Q 12-09-147JEE MainJEE Main 2022 (27 Jun, Shift 1)Medium
Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be
Answer: (D) $2\cos^{-1}\left(\sqrt{\dfrac{n}{2}}\right)$
Let the angle of refraction be $r$, so $i = 2r$. By Snell's law:
$$\sin 2r = \sqrt{2n}\,\sin r \Rightarrow 2\sin r\cos r = \sqrt{2n}\sin r$$
$$\cos r = \frac{\sqrt{2n}}{2} = \sqrt{\frac{n}{2}}$$
$$i = 2r = 2\cos^{-1}\left(\sqrt{\frac n2}\right)$$
Solution by Sreeraj P, M.Sc Physics