The exit surface of a prism with refractive index n is coated with a material having refractive index n 2 . When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is _ _ _ _ .

Step-by-step solution

Let the refractive index of the prism be n₁ = n and the refractive index of the coating on the exit surface be n₂ = n 2 . At the condition of minimum deviation, the angle of refraction at the first surface r₁ and the angle of incidence at the second surface r₂ are equal, i.e., r₁ = r₂ = A 2 , where A is the prism angle. The problem states that at the exit surface, the light meets the condition of critical angle. Therefore, r₂ = _c . The critical angle _c for the interface between the prism and the coating is given