For a 30^ prism when a ray of light is incident at an angle 60^ on one of its faces, the emergent ray passes normal to the other surface. Then the refractive index of the prism is:

Step-by-step solution

Given the prism angle A = 30^ . The angle of incidence i = 60^ . The emergent ray passes normal to the other surface, which means the angle of emergence e = 0^ . From the geometry of the prism, the angle of refraction at the first surface r₁ and the angle of incidence at the second surface r₂ satisfy r₁ + r₂ = A . Since the emergent ray is normal to the second surface, r₂ = 0^ . Therefore, r₁ + 0^ = 30^ , which gives r₁ = 30^ . Applying Snell's law at the first surface, = i r₁ . Substituting the values, = 60^ 30^ =