Q 12-09-161JEE MainJEE Main 2021 (22 Jul, Shift 1)Medium
A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i$. The reflected and refracted rays make an angle of $90^\circ$ with each other. The angle of reflection and refraction are respectively $r$ and $r'$. The critical angle is given by,
Answer: (D) $\sin^{-1}(\tan r)$
The reflected ray makes angle $r$ $(= i)$ and the refracted ray angle $r'$ with the normal. They are perpendicular, so $r + r' = 90^\circ$.
Snell's law (denser to rarer): $\mu\sin r = \sin r' = \cos r \Rightarrow \mu = \cot r$.
$$\sin C = \frac1\mu = \tan r \Rightarrow C = \sin^{-1}(\tan r)$$
Solution by Sreeraj P, M.Sc Physics