The prism has refracting angle A. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence 2A , reaches the second surface and returns back through same path due to reflection at the silvered surface. The refractive index of the material of prism is

Step-by-step solution

For a prism, the angle of the prism is given by A = r₁ + r₂ . Since the light ray retraces its path after reflection from the silvered second surface, it must strike the second surface normally. Thus, the angle of incidence at the second surface is r₂ = 0 . Substituting r₂ = 0 into the prism formula gives r₁ = A . Applying Snell's law at the first refracting surface: i = r₁ Given the angle of incidence i = 2A , we have: (2A) = A Using the trigonometric identity (2A) = 2 A A : 2 A A = A = 2 A Answer: 2 A