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.

Explanation

`(n+1)` divisions of vernier scale =n divisions of main scale
`therefore 1` vernier division `=(n)/(n+1)` main scale division
Least count `=1 M.S.D.-1V.S.D.`
`=(-(n)/(n+1))M.S.D.=((1)/(n+1))M.S.D=(a)/(n+1)`