Consider an equilateral prism (refractive index 2 ). A ray of light is incident on its one surface at a certain angle i . If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to _ _ _ _ .

Step-by-step solution

Given an equilateral prism, the angle of the prism is A = 60^ . The refractive index of the prism is = 2 . The emergent ray grazes the second surface, which means the angle of emergence is e = 90^ . Applying Snell's law at the second surface: (r₂) = 1 (e) . 2 (r₂) = (90^ ) = 1 . (r₂) = 1 2 , which gives r₂ = 45^ . For a prism, we know the relation r₁ + r₂ = A . Substituting the values: r₁ + 45^ = 60^ . r₁ = 60^ - 45^ = 15^ . The angle of refraction at the incident surface is r₁ = 15^ .