If $50$ Vernier divisions are equal to $49$ main scale divisions of a travelling microscope and one smallest reading of main scale is $0.5 \mathrm{mm}$ the Vernier constant of travelling microscope is:

The number of divisions on the vernier scale $=50$

Main scale division $\left(\mathrm{MSD}\right)=0.5 \mathrm{mm}$

As, $50$ divisions on the vernier scale coincide with $49$ divisions on the main scale,

$\mathrm{VSD}=\frac{49}{50}\mathrm{MSD}$

The minimum inaccuracy in the measurement of distance by a vernier scale,

$=$ Least count of the vernier scale

$=1 \mathrm{MSD}–1 \mathrm{VSD}$

$=1 \mathrm{MSD}-\frac{49}{50}\mathrm{MSD}$

$=\frac{1}{50}\mathrm{MSD}=\frac{1}{50}\times 0\mathrm{.}5 \mathrm{mm}$

$=0.01 \mathrm{mm}$.