Q 12-09-145JEE MainJEE Main 2022 (26 Jul, Shift 2)Medium
Light travels in two media $M_1$ and $M_2$ with speeds $1.5\times10^8\ \text{m s}^{-1}$ and $2.0\times10^8\ \text{m s}^{-1}$ respectively. The critical angle between them is
Answer: (A) $\tan^{-1}\dfrac{3}{\sqrt7}$
$M_1$ is denser. $\sin C = \dfrac{n_2}{n_1} = \dfrac{v_1}{v_2} = \dfrac{1.5}{2.0} = \dfrac34$, so $\cos C = \dfrac{\sqrt7}{4}$ and
$$C = \tan^{-1}\frac{3}{\sqrt7}$$
Solution by Sreeraj P, M.Sc Physics