A ray of light is incident on first face of an equilateral glass prism at an angle of incidence ' i '. The emergent ray just grazes along the adjacent face. The refractive index of the the prism is 2 . The value of angle of incidence at first face is ( 45^ = 1 2 , 90^ =1 )

Step-by-step solution

Angle of incidence at the first face is denoted by i and angle of refraction by r₁ . Angle of incidence at the second face is r₂ and angle of emergence is e . The equilateral prism has angle A = 60^ and refractive index n = 2 . Since the emergent ray grazes the adjacent face, e = 90^ . Applying Snell's law at the second interface (glass to air): n r₂ = e 2 r₂ = 90^ 2 r₂ = 1 r₂ = 1 2 r₂ = 45^ From the geometry of the prism: A = r₁ + r₂ 60^ = r₁ + 45^ r₁ = 15^ Applying Snell's law at the first interface (air to glass