is not limited to, categories of objects described below.

Archaeological material in the Designated List ranges in date from the Paleolithic period (c. 1.4 million years ago) through 1774 C.E. Ethnological material in the Designated List includes: ethnological religious and ritual objects, and objects related to funerary rites and burials dating from 200 C.E. to 1917 C.E.; ethnological manuscripts, written documents, and early prints dating from 900 C.E. to 1917 C.E.; ethnological architectural elements dating from 200 C.E. to 1917 C.E.; and ethnological paintings, military material, and traditional folk clothing and textiles dating from 1700 C.E. to 1917 C.E. The designated list set forth is representative only. Any dates and dimensions are approximate.

D. Plaster, Stucco, and Unfired Clay

A. Religious and Ritual Objects, and Objects Related to Funerary Rites and Burials

B. Architectural Elements

C. Manuscripts, Written Documents, and Early Prints

D. Ethnological Paintings

E. Military Material

F. Traditional Folk Clothing and Textiles

Approximate simplified chronology of well-known periods:

Paleolithic: c. 1.4 million years ago-8000 B.C.E.

Mesolithic: c. 7000-4500 B.C.E.

Neolithic: c. 6000-3000 B.C.E. (c. 6000-4000 B.C.E. on the right bank of the Dnipro River and 5000-3000 B.C.E. in Polissia and the left bank of the Dnipro River)

Copper Age (or Eneolithic): c. 4000-2000 B.C.E.

Bronze Age: c. 2100-800 B.C.E.

Early Iron Age: c. 800-400 B.C.E.

Ancient Greek Period: c. 650 B.C.E-47 B.C.E.

Roman Period: c. 47 B.C.E.-340 C.E.

Late Antiquity and Early Byzantine Periods: c. 340-880 C.E.

Kyivan Rus Period: c. 880-1240 C.E.

Late Medieval Period: c. 1240-1650 C.E.

Early Modern Period: c. 1650-1917 C.E.

Archaeological material includes categories of objects ranging in date from c. 1.4 million years ago through 1774 C.E.

1. Large Sculpture and Statues —Including anthropomorphic, zoomorphic, and multi-figure compositions. Made primarily of sandstone, limestone, marble, and shell rock. Neolithic menhir-like stones may represent stylized human images, while Bronze Age statues are usually rectangular with the head outlined and other body parts shown in relief. Scythian sculptures schematically depict warriors. Sculptures from the Eneolithic and Ancient Greek periods often take the form of schematic human busts. Ancient Greek and Roman sculptures often depict naturalistic images of various figures, including humans, mythological creatures, and animals. Medieval nomadic stelae depict humans schematically, often with pointed headdresses. Approximate date: 6000 B.C.E.-1774 C.E.

2. Miniature Sculptures and Statues —Made primarily of marble, quartz, and alabaster, these include anthropomorphic and zoomorphic forms and images of objects. Copper Age figurines vary in shape, often featuring prominent eyes, noses, or sex markers. Ancient Greek and Roman marble statuettes are naturalistic, depicting various figures. Approximate date: 6000 B.C.E.-1774 C.E.

3. Architectural Elements —Originating from religious, residential, and burial sites and used in walls, floors, vaults, and roofs. Constructed from slate, sandstone, limestone, ( print page 73282) marble, and other stones. Elements include, but are not limited to, capitals and parts of columns, pilasters, friezes, door and window frames, keystones, altars, altar screens, mosaics, and tiles. Stone slabs with relief and inlaid sculpted compositions, depicting religious figures, animals, and floral motifs, were embedded into railings or other parts of buildings. Approximate date: 650 B.C.E.-1774 C.E.

4. Mosaics —Composed of painted pebbles, marble, limestone, and bricks. Floors made of painted pebbles decorated Ancient Greek-period inner courts and rooms. Early Christian churches in Crimea and Kyiv were decorated with mosaics made of marble of various colors, limestone, and bricks. These mosaics were crafted from small cube-shaped stones (tesserae) measuring approximately 4-6 cm x 3-5 cm, set in a limestone mortar or cement. Motifs include, but are not limited to, geometric patterns, palmettes, depictions of people, borders with meanders, waves, braids, pairs of animals, and griffins. They show a variety of colors, including black, white, dark blue, and brown. Approximate date: 700 B.C.E.-1774 C.E.

5. Miniature Columns and Small Altars —Used to decorate shrines, burials, and churches, miniature columns range in size from 10 to 100 cm high and could be rounded, fluted, twisted, or composed of semi-columns. Made primarily of white marble, gray limestone, or shell rock. Small altars are movable architectural structures with rectangular or rounded bases, sometimes column-shaped with a shallow round surface, ranging in height from 10 cm to 1 m. These items are found at Ancient Greek, Roman, Byzantine, and Medieval sites. Approximate date: 650 B.C.E.-1774 C.E.

6. Furniture —Including, but not limited to, tables, tripods, and stool legs often shaped like lion's paws, as well as throne or stool backs and armrests decorated with reliefs or sculptures. Typically made of marble and other stones and dating from the Ancient Greek and Roman periods. Approximate date: 650 B.C.E.-1774 C.E.

7. Slabs with Relief Images and Inscriptions —Made of marble, limestone, and other local stones, these slabs have been produced since the Bronze Age. Locally quarried slabs are often gray, porous, and rough, while slabs carved in Ukraine on imported marble are white and gray. Motifs on Ancient Greek and Roman period slabs include humans, lions, sphinxes, and griffins, with reliefs sometimes combined with paintings. Inscriptions in various scripts, including Latin, Greek, and Cyrillic, are found on slabs of various shapes and sizes. Approximate date: 3000 B.C.E.-1774 C.E.

8. Sarcophagi, Ossuaries, and Gravestones —Sarcophagi and ossuaries are usually rectangular constructions made of jointed or carved slabs; their lids are also included, having roof-like shapes in the Roman period. Sizes vary depending on purpose: for cremations or inhumations, they range from half a meter to several meters. Gravestones are typically decorated with floral ornaments, rosettes, and cornices; usually rectangular with roof, arch, or cone-shaped tops. Late Antique, Medieval, and Early Modern gravestones include those shaped as crosses, tree trunks, or architectural structures. Approximate date: 650 B.C.E.-1774 C.E.

9. Crosses and Icons —Stone crosses are made primarily of marble or limestone and range in size from 10 cm to over half a meter. Stone icons are typically carved as rectangular or round plates usually from pink or blue slate or sandstone. Icons range from 5 to 25 cm in size. They are painted with images of single, frontally depicted, full-length or half-length figures of Christ, the Virgin Mary, or saints such as Nicholas, Theodore Stratelates, or others, or religious scenes with two to three figures shown frontally or in three-quarters view, such as the Annunciation, Presentation, Descent into Hell, and others. Icons usually have a frame, while crosses are sometimes set in frames made of other materials. Precious stones may be used in the decoration of small cultic objects. Approximate date: 300-1774 C.E.

10. Vessels —Made primarily of limestone, marble, and alabaster. Including, but not limited to, mortars and pestles of various sizes from the Bronze Age, and marble vessels for washing from the Ancient Greek and Roman periods. Alabaster vases and lamps were common in the Ancient Greek period. Church ceremonial vessels from the Medieval and Early Modern periods vary in shape from miniature narrow bottles (alabastra) to large open-shaped water basins (louteria). Approximate date: 3000 B.C.E.-1774 C.E.

11. Tools —Types include, but are not limited to, choppers, handaxes, axe heads, microlithic inlays, scrapers, blades, polishing tools, loom-weights, grindstones, wine-press stones, and anchors. Primarily made of flint, obsidian, granite, quartz, quartzite, shale, and steatite. Early Paleolithic tools were pebbles with chopped edges; later shapes continuing through the Copper and Bronze Ages include flaked tools. Loom-weights vary from conical to elongated shapes. Approximate date: 1.4 million years ago-1774 C.E.

12. Weapons —Types include, but are not limited to, arrowheads, spearheads, darts, maces, and cannonballs. Stone weapon heads have been used since the Paleolithic period. Stone maces from the Neolithic period are often smoothed. Cannonballs, often made of porous stone, range from 10 to 30 cm in diameter. Approximate date: 1.4 million years ago-1774 C.E.

13. Games —Represented primarily by dice and chess pieces. Chess pieces from the Kyivan Rus period have one flat side and a spherical or anthropomorphic shape. Ancient Greek dice are flat pebbles with ancient engravings and marks. Dice are about 2-4 cm in diameter. Approximate date: 650 B.C.E.-1300 C.E.

14. Adornments —Types include, but are not limited to, beads, pendants, and inlays made from materials such as turquoise, marble, quartz, emerald, carnelian, jasper, onyx, ruby, amethyst, and lazurite. Sarmatian jewelry contemporary with the Ancient Greek and Roman periods features inlaid precious stones. Byzantine and Kyivan Rus periods are known for amethyst and lazurite beads and inlays. Imported inlays were used in Medieval and later periods. Approximate date: 6000 B.C.E.-1774 C.E.

1. Coins —In gold, silver, bronze, copper, and lead. Some coin types minted in or commonly found in archaeological contexts in Ukraine in various periods are listed below.

a. Ancient Greek cities in Ukraine, including Olbia, Panticapaeum, Chersonesus, and Tyras, minted coins of various weights and metals. Cast currency in dolphin, sturgeon, and arrowhead forms was also produced in this period. See Zograph, A. Ancient Coinage, Part II, Ancient Coins of the Northern Black Sea Littoral. (Oxford, 1977). Approximate date: 600-47 B.C.E.

b. In the Roman period, Panticapaeum continued to mint coins, and other Roman imperial coins were also used. See MacDonald, D. An Introduction to the History and Coinage of the Kingdom of the Bosporus, Classical Numismatic Studies 5. (Lancaster, 2005). Approximate date: 47 B.C.E.-500 C.E.

c. Coins minted in the Kyivan Rus period include gold and silver zlatnyks with a portrait of the ruler and the trident (tryzub) symbol. Hexagonal cast ingots (hryvnia) were also produced. Bohemian deniers and dirhams of Islamic states were also used in the ( print page 73283) Medieval period. Pierced coins and exfoliated (flaked) coins, including half-coins and forgeries, were common. Approximate date: 880-1240 C.E.

d. Coins in use during the Late Medieval and Early Modern periods include, but are not limited to, Mongolian dirhams, Lithuanian denars, Polish ducats, Crimean Khanate akces, Austro-Hungarian talers, Ottoman coins, and Russian rubles. Approximate date: 1240-1774 C.E.

2. Medallions —Usually featuring relief images, known since the Early Iron Age, with gold, silver, and bronze phaleras used during the Roman period. Approximate date: 1000 B.C.E.-1774 C.E.

3. Relief Plaques and Reliefs —Made of gold, silver, bronze, and lead. Used to decorate clothes, wooden, or leather objects, such as horse harnesses, quivers, scabbards, belts, and vessels. Decorations include animals and floral ornaments. Approximate date: 650 B.C.E.-1774 C.E.

4. Jewelry —Types include, but are not limited to, diadems, earrings, rings, necklaces, bracelets, crosses, pendants, fibulae, beads, and tubes. Scythian jewelry in the Animal Style was typically made of gold, less often of silver and bronze. Usually, these pieces depict predators attacking herbivorous animals and mythological creatures. Small gold pendants and beads were used to decorate clothes of these and later nomads. Byzantine and Kyivan Rus jewelry featured floral and geometric designs. Medieval period pendants include moon-shaped examples decorated with ornaments and temporal or temple rings of various shapes, including plain wrapped wire or featuring plates, pendants and ornaments. Bronze and silver fibulae of the Early Iron Age show a variety of forms and are much smaller than the massive Early Medieval fibulae shaped as anthropomorphic figurines or five-rayed ornaments. Approximate date: 3000 B.C.E.-1774 C.E.

5. Vessels— Primarily made of bronze, silver, and gold. Large riveted bronze cauldrons with thick walls and short stems or feet, up to 1 meter in diameter, known since the Bronze Age. Smaller Scythian vessels include, but are not limited to, cones, rhytons, kylixes, phiales, cups, ceremonial plates, kraters, ladles, and strainers. Sarmatians widely used Roman-type vessels like situlas and pans. Vessels corresponding to Greek, Roman, Celtic and Late Roman bronze vessel types are also known. Metal handles from Scythian, Greek-period, and other vessels are often shaped as anthropomorphic or zoomorphic figures. Approximate date: 2500 B.C.E.-late 1774 C.E.

6. Sculpture and Small Figurines— Include bronze sculptures from the Ancient Greek and Roman periods, often fragmentary. Small figurines typically depicted deities, animals, and mythological creatures. Medieval examples show a more schematic style. Approximate date: 2500 B.C.E.-1774 C.E.

7. Horse Harness Elements —Including, but not limited to, shuffrons or chanfrons (face covers), often decorated in relief, psalia (bit and cheek-pieces), horseshoes, spurs, and stirrups. Scythian horse bridles were composed of bronze bits with stirrup-shaped ends, iron bits with looped ends, three-looped iron or bronze cheek-pieces, and nose plates. Sarmatian sets often included silver and lead bridle roundels, iron bits, cheek-pieces, frontlets with a hook, and phaleras. Medieval horse harnesses also featured phaleras, psalia, and other details made of precious metals. For example, the Khazar psalia were nail-shaped, and Kyivan Rus sets sometimes included horse head-covers made of several plates. Approximate date: 1000 B.C.E.-1774 C.E.

8. Armor Elements —Including, but not limited to, mail, knee and elbow guards, shields (and shield bosses or umbos), helmets, and belt sets. Scale armor consisted of iron, bronze, or bone scales sewn onto leather. Chain mail made of iron links was known in the Roman period and more frequent in the Kyivan Rus period. Approximate date: 900 B.C.E.-1774 C.E.

9. Weapons —Including, but not limited to, swords (including folded ones), daggers, arrowheads, spearheads, darts, maces, scepters, crossbows, cannons and cannonballs, and sabers. Scythians used leaf-shaped spearheads, bronze or sometimes iron arrowheads with a socket and two or three edges, iron swords and daggers, long swords, and war axes. Kyivan Rus warriors used star-shaped maces, axes, spears, swords, and arrows. Approximate date: 2500 B.C.E.-late 1774 C.E.

10. Vehicle Element s—Including, but not limited to, anchors, cart elements, and chariot wheels. Ancient Greek- and Roman-period chariot details often featured figurines. Approximate date: 2000 B.C.E.-300 C.E.

11. Tools —Including, but not limited to, knives, axes, tongs, needles, thimbles, medical instruments, strigils, miniature spoons, nails, hoes, plows, and sickles. May be made of bronze, copper, iron, silver, and gold. Precious metals were sometimes applied to miniature or ceremonial tools, which are often decorated with ornaments or figurative terminals. Approximate date: 2500 B.C.E.-1774 C.E.

12. Bells —Typically made in bronze or iron, in various shapes and sizes, including spherical, with holes and balls inside; dome-shaped; cylindrical; and pear-shaped. Bells adorned jewelry and dress, as well as carts, chariots, and horse harnesses. Examples for cultic use were hollow, with slits and small balls inside; they were positioned on elongated sockets and crowned with images of animal- or bird-heads or figures. Approximate date: 700 B.C.E.-1300 C.E.

13. Lighting Devices —Including oil lamps and candle holders, sometimes elaborately decorated and typically made of bronze. Oil lamps were rounded or elongated containers with one or more nozzles and a handle. Candle holders are found in hanging, table, and standing varieties. They are often decorated with separately produced ornaments. Approximate date: 650 B.C.E.-late 1774 C.E.

14. Seals or Sealings —Medieval hanging lead seals used to certify documents are called molybdobulas or bullas. They have at least one round flat side with a relief, and they often resemble medallions and were pierced to be hung. Later bullas take the shape of gold chrysobulls. They begin at about 2 cm in diameter, and their color varies from gray to brown. Approximate date: 200-1774 C.E.

15. Icons and Crosses —Including, but not limited to, relief metal icons, crosses, and encolpions (icon medallions). Encolpions, relief metal icons, and their frames were often made of mixed materials and carved, inlaid with precious stones and metals, or engraved. Both icons and crosses are found in various sizes, including smaller examples for wearing on the chest and large ceremonial ones. Approximate date: 300-1774 C.E.

16. Mirrors —Including, but not limited to, hand mirrors made of silver and bronze, with one polished flat side and carved decoration on the back. May be round with a handle or a loop at the center of the back. Handles typically take the form of either a loop or a plaque raised above two small posts; they are sometimes decorated with sculpted or carved animals on the terminals, or made in anthropomorphic form. Approximate date: 600 B.C.E.-200 C.E.

17. Keys and Locks —Including, but not limited to, cylindrical locks with C-shaped shackles. Later examples were flattened with more complex keyways. Some examples had protective shields. Approximate date: 800-1774 C.E. ( print page 73284)

18. Lead Plates —Including inscribed and uninscribed examples. May be folded or unrolled. Lead plates with traces of cast ornamentation are known. Vary in color from light gray to almost black with green or brown tints. Approximate date: 700 B.C.E.-1300 C.E.

19. Games —Including dice and simple chess pieces, made from lead and bronze, shaped as knucklebones or cylinders with or without carving. Used across various periods, in sizes around 2-4 cm in diameter. Approximate date: 650 B.C.E.-1300 C.E.

1. Architectural Ceramics —Including, but not limited to, terracotta roof tiles with stamps, antefixes (ornamented or anthropomorphic), sculpted rainwater spouts (typically in a lion-head shape), drainpipes, stamped or engraved bricks, including “plinths” (wide and flat fired bricks resembling tiles). Roof-tile styles include ridge tiles, raised tiles (imbrices), and tegulae. May be decorated with stamped relief designs. Antefixes may be decorated with palmettes, anthropomorphic images, or painted. Includes relief plaques and medallions that may be part of antefixes and are decorated with mythological scenes. Bricks may have traces of graffiti or be stamped. Kyivan Rus bricks used in churches may bear trident-shaped relief marks. Approximate date: 650 B.C.E.-1774 C.E.

2. Stove Tiles— Including glazed and unglazed stove tiles. Glazed types may be smooth or have relief decoration. Glazed stove tiles are typically decorated in green, blue, white, brown, red, and other colors. Unglazed stove tiles are typically created from clays in brown, buff, pink, red, and yellow colors, and may have negative relief decoration. Stove tiles may be decorated with painted ornaments, such as heraldic, floral, anthropomorphic, and/or zoomorphic motifs, or state and family symbols. Sizes vary, but they are typically 10 to 50 cm in height. Approximate date: 1200-1774 C.E.

3. Vessels —Including utilitarian vessels, fine tableware, and special-purpose vessels, in conventional shapes such as amphorae, bowls, bottles, goblets, jars, pitchers, plates, storage vessels, and vases, as well as unconventional shapes such as anthropomorphic and zoomorphic forms. Includes vessel lids and fragments of vessels. Clay colors vary but are typically gray or red. Vessels may be glazed (typically black or red), enameled, or engobed. Vessels may be painted, incised, molded or stamped in relief, or incrusted, or bear applied decoration. Types and characteristics of various periods are described below.

a. Neolithic and Copper Age— Vessel styles include Linear Band Ware or Linear Spiral-Meander Pottery with a globular shape and linear incised ornamentation such as spirals, and Cucuteni-Trypillia wares that may be decorated with incised or stamped designs, sometimes filled with white or red paste, or painted in monochrome, bichrome, or polychrome designs in white, red, brown, and black and engobed in red, orange, white, and other colors. Painted designs include geometric and organic motifs. Characteristic Trypillia forms include biconical pots and binocular-shaped cultic vessels, as well as anthropomorphic and zoomorphic vessels. Includes vessels that may have applied zoomorphic ornaments. Approximate date: 6000-2000 B.C.E.

b. Bronze Age —Vessel styles include types related to Corded Ware pottery with impressed or incised rope-like decorations and globular forms. Approximate date: 2100-800 B.C.E.

c. Greek and Roman Pottery —Ancient Greek pottery most often found in Ukraine includes, but is not limited to, kraters, table amphorae, bomoi, olpes, jars, oinochoes, kylixes, skyphoi, cups, pateras, phiales, lekythoi, plates, lekanes with lids, flasks, and gutti. The most recognizable types of painted vessels are Geometric, Black-figure, Red-figure, and White-ground. Greek and Roman tableware also includes vessels cast in molds such as Hellenistic cups and Roman Sigillata. Black glazed (lacquered) pottery includes several types with stamped ornaments. May bear short painted inscriptions (dipinti) or incised inscriptions (graffiti). The rims of pithoi were often incised with letters or ornaments. Approximate date: 700 B.C.E.-340 C.E.

d. Byzantine and Medieval —Vessels may be glazed and/or decorated with paint or relief ornaments. Transport amphorae are also found in this period. Approximate date: 340-1650 C.E.

e. Miniature Vessels —Miniature vessels are typically found in the above-mentioned shapes and styles, but in sizes as small as 1 cm in diameter. May be painted. Includes miniature clay spoons. Approximate date: 4000-47 B.C.E

4. Figurines and Models —Including figurines representing anthropomorphic, zoomorphic, and mythical figures and models of objects, buildings, or vehicles. Styles common in various periods are described below. Approximate date: 4000 B.C.E.-1774 C.E.

a. Copper Age Trypillian— Figurines are typically abstract and stylized with pierced, incised, and pinched details. Models of houses, boats, and sleighs drawn by oxen are typical in this period.

b. Ancient Greek and Roman Period— Figurines are usually naturalistic images of humans, half-human creatures, animals, and objects. Some figurines are made with separate movable limbs. Most figurines are hollow inside, with a technical opening (rounded, square, or triangular). May be painted, gilded, and/or decorated with applied elements, such as small clay balls, fruits, flowers, rosettes, leaves, and/or wreaths, which may bear incised details. Some figurines may have been created in molds. Clay cart models drawn by a horse are also found in the Roman period.

c. Late Antique to Early Modern Period— Figurines may be handmade or molded in anthropomorphic and zoomorphic forms. May be painted or incised.

5. Miniature Altars —Typically in cubic, rectangular, and rounded forms, but may also take the form of the club of Heracles. They are usually profiled, but sometimes bear relief images on their sides. Sizes typically vary from 10 to over 50 cm in height. Approximate date: 650 B.C.E.-300 C.E.

6. Molds —Types include jewelry molds and figurine molds. Sizes vary, but jewelry molds are typically 5-15 cm in length, while figurine molds reach up to 25-30 cm. Approximate date: 1000 B.C.E.-1300 C.E.

7. Tools —Including, but not limited to, loom-weights (may be round or pyramidal), coils, and fishing sinkers (may be pyramidal or quadrangular). Loom-weights and sinkers are typically pierced and smoothed but undecorated. Sizes vary, but are typically between 5-10 cm in diameter (rounded shapes) or up to 15 cm in height (pyramidal and quadrangular shapes). Approximate date: 6000 B.C.E.-1300 C.E.

8. Musical Instruments —Including wind and rattle-like instruments or toys that may be shaped like birds, eggs, boars, tortoises, other zoomorphic forms, and coffins. Approximate date: 3500 B.C.E.-1774 C.E.

9. Lamps and Lighting —Including, but not limited to, oil lamps and candle holders. Oil lamps vary in shape and type, ranging from open-shaped and hanging types to closed types with narrow nozzles, thin handles, and reliefs on the discus. Typically made from gray or red clay. May also be black-glazed or painted. Approximate date: 600 B.C.E.-1774 C.E.

10. Smoking Pipes —Early forms are typically short and rounded. Later forms are typically decorated and sometimes ( print page 73285) stamped. Approximate date: 600 B.C.E.-1774 C.E.

11. Items of Personal Adornment —Includes, but not limited to, beads and pendants. May be plain, glazed, painted, and/or engraved. Some beads and pendants have a zoomorphic form. Beads and pendants of Egyptian faience (sintered quartz) are typically light blue and may retain traces of glaze. Forms in this material include, but are not limited to, scarabs, Bes, Horus-Harpocrates, and other Hellenized Egyptian deities, as well as lions. Approximate date: 3500 B.C.E.-1774 C.E.

12. Games and Toys —Includes, but is not limited to, gaming pieces such as dice, chess pieces, painted eggs, and disc- or square-shaped tokens. Tokens may bear the impression of a coin on one side. Clay eggs may be plain or painted. Approximate date: 2500 B.C.E.-1774 C.E.

Including fragments of plaster used in architectural contexts from the Ancient Greek period and from the Kyivan Rus through Early Modern periods. May be painted, incised, or stamped. Approximate date: 650 B.C.E.-1774 C.E.

1. Plaques and Decorated Bones —Made from the bones of bulls, goats, mammoths, and other animals or from fossilized bone. The bone may be untreated, polished, painted, cut, incised, and/or engraved. Bone plaques may be decorated with linear and geometric incisions (such as coils), images, symbols (such as tamgas) and/or inscriptions. Approximate date: 1.4 million years ago-1774 C.E.

2. Figurines —Decoration includes crosses; humans; animals, particularly camels, ibex, and snakes; geometric and/or floral designs; and other designs; includes fragments. Painted on wood, stone, and plaster. May be on domestic or public walls or tombs. Approximate dates: 1200 B.C. to 1773 C.E.

3. Miniature Vessels and Boxes —Including, but not limited to, pyxides and their lids and narrow boxes for needles. Often bear engraved decorations. Approximate date: 1000 B.C.E.-1650 C.E.

4. Tools —Including, but not limited to, harpoons, needles, coils, awls, knife- and sickle-handles, miniature spoons, and writing implements (styli). Sizes vary, but typically range from 2 to 10 cm in length. Handles may be sculpted. Approximate date: 1 million years ago-1774 C.E.

5. Musical Instruments —Including parts of wind instruments such as the aulos, syrinx, syringa, and pan flute, and parts of stringed instruments such as the chelys or lyre, made from tortoiseshell. Approximate date: 650 B.C.E.-1300 C.E.

6. Horse and Warrior's Equipment —Including, but not limited to, bone psalia (bit and cheek-pieces), whip handles, plaques for maces, bows, and quivers, and arrowheads. Approximate date: 2500 B.C.E.-1300 C.E.

7. Items of Personal Adornment —Including, but not limited to, pins, bracelets, beads, rings, buckles, buttons, combs, furniture inlays, incrustations, box inlays, crosses, mirror handles, pommels, and powder containers. Combs may have engraved decoration, typically in circular form, and may be double-sided. Pommels are often carved as figurines. Amulets are often made of animal teeth and rings of tubular bones. Engraved pieces are commonly decorated with ornaments, marks, signs, and more. Plaques applied to decorate furniture, coffins, chests, and small boxes may bear elaborate reliefs. Buckles, buttons, and other accessories frequently feature engraved designs, images, and sometimes graffiti or carvings. Mirror handles and pins of the Ancient Greek and Roman periods may bear figurative carvings. Crosses and their inlay details were often made of bone, either engraved or carved. Trifold bone containers, approximately 10 cm in height, are interpreted as powder containers. They date to the Late Medieval to Early Modern periods and are often decorated with engravings. Approximate date: 1 million years ago-1774 C.E.

8. Games —Including gaming pieces such as dice, knucklebones, simple chess pieces, and other types. Knucklebones often have a variety of engraved marks on them. Chess pieces often have one flat side and a spherical or anthropomorphic shape; some may have a polychrome decoration. Approximate date: 650 B.C.E.-1774 C.E.

1. Architectural Elements —Including, but not limited to, elements of towers, wells, churches, dwellings, and fences, particularly from the Medieval period. Carved wooden house decorations are found in the Medieval and Early Modern periods. Large elements may reach over 2 m, while carved elements may be smaller. Approximate date: 6000 B.C.E.-1774 C.E.

2. Vehicle Elements —Including, but not limited to, part of cartwheels, chariots, and boats. Cartwheels and fragments thereof, in both solid and spoked forms, may be found in Bronze Age burials. Includes elements of Ancient Greek and Roman period chariots. Boats and parts thereof from the Medieval period were sometimes used as coffins. Approximate date: 2500 B.C.E.-1774 C.E.

3. Furniture and Coffin Elements —Including, but not limited to, parts of tables, tripods, thrones, chairs, and klines (beds), sometimes carved with sculptural details. Carved and inlaid furniture is particularly common in the Medieval and Early Modern periods. Approximate date: 650 B.C.E.-1774 C.E.

4. Vessels —Including, but not limited to, Scythian-period cups and trays, which are sometimes set with precious metal plaques, and Medieval-period plates, which may be engraved. Also includes barrels from the Medieval and Early Modern periods. Approximate date: 1000 B.C.E.-1774 C.E.

5. Tools and Weapons —Including, but not limited to, distaffs, knife handles, quivers, and weaving combs. Approximate date: 1000 B.C.E.-1774 C.E.

6. Crosses and Icons —Including both large ceremonial and smaller personal crosses or carved wooden inlays for crosses. Crosses from the Medieval period and later are often made of cypress. Ceremonial crosses may reach up to 1 m, while personal crosses range from 1 to 15 cm in height. Icons are typically made of from one to three panels of coniferous or deciduous wood that have been joined together, painted, and finished with transparent varnish. Painted images include single, frontally depicted, full-length or half-length figures of Christ, the Virgin Mary, or saints such as Nicholas, Theodore Stratelates, or others, or religious scenes with two to three figures shown frontally or in three-quarters view, such as the Annunciation, Presentation, Descent into Hell, and others. Icons range in size from 20 cm to 2 or 3 m. Approximate date: 300-1774 C.E.

7. Musical Instruments —Including, but not limited to, stringed instruments, wind instruments, and percussion instruments. Beck-flutes are typical of the Medieval period. Approximate date: 3000 B.C.E.-1774 C.E.

8. Objects of Ceremonial and Daily Use —Including, but not limited to, wooden and bark shoes, lids from Ancient Greek-type mirrors, chests, caskets, games-such as simple chess pieces-and game boards. Also includes inscriptions in various scripts and languages on wooden plaques, birchbark, and paper. Chests may be painted or engraved and range in size from 5 to 50 cm. Approximate date: 2000 B.C.E.-1774 C.E.

9. Leather Objects —Including, but not limited to, tokens, elements of dress ( print page 73286) such as shoes and belts, saddle elements, quivers, and casket elements. Approximate date: 1000 B.C.E.-1774 C.E.

10. Textiles —Textiles and textile fragments are attested beginning in the Bronze Age and particularly in the Scythian period. May have floral ornaments in gold thread. Approximate date: 2500 B.C.E.-1774 C.E.

11. Amber Objects —Including, but not limited to, sculptures or figurines, usually schematic in style, dating particularly to the Copper and Bronze Ages and the Kyivan Rus period. Also includes jewelry and adornments such as beads, pendants, and inlays. Approximate date: 4000 B.C.E.-1240 C.E.

1. Items of Personal Adornment —Including, but not limited to, intaglios (also called gems), plain jewelry inlays, beads, rings, and bracelets. Intaglios are of various colors, but most commonly red or white. They have one flat surface with an engraved image, such as mythological figures and symbols. Inlays were most commonly made for rings, seals, and earrings. Beads, rings, and bracelets were made in a variety of colors, including red, blue, and yellow. Approximate date: 1000 B.C.E.-1774 C.E.

2. Vessels —Including both thicker, colored glass and transparent glass. Early vessel shapes include, but are not limited to, aryballoi (globular flasks). Thin transparent glass vessels, often with colored waves, are found beginning in the Roman period. Approximate date: 700 B.C.E.-1774 C.E.

3. Games —Including, but not limited to, dice and simple chess pieces. Chess pieces may be spherical or anthropomorphic in form; they are usually made of white, green, and brown glass and may be polychromatic. Approximate date: 700 B.C.E.-1300 C.E.

4. Mosaics —Glass tesserae were used for mosaics decorating floors, walls, and ceilings of Christian temples, as well as icons. Mosaic tesserae are around 1-2 cm and appear in various colors, including gold and blue. May be cobalt glass. Approximate date: 400-1300 C.E.

Including human remains and fragments of human remains, such as skeletal remains, soft tissue, and ash from the human body that may be preserved in burials, reliquaries, ossuaries, and other contexts. Bronze Age remains may include elongated skulls and mummified remains. Also includes Bronze Age skulls that have been painted and/or modeled, pierced, or given other decorations, as well as bones painted with red ochre or other materials. Approximate date: 1.4 million years ago-1774 C.E.

Ethnological material includes the following categories: ethnological religious and ritual objects, and objects related to funerary rites and burials dating from c. 200 to 1917 C.E.; ethnological manuscripts, written documents, and early prints dating from c. 900 to 1917 C.E.; ethnological architectural elements dating from c. 200 to 1917 C.E.; and ethnological paintings, military material, and traditional folk clothing and textiles dating from c. 1700 to 1917 C.E.

A. Religious and Ritual Objects, and Objects Related to Funerary Rites and Burials —Religious and ritual objects include moveable objects typically used in Ukrainian communal religious and ceremonial settings in all materials, as well as objects related to funerary rites and burials. Primarily in stone, wood, ceramic, metal, hand mixed paints, and textiles. Approximate date: c. 200-1917 C.E.

1. Sculptures —Including stone icons, relief plates, facade reliefs on religious structures, large free-standing sculpture found in both exterior and interior religious settings, small decorative sculptures, roadside crosses or figures, baptismal fonts (sometimes lotus-shaped), altars, lamps, and candlesticks. Primary materials include local stone (pink or blue slate or sandstone), white limestone, and imported materials such as jasper, steatite, alabaster, or wood. Stone icons are small stone plates (5-25 cm) depicting Christ, the Virgin Mary, Nicholas, and other religious figures. Reliefs often feature religious and narrative images such as a warrior fighting a lion, two saintly warriors on horseback, nativity scenes (vertep), and others.

2. Memorial Objects —Including sarcophagi, epitaph plaques, and tombstones, such as Jewish matzevah, Crimean Tatar mezartash and bashtash (gravestones bearing the name, place, and dates of birth and death), grave crosses and sculptures, made of stone, marble, slate, and other materials. Objects are often adorned with intricate carvings (floral, human, and zoomorphic motifs) and inscriptions.

3. Ritual Processional and Altar Objects —Includes wooden and stone icons of various sizes. Icons are a type of religious image carved from rectangular or round stone plates (usually pink or blue slate or sandstone, 5-25 cm) or painted on wood panels, depicting single saints (Christ, the Virgin Mary, Nicholas, Theodore Stratelates, etc.) frontally in either full-length or half-length, or religious scenes with two to three figures (Annunciation, Presentation, Descent into Hell, etc.) shown frontally or in three-quarter view. Intended for private use and close viewing. Wooden icons are made of one to three coniferous or deciduous wooden panels, joined together, prepared, covered with tempera paint (pigments ground in egg yolk), and finished with a transparent varnish. May be used in processions, altars, iconostases, or be free-standing. Size usually ranges from 20 cm to 2-3 m.

This category also includes ritual and ceremonial vessels, such as donation bowls, jugs and pitchers for holy water, Easter baskets (paskivnyk), vessels used in wedding ceremonies (lembyk, perepiytsia), Jewish seder plates, and Hanukkah menorah. Lembyk drinking vessels often take human or animal forms. Jewish objects are frequently glazed and decorated with flowers, birds, and animal motifs. The category also includes tabernacles (kivot; sometimes resembling miniature architecture), seven-branched candlesticks, reliquaries, icon cases (kiot), processional icons (feretron), altar crosses, backdrop crosses, hand-held crosses used in benedictions, collection boxes (skarbnychka), and processional staffs (pateritsa, bakulus, pastoral). These objects frequently bear relief carvings, gilding, and symbolic ornamentation. Metal liturgical and ceremonial objects include chests or arks, tabernacles, reliquaries, small portable arks (pyxes), royal doors, metal covers for icon-painted surfaces (shata, ryza, oklad), book covers, fans on long handles (rypida), large hanging chandeliers (panikadylo), wall-mounted lighting fixtures that reflect candlelight in synagogues (reflectors), Hanukkah lamps, thuribles (kadylo), ritual boxes for storing Sabbath spices (bsamim), Torah crowns, Torah shields (tas), small boxes for storing Torah scrolls (mezuzah), Torah pointers, chalices (potyr), Eucharistic plates (diskoi), metal arches to cover diskoi (stars), double-edged knives with short triangular blades (spears), clergymen's headwear (miters), cross-reliquaries (encolpion), pectoral crosses, clergymen's round-form insignia (panagia), and pastoral staffs (crosiers). These items were often made of bronze, copper, gold, or silver, adorned with precious stones, pearls, and enamels, and featured intricate decorations depicting religious scenes. Ceramic altar crosses sometimes imitate those of wood or metal, and sometimes adorn church ( print page 73287) facades. This category also includes fragments of objects of the above-mentioned types.

4. Church Furniture and Fixtures —Including iconostases and altars, as well as their decorative frames, columns, cartouches, consoles, cornices, royal doors, and deacon's doors. Component parts when installed in the context of churches may form multi-tiered ensembles and serve as the framing structures for painted icons. These are typically carved from softwood or hardwood, decorated with chalk gesso, gilding, silver gilding (vermeil), and colored lacquers. Stylized grapevines are the most frequently occurring decorative motif. This category also includes altar tables (prestol), protheses (proskomydiynik), canopies (kivoriy), anoloys (analoy), tetrapods (tetrapod), golgothas, tombs of the Lord, ambos (pulpits), thrones (synthronon), monastic benches (stasidias), pews, large chandeliers, and candelabrums of varying sizes. Most frequently carved from wood and embellished to a greater or lesser degree with reliefs, painting, and gilding.

5. Religious Fabrics —Including Christian processional banners (horuhva), various liturgical service cloths, katasarka indittion, ilyton, antimension fabrics made with woodcut or copperplate printing techniques with relics sewn inside, antymins depicting the Burial of Christ, pokrivets, chalice and diskos coverings (vozdukh, plaat, pelena), decorative curtains such as those for the royal doors of iconostases (Katapetasmas), or those for covering a Torah ark (parokhet), decorative elements for synagogue curtains (lambrequin kaporets). Materials include velvet or homespun cloth, sometimes bearing embroidered or appliqué icons, ornamental motifs, and religious scenes or symbolism, and knotted wool. Religious garments include vestments for priests, deacons, and bishops made of white, gold-embroidered fabrics, miters, kippahs, yarmulkes, and prayer shawls (tallits) made of wool, cotton, silk, or linen.

B. Architectural Elements —Objects in this category were produced by skilled craftspeople in a nonindustrial society, with materials often hand-carved and/or made from joined wood, modeled, formed, or painted. Architectural elements are found in stone, wood, ceramic, plaster or stucco, and other painted media used to decorate civic and religious architecture. Approximate date: 200-1917 C.E.

1. Stone —Including capitals, balustrades and parapets, vases, lanterns, brackets or consoles, facade reliefs, mascarons (sculpted faces), and cartouches (scrolls, coats of arms).

2. Wood —Including carved beams (svolok), carved doorways, balustrades, horse-head brackets (konyk), carved or painted window frames (lyshtvy), and shutters. May be adorned with symbolic carvings reflecting traditional Ukrainian styles.

3. Ceramic and Terracotta —Including exterior decorative elements, pipes, roof coverings, chimneys, and echea (acoustic jars). More rarely, may include ceramic cupolas with crosses, capitals, bell towers, and other exterior decorations. Interior architectural elements include ceramic icon cases, altars, and iconostases, frequently decorated with techniques such as relief appliqué, stamping, engraving, and colorful glazes or underglaze painting, tiles for wall and floor cladding, and stoves. Thick wall tiles, especially from the Lviv and Chernihiv regions, feature underglaze painting, imitating Dutch tiles. Hutsul folk tiles depict everyday or military scenes, or vegetal and animal motifs rendered in dark outlines and underglaze painting (engobes) in green, yellow, and brown. Ichnia tiles bear white surfaces and bird motifs.

4. Metal —Including bells and crosses on domes. Bells are hollow, pear-shaped, with bronze, brass, gold, or silver alloy clappers. These are often decorated with relief friezes, figures of saints, dedicatory inscriptions, and coats of arms. Crosses vary in form and may be adorned with geometric patterns ( e.g., wavy, bent rods), plant motifs, or smaller crosses.

5. Glass —Including monumental mosaics and stained glass, colored stained glass found in domestic and religious settings, and small colored glass fragments (smalta) used in mosaics that bear ornamental, figural, or landscape scenes.

C. Manuscripts, Written Documents, and Early Prints —Manuscripts, portions of manuscripts, and works on paper include handmade, handwritten, hand-illustrated and/or illuminated sheets, bound volumes and their bindings, manuscript books, and non-industrial print media. Includes fragments. Approximate date: 900-1917 C.E.

Types include charters, bulls, autographs, and other paper artifacts; liturgical manuscripts, illuminated manuscripts, early printed books adorned with fabric, leather, and metal covers, and parchment. Early pre-industrial centers of printing include Lviv, Ostrih, Derman, Pochaiv, and Kyiv. Prints include woodcuts, engravings, etchings, and lithographs. These may feature images of Jesus Christ, the Virgin Mary, saints, and religious feast scenes, sometimes illuminated with watercolors.

D. Ethnological Paintings —Paintings were made by artists who progressed from traditional icon painters, using similar techniques, hand mixing paints, and trained in workshops as apprentices to masters of the craft. Approximate date: 1700-1917 C.E.

1. Icon Paintings on Glass —A popular form of folk art especially in the nineteenth and early twentieth centuries, Hutsulshchyna, Bukovyna, and Pokuttya ethnographic regions; notable for their bright colors and rich floral ornamentation.

2. Paper Cutouts —This category also includes paper cutouts, another type of folk art. These objects are created by cutting forms from paper or thin cardboard and were used in interior decoration mainly in the nineteenth and early twentieth centuries.

E. Military Material —Military material was made by skilled metalworkers and armorers, traditionally working out of a small shop or house—or as employed by an imperial authority—using the same hand-striking process to produce weapons and armor. Approximate date: 1700-1917 C.E. Including standards (bunchuk), maces (pernach), including but not limited to those with metal spikes (buzdyhan), and those with wooden or metal handles, sometimes decorated with precious stones, horsehair, and gold spherical ornaments; sabers, axes (bartka), knives, battle hammers bearing a sharp iron hook attached to a thin handle, pistols, and rifles. Sabers may be decorated with valuable materials such as ivory and gold, and intricate designs. Hutsul bartkas (shepherd's axes) consist of long wooden handles adorned with geometric patterns using embossing, engraving, and inlay techniques. The Crimean Tatars' axe (ay balta) consists of heavily-ornamented, crescent-shaped blades. Pistols and rifles, especially ceremonial ones, feature detailed decorations with engraving, niello, and inlays.

F. Traditional Folk Clothing and Textiles —Traditional folk clothing and textiles were handwoven and sewn by members of guilds, operating in small businesses run out of weavers' homes. Approximate date: 1700-1917 C.E.

1. Traditional Textiles —Including woven or knotted woolen carpets with floral motifs, tapestries, gold-woven products that adorned the walls of magnates' rooms (makata), pile carpets made on vertical looms (kots), rectangular fabrics made of coarse wool, initially woven on a horizontal loom as smooth double-sided carpets (lizhnyk), ( print page 73288) fabric for covering beds, woven on a horizontal loom with plain or twill weave from hemp or linen threads (vereta), and other domestic textiles, embroidered (rushnyks) or bearing hand-printed ornamental motifs.

2. Folk Clothing —Including items from the Hutsul regions and Carpathian regions such as fur coats made from sable, lynx, and fox fur (shuba), protective vests with sewn-on metal plates (kuyak), sleeveless leather cloaks made from fur and lined with satin (vilchura), fur hats (kuchma), wide belts with up to six buckles with rich metal décor (cheres), small bags (tabivka), and narrow bags for arrows (sahaidak, kolchan). Other garments include embroidered shirts, waist garments, wide-cut pants, narrow trousers, upper garments, jackets, belts, aprons, (all of which may be made of woolen fabric, sometimes dyed red or black), sometimes richly embroidered or brocaded. Embroidered fabrics bear regionally unique decorative and color schemes.

a. Garments of the Cossack type are sewn from long panels (kaftans, zhupans). Items may be made of red, gold-woven, gray, or blue cloth, or silk, with velvet, brocade, or fur details. Outer garments include coats made of sheepskin (kobenyak), cloth coats lined with cotton with fur (bekesha), or loose-cut coats with slit elbow sleeves (delia). Wide belts are made of gold-woven fabric, often highly embellished.

b. Crimean Tatar costume includes wide trousers (don, duman), wide-cut shirts, striped silk dress-coats, linen shirts (colmek-keten), vests (bagr-elek), jackets (marka), kamzols, eastern-style coats (anteri, havtani), sleeveless leather coats, and various types of trousers. These garments are often decorated with braids, cords, lace, and unique handmade buttons.

3. Leather Footwear —Including footwear made of thick cow or pig rawhide (postoly) or Moroccan leather in various colors (sapyantsi), low-heeled women's shoes (cherevyky), and Crimean Tatar soft-soled boots of yellow or black leather (mest).

This regulation involves a foreign affairs function of the United States and is, therefore, being made without notice or public procedure under 5 U.S.C. 553(a)(1) . For the same reason, a delayed effective date is not required under 5 U.S.C. 553(d)(3) .

Executive Orders 12866 (Regulatory Planning and Review), as amended by Executive Order 14094 (Modernizing Regulatory Review), and 13563 (Improving Regulation and Regulatory Review) direct agencies to assess the costs and benefits of available regulatory alternatives and, if regulation is necessary, to select regulatory approaches that maximize net benefits (including potential economic, environmental, public health and safety effects, distributive impacts, and equity). Executive Order 13563 emphasizes the importance of quantifying costs and benefits, reducing costs, harmonizing rules, and promoting flexibility. CBP has determined that this document is not a regulation or rule subject to the provisions of Executive Orders 12866 and 13563 because it pertains to a foreign affairs function of the United States, as described above, and therefore is specifically exempted by section 3(d)(2) of Executive Order 12866 and, by extension, Executive Order 13563 .

The Regulatory Flexibility Act ( 5 U.S.C. 601 et seq. ), as amended by the Small Business Regulatory Enforcement Fairness Act of 1996, requires an agency to prepare and make available to the public a regulatory flexibility analysis that describes the effect of a proposed rule on small entities ( i.e., small businesses, small organizations, and small governmental jurisdictions) when the agency is required to publish a general notice of proposed rulemaking for a rule. Since a general notice of proposed rulemaking is not necessary for this rule, CBP is not required to prepare a regulatory flexibility analysis for this rule.

This regulation is being issued in accordance with 19 CFR 0.1(a)(1) pertaining to the Secretary of the Treasury's authority (or that of the Secretary's delegate) to approve regulations related to customs revenue functions.

Troy A. Miller, the Senior Official Performing the Duties of the Commissioner, having reviewed and approved this document, has delegated the authority to electronically sign this document to the Director (or Acting Director, if applicable) of the Regulations and Disclosure Law Division for CBP, for purposes of publication in the Federal Register .

• Cultural property
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• Reporting and recordkeeping requirements

For the reasons set forth above, part 12 of title 19 of the Code of Federal Regulations ( 19 CFR part 12 ) is amended as set forth below:

1. The general authority citation for part 12 and the specific authority citation for § 12.104g continue to read as follows:

Authority: 5 U.S.C. 301 ; 19 U.S.C. 66 , 1202 (General Note 3(i), Harmonized Tariff Schedule of the United States (HTSUS)), 1624.

Sections § 12.104 through 12.104i also issued under 19 U.S.C. 2612 ;

2. In § 12.104g, the table in paragraph (b) is amended by adding Ukraine to the list in alphabetical order to read as follows:

State party Cultural property Decision No.   *         *         *         *         *         *         * Ukraine Archaeological material of Ukraine ranging in date from approximately the Paleolithic period (c. 1.4 million years ago) through 1774 C.E., and ethnological material of Ukraine ranging in date from approximately 200 C.E. to 1917 C.E CBP Dec. 24-16.   *         *         *         *         *         *         *

Robert F. Altneu,

Director, Regulations & Disclosure Law Division, Regulations & Rulings, Office of Trade U.S. Customs and Border Protection.

Aviva R. Aron-Dine

Acting Assistant Secretary of the Treasury for Tax Policy.

[ FR Doc. 2024-20385 Filed 9-9-24; 8:45 am]

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