Q 12-09-141JEE MainJEE Main 2022 (25 Jul, Shift 1)Medium
The times taken by light to travel through two different materials $A$ and $B$ of refractive indices $\mu_A$ and $\mu_B$ of the same thickness are $t_1$ and $t_2$ respectively. If $t_2 - t_1 = 5\times10^{-10}\ \text{s}$ and the ratio of $\mu_A$ to $\mu_B$ is $1 : 2$, then the thickness of material, in metre, is: (Given $v_A$ and $v_B$ are velocities of light in $A$ and $B$ materials respectively)
Answer: (A) $5\times10^{-10}v_A$
$v\propto\dfrac1\mu$, so $v_B = \dfrac{v_A}{2}$.
$$t_2 - t_1 = \frac{d}{v_B} - \frac{d}{v_A} = \frac{2d}{v_A} - \frac{d}{v_A} = \frac{d}{v_A}$$
$$d = 5\times10^{-10}\,v_A$$
Solution by Sreeraj P, M.Sc Physics