Q 12-10-077JEE MainJEE Main 2023 (29 Jan, Shift 2)Medium
Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are $2.8$ (medium 1) and $6.8$ (medium 2), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be $\tan^{-1}\left(1+\dfrac{10}{\theta}\right)^{1/2}$, the value of $\theta$ is ______. (Given for dielectric media, $\mu_r=1$)
Numerical value type. Enter your answer.
Answer: 7
Reflected and refracted rays are perpendicular at Brewster's angle: $\tan i_B=\dfrac{n_2}{n_1}$. With $\mu_r=1$, $n=\sqrt{K}$:
$$\tan i_B=\sqrt{\frac{6.8}{2.8}}=\sqrt{1+\frac{4}{2.8}}=\sqrt{1+\frac{10}{7}}$$
So $\theta=7$.
Solution by Sreeraj P, M.Sc Physics