Question

If n^(th) division of main scale coincides with (n + 1)^(th) divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.

Answer 1

Hence the least count of the vernier is  a / n + 1

Explanation:

• Given data states that the nth division on main scale coincide with (n+1)th division of Vernier scale, least count has to be calculated.
• Least count is the difference between the main scale division (MSD) and the Vernier scale division (VSD).

Additional data is that 1 MSD equals "a", therefore,

n MSD = (n+1) VSD

=> (n / n+1)  MSD = 1 VSD

1 MSD = a

1 VSD = (n / n+1 x a )

Least count = a - ( na / n +1) = a / n + 1

Hence the least count of the vernier is  a / n + 1