Units and Measurement

## Vernier Calipers : Measuring Small Lengths

We know that a metre rule can be used to measure length correct only up to 1 mm. It means it cannot measure lengths which needs measurement like 1.1 mm or 1.2 mm etc. Pierre Vernier designed the device to measure lengths such as these. This device is known as vernier calipers.

This device uses two scales for the purpose of measurements. Let us see the diagram of a vernier calipers to understand its construction.
Construction of a vernier caliper
1. Outside jaws or external jaws : It is used to measure external diameter or width of an object
2. Inside jaws or internal jaws : It is used to measure internal diameter of an object
3. Depth gauge : It is used to measure depths of an object or a hole
4. Main scale in mm: scale marked every mm
5. Main scale in inches and fractions
6. Vernier scale : gives interpolated measurements to 0.02 mm or better
7. Vernier scale : gives interpolated measurements in 1/1000 th of an inch
8. Retainer or stop :used to block movable part to allow the easy transferring of a measurement
In the vernier caliper, main scale is fixed while the vernier scale slides along the main scale.
Principle of the vernier

“n divisions of the vernier coincides with (n-1) divisions of the main scale.”

Generally, a vernier scale has 10 divisions.
The total length of these 10 divisions is equal to the length of (10 – 1 = 9) divisions of the main scale.
Now, length of 9 divisions of main scale = 9 mm
Length of 10 divisions of vernier scale = 10 mm
Therefore, length of 1 divisions of vernier scale = 9/10 mm = 0.9 mm
It means that each vernier division is 1/10 mm = 0.1 mm smaller than a main scale division.
Least count of a vernier or vernier constant
The least count of a vernier caliper is equal to the difference between the values of one main scale division and one vernier scale division. It is also known as the vernier constant.

Least Count (L.C.) = Value of 1 main scale division – Value of 1 vernier scale division

Let n divisions of vernier be of length equal to that of $(n-1)$ divisions on main scale.
Let the value of 1 main scale division (M.S.D. = Main Scale Division) be $x$ . Then,
Value of n divisions on vernier ( V.S.D. = Vernier Scale Division) = $(n-1) x$
Value of 1 division on vernier = $\frac{(n-1)x}{n} \$
Therefore,
Least Count = 1 M.S.D. – 1 V.S.D.
= $x - \frac{(n-1)x}{n} \$
= $\frac{x}{n} \$
Or Least count
= $\frac{\text{Value of one main scale division (x)}}{\text{Total number of division on vernier (n)}} \$
So, the least count of a vernier is obtained by dividing the value of one main scale division by the total number of division on the vernier.
Example :
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Published on September 17th, 2020 | by Abhishek Mandal