Q 12-09-059JEE MainJEE Main 2026 (24 Jan, Shift 1)Medium
The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\dfrac n2$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is ______ .
Answer: (A) $60^\circ$
At minimum deviation the ray inside the prism is symmetric: the angle of incidence on the exit face is $r = \dfrac A2$.
Critical angle for going from $n$ into the coating $\dfrac n2$: $\sin C = \dfrac{n/2}{n} = \dfrac12$, so $C = 30^\circ$.
Exactly meeting the critical condition: $\dfrac A2 = 30^\circ\Rightarrow A = 60^\circ$.
Solution by Sreeraj P, M.Sc Physics