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

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

JEE MainJEE Main 2022Physical World, Units and Measurements

Solution:

$50 VSD =49 MSD$
$1 VSD =\frac{49}{50} MSD$
Least count $=1 MSD -1 VSD$
$=\left(1-\frac{49}{50}\right) MSD =\frac{1}{50} MSD$
$1 MSD =\frac{1}{40} cm$
Least count $=\frac{1}{50 \times 40} cm$
$=\frac{1}{2000} cm =\frac{1}{2} \times 10^{-5} m $
$=0.5 \times 10^{-5} m$
$=5 \times 10^{-6} m$