A ray of light is incident at an angle of 45^ on one face of a prism of refracting angle 30^ . The opposite face of the prism is silvered. If the ray retraces its path after reflection from the silvered face, the refractive index of the material of the prism is

Step-by-step solution

For the ray to retrace its path, it must strike the silvered face normally. Thus, the angle of incidence at the second face is r₂ = 0^ . For a prism, the refracting angle A = r₁ + r₂ . Given A = 30^ , we have 30^ = r₁ + 0^ r₁ = 30^ . Applying Snell's law at the first face: ₁ i = ₂ r₁ 1 45^ = 30^ 1 2 = 1 2 = 2 Answer: 2