vernier caliper experiment theory

Calipers, Micrometers & Vernier Scales ( OCR A Level Physics )

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Calipers, Micrometers & Vernier Scales

Micrometer screw gauge.

• For example, the diameter of a copper wire
• It has a resolution of 0.01 mm
• The main scale - this is on the sleeve (sometimes called the barrel)
• The thimble scale - this is a rotating scale on the thimble

Components of a micrometer

• This should be tight enough so the object does not fall out but not so tight that is deformed
• Never tighten the spindle using the barrel , only using the ratchet . This will reduce the chances of overtightening and zero errors
• This should always be recorded to 2 decimal places (eg. 1.40 mm not just 1.4 mm)

The micrometer reading is read when the thimble scale aligns with the main scale

Vernier Calipers

• They can also be used to measure diameters and thicknesses, just like the micrometer
• However, they can also measure the length of small objects such as a screw or the depth of a hole
• Vernier calipers generally have a resolution of 0.1 mm , however, some are as small as 0.02 mm - 0.05 mm
• The main scale
• The vernier scale
• The sliding vernier scale will follow this and can be held in place using the locking screw

• This should always be recorded to at least 1 decimal place (eg. 12.1 mm not just 12 mm)

The vernier caliper reading is read when the vernier scale aligns with the main scale

• In general, the micrometer has a smaller measuring range than a vernier caliper
• However, the micrometer has a better accuracy (due to better resolution)
• Therefore, to take many measurements, a caliper would be easier to use

Make sure you're comfortable with reading from a micrometer or vernier caliper scale. This will be expected not just in your practical endorsement, but also in written practical questions.

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Physics practicals class xi, measurement of length :, vernier calipers (principle & description), our objective.

• To know the use of the Vernier Calipers.
• To measure the diameter of a small spherical / cylindrical body.
• To measure the length, width and height of the given rectangular block.
• To measure the internal diameter and depth of a given beaker/calorimeter and hence find its volume.

What is a Vernier Caliper?

A calliper is a device used to measure the distance between two opposing sides of an object. It can be as simple as a compass with inward or outward-facing points. First the tips of the calliper are adjusted to fit across the points to be measured and the calliper is then removed and the distance between the tips is measured using a ruler. The modern Vernier calliper was invented by Joseph R. Brown in 1851. It was the first practical tool for exact measurements that could be sold at an affordable price to ordinary machinists.   The Vernier Calliper consists of a main scale fitted with a jaw at one end. Another jaw, containing the vernier scale, moves over the main scale. When the two jaws are in contact, the zero of the main scale and the zero of the Vernier scale should coincide. If both the zeros do not coincide, there will be a positive or negative zero error.

Parts of a Vernier Caliper

1.main scale.

The main scale consists of a steel metallic strip graduated in centimeters at one edge and in inches at the other edge . It carries the inner and outer measuring jaws. When the two jaws are in contact, the zero of the main scale and the zero of the Vernier scale should coincide. If both the zeros do not coincide, there will be a positive or negative zero error.

2. Vernier Scale

A vernier scale  slides on the strip. It can be fixed in any position by the retainer. On the Vernier scale, 0.9 cm is divided into ten equal parts.

3. Outer Measuring Jaws

The outer measuring jaws helps to take the outer dimension of an object

4. Inner Measuring Jaws

The inner measuring jaws helps to take the inner dimension of an object.

5. Retainer

The retainer helps to retain the object within the jaws of the Vernier calipers.

6. Depth Measuring Prong

The depth measuring prong helps to measure the depth of an object.

Least Count

Calculating the Reading

Finding the Volumes

Volume of a beaker / calorimeter.

Volume of a Sphere

Volume of a Rectangular Block

Learning Outcomes

• Students get to know the use of vernier calipers.
• Students know what is the Least count of vernier callipers.

Viva-Voce [Vernier Caliper Basics]

For: Physics Class 11

Q.1: What is the vernier callipers?

Ans. It is the simple instrument by which length of an object can be measured accurately up to one-tenth of a millimetre or one-hundredth of a centimetre.

Q.2: What is the use of Vernier Scale?

Ans. To increase the accuracy of the main scale.

Q.3: What is the least count (L.C.)?

Ans. The minimum measurement that can be taken by an instrument.  

Q.4: What is the least count of 

(a) meter scale (b) Stop Watch (c) Vernier Calliper ?

Ans. The least count of:

(a) meter scale = 0.1 cm or 1 mm.

(b) stopwatch = 0.01 sec or 1/100 sec. or according to the stopwatch.

(c) vernier scale = 0.01 cm or 0.1 mm  

Q.5: What are the units of the vernier scale?

Ans. Vernier has no units of its own.

Q.6: What is the difference in the measurement of one smaller division on the main scale (M.S.) and that of vernier scale (V.S.)? Ans. (1 smallest Div. on M.S.) – (1 smallest Div. on V.S) = 0.1 – 0.09 = 0.01 cm = Least count.

Q.7: How the L.C. of a vernier is determined?

Ans. By using the relation: L.C. = (the Smallest division on Main Scale ) / (Total number of divisions on Vernier Scale) Q.8: Will the accuracy of a vernier will increase or decrease if 20 divisions are made in the same length? Ans. The accuracy will increase since the L.C. will decrease i.e. Accuracy α = 1 / Least count

Q.9: Which one is smaller M.S. div. or V.S. div.?

Ans. V.S. division.

Q.10: 1 division on V.S. = _____ cm.

Ans. 0.09 cm. 10 div. on V.S. = 0.9 cm 1 div. on V.S. = 0.9/10 cm = 0.09 cm  

Q.11: What are the functions of (a) Sliding strip (b) Upper jaws ?

Ans. (a) For measuring depth. (b) For measuring the inner diameter.

Q.12: What is meant by zero error (Z.E.)?

Ans. The error which arises when zeros of M.S. and V.S. do not coincide upon joining the two jaws.

Q.13: When Z.E. is positive?

Ans. The Z.E. is positive when the zero of V.S. is to the right of the zero of M.S.

Q.14: How we find the corrected reading?

Ans. Corrected reading = Meaning reading – ( + Z.E.)  

Q.15: Do you know any use of vernier scale?

Ans. It is used in the spectrometer, barometer, travelling microscope, etc.  

Q.16: What are the significant figures?

Ans. Numbers 0, 1, 2, 3, ……. are called significant figures when they occur. The zero is not a significant figure if it is at the extreme left or extreme right of a number, e.g. 1.02 has three significant figures, but 1.20 has two significant figures.  

Q.17: What is meant by the degree of accuracy?

Ans. It is the measurement estimated by the number of significant figures in the result.  

Q.18: Why is the vernier callipers so-called?

Ans. A French mathematician named Pierre Vernier invented it and it is named after him.  

Q.19: How does temperature affect the length of a cylinder?

Ans. The length of a cylinder increases with the increase of temperature and decreases with the decrease of temperature.  

Q.20: What is the unit of volume?

Ans. In the MKS system, the unit of volume is m3. In the CGS system, the unit of volume is cm3. In the FPS system, the unit of volume is ft3.

Vernier Caliper: Parts, Principle, Formula, Least Count, Range, Resolution, Applications, Advantages, and Disadvantages [PDF]

Vernier Caliper is used to measure the dimensions of the given specimen like diameter (Outer Dia and Inner dia), length and depth, etc very accurately that's the reason it is also called as Precision measuring Instrument.

In the last class, we had discussed the concepts on Angular Measurements &  Linear Measurements and in today's paper, we will discuss Vernier Caliper in detail.

The Invention of Vernier Caliper:

They usually show either metric or imperial measurements and in some of the cases, it measures both. 

Parts of Vernier Caliper:

Working principle of vernier caliper:.

The Vernier Caliper is a Precision Measuring Instrument which is used to measure length, depth, diameter of the given specimen.

The detailed explanation of Vernier Caliper is as follows.

How to Measure the Depth of the given specimen?

The measuring depth probe is used to measure the depth of the given specimen.

How can you check any Measurement?

Formula of vernier caliper:.

Measurement= M.S.R + (V.S.R*L.C)

Least Count of Vernier Caliper:

Least Count (L.C)= 1 MSD - 1VSD

How to Read Vernier Caliper in mm?

Calculation of main scale division:.

If the zeroth division of the vernier scale is coincided with (some number) on the Main scale(consider it as 10) then 10mm is the Main scale Reading(M.S.R).

M.S.R = 10mm.

Calculation of Vernier Scale Division:

Therefore,upto (0-10),it is 50 divisons.So,take the Vernier Scale Divison is 50.

Calculation of Least Count:

As we know the formula of Least Count (L.C)= 1 MSD - 1VSD

1 VSD= (49/50) MSD = 0.98 MSD

Least Count (L.C) =1 MSD - 0.98 MSD = 0.02 mm

Measurement= M.S.R + (V.S.R*L.C) = 10+ (50*0.02) = 10+1 = 11mm

Here is a Video on How You Can Measure on Vernier Caliper:

Range of vernier caliper:.

Mostly, vernier calipers have a range of 6 inches i.e. 300mm.

Resolution of Vernier Caliper:

A Caliper's resolution is indicated at the end of the vernier scale and it is the smallest distance that the caliper can measure. 

The resolution of Vernier Caliper are:

What is the difference between a dial caliper and a Vernier caliper?

Dial Caliper or Digital Vernier: Direct Reading (Perfect Reading) will be displayed.

Instrument error or Tolerance:

Low tolerance measuring tools provide very accurate results with a small margin for error and Vernier calipers is one of them.

Applications of Vernier Caliper:

Advantages of vernier caliper:, accuracy and precision:, versatility:.

It can have the ability to measure any type of dimensions of a component , for example:

Durability:

As the Vernier is made up of Stainless steel(Anti-Corrosive material), it can sustain for a long period of time and thereby its durability will be high.

Ruler or Measuring Tapes:

Disadvantages of vernier caliper:, possibility of errors:.

It needs much concentration to read a dimension of the component else there is a possibility of error.

Accurate Tools:

Magnifying glass or eyesight:.

Good Magnifying glass is required during taking the measurement of any component if your eyesight is not proper else it results in taking the errors as the original measurement.

This is the detailed explanation of Vernier Caliper along with its Formula, Construction, Experiment. If you like this article, Then share it with all your friends.

READ MORE FROM US Sine bar – Principle, Formula, Construction, Limitations&Factors 3 Types of Marking Out Tools used in Fitting – Engineering Workshop

References [External Links]:

Media credits:, about mohammed shafi, continue reading, notes on limits fits and tolerances [pdf], types of angular measuring instruments [pdf], linear measurements: definition, standards, methods & instruments [pdf], types of measuring instruments and their uses in engineering workshop [pdf], sine bar: working principle, construction, formula, limitations & viva questions [pdf], types of fits: clearance fit, transition fit, interference fit [pdf].

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Experiment 1 - Vernier Calipers

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Vernier Calliper

What is vernier calliper.

A vernier calliper is defined as a measuring device that is used for the measurement of linear dimensions. It is also used for the measurement of diameters of round objects with the help of the measuring jaws.

Vernier Calliper Diagram

French mathematician Pierre Vernier invented the vernier scale in 1631. The main use of the vernier calliper over the main scale is to get an accurate and precise measurement.

Least Count of Vernier Calliper

The least count of vernier callipers is also known as the vernier constant. It is defined as the difference between one main scale division and one vernier scale division.

It is mathematically given as:

When there are n divisions on the vernier scale, which coincides with (n-1) division on the main scale, then the least count of vernier calliper is:

Therefore, the least count of vernier calliper is 0.1 mm.

• VC is the vernier constant
• MSD is the main scale division
• VSD is the vernier scale division
• LC is the least count

Read More: Measurement, Accuracy and Precision

What Is Zero Error?

Zero error is defined as the condition in which the measuring device registers a reading when there should not be any reading.

The zero error of the vernier calliper is calculated as:

Actual reading = Main scale + Vernier scale – (Zero error)

There are two types of zero error:

• Positive zero error: When the jaws of the vernier calliper are closed, the reading is positive and away from the actual reading of 0.00 mm. For instance, if the reading is 0.08 mm, then the zero error is +0.08 mm.
• Negative zero error: When the jaws of the vernier calliper are closed, the reading is negative and away from the actual reading of 0.00 mm. For instance, if the reading is 0.10 mm, then the zero error is -0.10 mm.

Solved Examples

If the jaws of the vernier callipers are in contact with each other, then determine the zero error of the vernier calliper if the VSD is 3.

The jaws of the vernier calliper are in contact with each other.

Therefore, the least count of the vernier calliper is given as:

LC = MSD – VSD

LC = 1 – (9/10) = 0.1 mm

The main scale reading, MSR = 0 mm

The vernier scale reading, VSR = 3

Zero error = MSR + VSR x LC

Zero error = 0 + 3 x 0.1 = 0.3 mm

1 mm marks are present on the main scale of the vernier scale. The total no.of divisions on the vernier scale are 20 which matches the 16 main scale divisions. Calculate the least count of this vernier scale.

One main scale division, MSD = 1 mm

20 vernier scale divisions, VSD = 16 main scale divisions, MSD

Therefore, 1 VSD = 16/20 MSD = 0.8 mm

The least count, LC = 1 MSD – 1 VSD = 1 – 0.8 = 0.2 mm

How to Read Vernier Calliper?

• The first step is to measure nothing through which we can check if the main and the vernier scales are aligned.
• When the main scale reading and the vernier scale reading are at zero, it means there is no zero error.
• Now, place a ball between the two jaws of the vernier scale.
• Look at the 0 mark on the vernier scale lining with the main scale.
• That gives the main scale reading.
• Next, look for the point on the vernier scale, which is aligned with the main scale, which gives the vernier scale reading.
• It is important to note that the readings will most of the time be in decimals.
• The number before the decimal point is the main scale reading, while the number after the decimal point is the vernier scale reading.

Read More: Errors in Measurement

It is a large scale that runs along the body of the vernier calliper. Depending on the usage, the reading on the main scale could be either in centimetres or millimetres. 1 mm is the lowest main scale division according to the SI units. The main scale is stationary.

Read More: SI units

Vernier Scale

This is the smaller scale attached to the main scale, moving along the main scale. The vernier scale’s movement depends on the jaws’ opening. The main function of the vernier scale is to provide accuracy to the main scale reading by dividing the reading into smaller increments. The vernier scale in a metric calliper can have divisions up to 50 increments, each of which measures 0.02 mm.

These jaws are considered one of the most prominent features of vernier calliper. One of the jaws is fixed and attached to the main scale. While the other jaw is movable and is attached to the vernier scale. These jaws are designed mainly to grip the objects firmly. The main function of the lower jaw is to measure the outer dimensions such as diameter, width and length.

These jaws are similar to the lower jaws but are smaller than, the lower jaws. These jaws are attached to the upper part of the vernier scale. One of the jaws is fixed, while the other jaw is movable. The main function of the upper jaw is to measure the inner dimensions of the objects. The jaws are opened until they touch the objects’ edges before taking the reading. The inside diameters of objects such as hollow pipes and jars can be measured using upper jaws.

The depths of the jars can be measured using the depth rod. It is a thin rod located at the end of the main scale. Using a depth rod for measuring is simple. The edge of the main scale is placed on the object’s top surface. Then the jaws are slowly opened. The opening of the jaws results in the extension of the depth rod. The jaws need to be opened until the depth rod reaches the bottom of the object.

Thumb Screw

This screw is located at the bottom of the vernier scale. The main function of the thumbscrew is to provide grip to the users so that the sliding of the jaws becomes easy.

The main use of the lock screw is to fix the position of the jaws once the object is firmly fixed between the jaws. This also makes it easy to take proper readings.

Applications of Vernier Callipers

• Medical usages
• Science labs
• Industries such as steel and aerospace
• Educational sectors

Read More: Uses of Vernier Calliper

The below video is a quick revision of what is vernier calliper and its parts

Frequently Asked Questions – FAQs

What is the principle of vernier calliper.

The vernier calliper’s principle is that the vernier scale’s graduations are of the length n division, which is equal to the n-1 division on the main scale. The number of divisions on the vernier scale, in general, is 10 divisions. Therefore, the number of divisions on the main scale is given as n-1 = 10 – 1 = 9, which is equal to 9 mm. Therefore, we can say that each division on the vernier scale is equal to 1/10 mm.

Why is the vernier calliper more accurate?

Vernier calliper is more accurate because it measures up to one-hundredth of a millimetre and one-thousandth of an inch.

What are the advantages of vernier calliper?

There are two main advantages of vernier calliper:

• The measurements provided by the vernier calliper are accurate and precise.
• It can be used for measuring both inner and outer surface dimensions.

What are the limitations of vernier calliper?

• The improper angle of vision might result in the noting of wrong reading.
• The least attentiveness might lead to the recording of the wrong reading.

How to read the depth using vernier calliper?

The following are the steps to be followed for measuring depth with a vernier calliper:

• Place the edge of the main scale on the brim of the beaker.
• Rotate the thumbscrew till the tip of the depth rod reaches the bottom of the beaker.
• Tighten the lock screw so the jaws are held firmly.
• Record the measured readings.

What are the types of vernier callipers?

There are three types of vernier callipers:

• Manual readout, which is the original vernier calliper
• Dial readout
• Digital readout

Stay tuned with BYJU’S to learn more about other measuring instruments.

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vernier caliper

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• Physics LibreTexts - Reading a Vernier
• University of Cape Town - Department of Physics - Using the Vernier Calipers and Micrometer Screw Gauge

vernier caliper , instrument for making very accurate linear measurements introduced in 1631 by Pierre Vernier of France. It uses two graduated scales: a main scale similar to that on a ruler and an especially graduated auxiliary scale, the vernier, that slides parallel to the main scale and enables readings to be made to a fraction of a division on the main scale. Vernier calipers are widely used in scientific laboratories and in manufacturing for quality control measurements.

In the figure , the vernier scale has 25 divisions, whereas the main scale has 24 divisions in the same length. This means that the divisions on the vernier scale are shorter than those on the main scale by 1 / 25 of a division on the main scale. In the figure, line 8 on the vernier coincides with line x on the main scale. To align lines 7 and y , the vernier would have to be moved to the left by 1 / 25 of a main-scale division; to align lines 6 and 40, the movement would be 2 / 25 , and so on. By similar reasoning, the 0 line on the vernier would have to be moved a distance equal to 8 / 25 of a main-scale division to align it with the 8.50 line (before the 40 line, therefore this is the 38.50 line) on the main scale. This means that in the position shown in the figure the 0 line is 8 / 25 of a main-scale division to the right of the 8.50 line. The reading of the vernier is therefore 30 + 8.50 + 0.08 = 38.58.

Vernier scales are also made with 10 divisions in the same length as 9 on the main scale; the technique of reading such a scale is similar to that described above. A vernier scale can be used to increase the accuracy of angular as well as linear measurements.

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All About Vernier Caliper’s History & Theory Description

What is a Vernier Caliper?  A vernier caliper is a caliper consisting of two pieces joined together with one being stationary while the other slides on top of it. The fixed part features a graduated scale while the sliding part has a vernier scale on it. It can also be described as two L-shaped frames joined together with the smaller one able to slide on top of the larger one. Both are graduated along their longer lengths and the dimensions of an object are obtained by measuring the distance between the edges of the shorter arms.

The Guy Who Invented Vernier Caliper 

French scientist Pierre Vernier(1580-1637) is credited with the invention of the Vernier Caliper which is also named after him. Born in 1580 in the city of Ornans in France, Pierre obtained his scientific education from his father and went on to become a mathematician and inventor. The King of Spain also chose him to be the captain and custodian of the castle at Ornans. Later he also served as the director of finance and the councilor of the county of Burgundy.

Theory of Vernier Caliper:

The Vernier Caliper is widely used to measure lengths precisely. It contains two graduated scales. A main scale which is graduated similar to a normal ruler and a Vernier scale which can slide along the main scale. The two scales contain a very small relative pitch difference which is responsible for the greater accuracy. If the relative pitch difference is 1/10 then the enhancement factor of any displacement is equal to the inverse of that number i.e 10.

The vernier caliper is mainly used for measuring diameters of objects, both internal and external. The technique for measurement is to first read the main scale to the nearest division. Then the vernier scale is used to measure the distance between the two main scale divisions which provides more accurate measurements.

The Vernier scale is designed in such a way that the distance between each division on the vernier scale is a fraction of that between the divisions on the main scale. Usually it is so that 10 small divisions on the vernier scale equal 9 small divisions of the main scale. This way when the zero points of both scales are coincident, the first mark on the vernier scale is one tenth behind the first mark on the main scale. Consequently the second mark is behind by 2/10 and so on. Only the tenth mark will coincide with the markings on the main scale since it is 10/10 i.e one whole unit behind the main scale and it would be coincident with the ninth mark on the main scale.

This is the principle behind the vernier caliper which means that for any distance the division on the vernier scale which coincides with the main scale provides us with the difference of that division with the main scale and allows us to measure distances in decimal points.

Vernier Caliper – Working, Calculation Of Least Count & Zero Error

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June 28, 2024

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility:

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New NOvA results add to mystery of neutrinos

by Tracy Marc, Fermi National Accelerator Laboratory

The international NOvA collaboration presented new results at the Neutrino 2024 conference in Milan, Italy, on June 17. The collaboration doubled their neutrino data since their previous release four years ago, including adding a new low-energy sample of electron neutrinos.

The new results are consistent with previous NOvA results, but with improved precision. The data favor the "normal" ordering of neutrino masses more strongly than before, but ambiguity remains around the neutrino's oscillation properties.

The latest NOvA data provide a very precise measurement of the bigger splitting between the squared neutrino masses and slightly favor the normal mass ordering. That precision on the mass splitting means that, when coupled with data from other experiments performed at nuclear reactors, the data favor the normal ordering at almost 7:1 odds.

This suggests that neutrinos adhere to the normal ordering, but physicists have not met the high threshold of certainty required to declare a discovery.

NOvA , short for NuMI Off-axis νe Appearance, is an experiment managed by the U.S. Department of Energy's Fermi National Accelerator Laboratory, located outside of Chicago.

Fermilab sends a beam of neutrinos 500 miles north to a 14,000-ton detector in Ash River, Minnesota. By measuring the neutrinos and their antimatter partners, antineutrinos, in both locations, physicists can study how these particles change their type as they travel, a phenomenon known as neutrino oscillation.

NOvA aims to learn more about the ordering of neutrino masses. Physicists know that there are three types of neutrinos with different masses, but they don't know the absolute mass, nor which is heaviest.

Theoretical models predict two possible mass orderings, normal or inverted. In the normal ordering, there are two light neutrinos and one heavier neutrino; in inverted, there is one light neutrino and two heavier ones.

"Getting additional information from reactor experiments enhances our knowledge of the mass ordering and gets us close to exciting territory," said Erika Catano-Mur, a postdoctoral research associate at William & Mary and co-convener of the analysis. "We almost have an answer to one of those big questions that we have in neutrino physics. But we're not there yet."

The solution to neutrino oscillation remains ambiguous in the new results. Physicists don't currently have enough data to disentangle two effects on the oscillation: mass ordering and a property called charge parity violation.

The collaboration observed a moderate amount of oscillation that could be explained in either mass ordering scenario with different amounts of CP violation, so they cannot tease apart the mass ordering and CP violation. However, the physicists were able to rule out specific combinations of the two properties.

"It really takes more than one measurement for us to learn everything we need to know," said Jeremy Wolcott, a postdoctoral fellow at Tufts University, one of NOvA's analysis coordinators and the speaker at the conference.

"NOvA is an important player in this because there are unique aspects to all of the various experiments that are trying to measure the same parameters," said Wolcott. "We're starting to see a picture come together, but it's murky. Having different measurements that all work together is really important."

The NOvA experiment started taking data in 2014 and will continue running through early 2027, during which time the collaboration hopes to double their antineutrino dataset. They also continue to implement analysis improvements to maximize the sensitivity of the experiment.

Their efforts are also paving the way for future experiments that will seek to contribute even more to solving the mysteries around neutrino properties.

"We want to make the most that we can out of the data," said Catano-Mur. "What we learn—not only from the results themselves, but in the process, what we're learning about the analysis methods—is going to be useful for the next generation of experiments that right now are under construction."

Still, NOvA has the potential to reveal more about the elusive neutrino. "This result is an important reminder that the current generation of experiments, including NOvA, continues to collect valuable data and produce physics insights," said Zoya Vallari, postdoctoral researcher at CalTech and co-convener of the analysis. "They are our best shot at a discovery right now."

The NOvA collaboration is made up of more than 200 scientists from 50 institutions in eight countries. With the additional data and further analysis improvements, NOvA will bring physicists closer to understanding the identity-changing behavior of neutrinos.

Provided by Fermi National Accelerator Laboratory

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