JEE MAIN - Physics (2023 - 29th January Evening Shift - No. 19)
In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 20 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $$\frac{x}{10}\times10^{-3}$$, where $$x$$ is ___________
Answer
41
Explanation
$$\mu=\frac{\mathrm{real\,depth}\,(l_1)}{\mathrm{apparent\,depth}\,(l_2)}$$
$$=\frac{5.25}{5}=1.05$$
$$\frac{d\mu}{\mu}=\frac{dl_1}{l_1}+\frac{dl_2}{l_2}$$
$$d\mu = \left( {{{d{l_1}} \over {{l_1}}} + {{d{l_2}} \over {{l_2}}}} \right)\mu $$
$$ = \left( {{{0.01} \over {5.25}} + {{0.01} \over {5.00}}} \right) \times 1.05$$
$$ = {{41} \over {10}} \times {10^{ - 3}}$$
so $$x = 41$$
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