Question

A travelling microscope is used to determine the refractive index of a glass slab. If $40$ divisions are there in $1\text{cm}$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is $\times {10}^{-6}\text{m}$

Answer 1

Given, $40\text{MSD}=1\text{cm}$
$\Rightarrow 1\text{MSD}=0.025\text{cm}\cdots \left(1\right)$
Also, $50\text{VSD}=49\text{MSD}$
$\Rightarrow$ Least count $=1\text{MSD}-1\text{VSD}=1\text{MSD}-\frac{49}{50}\text{MSD}$
$=\frac{\text{MSD}}{50}$
$\Rightarrow LC=\frac{0.025}{50}\text{cm}=\frac{250}{50}\times {10}^{-6}\text{m}$
$\Rightarrow LC=5\times {10}^{-6}\text{m}$
Comparing the asking LC value, answer will be $5.$