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THE VERNIER

1 Introduction

It is a device used for measuring the fractional part of one of the smallest divisions of a

graduated scale.

It consists of two scales: (a) Main scale, (b) Vernier scale.

Vernier scale slides alongside the main scale.

Principle of Vernier:

o Our eye can perceive with considerable precision when two graduations coincide

to form a continuous straight line.

Classification based on number of directions along which graduations of main scale are

numbered:

o Single vernier: Graduations of the main scale are numbered in one direction only.

o Double vernier: Graduations of main scale are numbered in both directions.

Primary classification of vernier is shown in figure below:

Least count (LC): It is defined as the difference between value of smallest division on

main scale and value of smallest division on vernier scale.

It can be calculated as:

Here, s = value of smallest division on main scale, and n = number of divisions on vernier

scale.

This formula for LC can be used for both direct and retrograde vernier.

• Vernier extends in the same direction as main scale

• Smallest division on vernier scale is smaller than smallest division on main scale

• (n-1) divisions of main scale = n divisions of vernier

Direct vernier

• Vernier extends in opposite direction as main scale

• Smallest division on vernier scale is longer than smallest division on main scale

• (n+1) divisions of main scale = n divisions of vernier

Retrograde vernier

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2 Direct vernier

2.1 Single vernier

Fig. 1 shows a single direct vernier. Observe that 9 divisions on main scale coincide with 10

divisions on vernier scale.

Calculation of least count (LC)

Method 1

We know that:

Here, value of smallest division on main scale, s = 0.1

Number of divisions on vernier scale, n = 10

Therefore, LC = 0.1/10 = 0.01

Method 2

LC = Value of smallest division on main scale – Value of smallest division on vernier scale

Value of smallest division on main scale = 0.1

Now, 10 vernier divisions coincide with 9 main scale divisions. Therefore, 1 vernier

divisions will coincide with 9/10 = 0.9 divisions on main scale.

Value of 0.9 division = 0.9 × 0.1 = 0.09

Therefore, LC = 0.10 – 0.09 = 0.01

See Fig. 2. The reading on the vernier is _______.

2.2 Double vernier

Fig. 3 shows a double direct vernier. Main scale is graduated in both directions and vernier also

extends to both sides of zero mark. Observe that 9 divisions on main scale coincide with 10

divisions on vernier scale. The left-hand vernier is used with upper figures on main scale and

vice-versa.

Calculation of least count (LC)

Method 1

We know that:

Here, value of smallest division on main scale, s = 1

Number of divisions on vernier scale, n = 10

Therefore, LC = 1/10 = 0.1

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Method 2

LC = Value of smallest division on main scale – Value of smallest division on vernier scale

Value of smallest division on main scale = 1

Now, 10 vernier divisions coincide with 9 main scale divisions. Therefore, 1 vernier

divisions will coincide with 9/10 = 0.9 divisions on main scale.

Value of 0.9 division = 0.9 × 1 = 0.9

Therefore, LC = 1 – 0.9 = 0.1

See Fig. 4. The reading on the vernier is _______ from left and _______ from right.

3 Retrograde vernier

Fig. 5 shows a retrograde vernier. Observe that the vernier scale extends in opposite direction as

the main scale. Also observe that 10 divisions on the vernier scale coincide with 11 divisions on

main scale.

Calculation of least count

Value of smallest division on main scale, s = 0.1

Number of divisions on vernier scale, n = 10.

Therefore, LC = 0.1/10 = 0.01.

See Fig. 6. The reading on the vernier is ______.