A light ray is incident normally on one of the mutually perpendicular faces of a right-angled thin prism. The refractive index of the material of the prism is 1.6 . If the ray emerges from the inclined face at an angle of 8^ with respect to the normal of that face, the angle of the prism is

Step-by-step solution

For normal incidence on the first face, the angle of incidence i₁ = 0^ , which implies the angle of refraction r₁ = 0^ . For a prism, the angle of the prism A = r₁ + r₂ . Therefore, the angle of incidence at the second face is r₂ = A . Applying Snell's law at the second face (from prism to air) and using the small angle approximation for a thin prism: r₂ = 1 e A = e Substituting the given values ( = 1.6 and e = 8^ ): 1.6 A = 8^ A = 8^ 1.6 = 5^ Answer: 5^