As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface. If refractive index of the material of prism is 2 , the angle of prism is.

Step-by-step solution

From the geometry of the prism, the angle of the prism is A = 180^ - (45^ + ) . The incident ray is parallel to the base, so the angle of incidence i at the first surface is equal to the base angle 45^ . Thus, i = 45^ . Applying Snell's law at the first surface: 1 (45^ ) = (r₁) . Given = 2 , we have 1 2 = 2 (r₁) (r₁) = 1 2 r₁ = 30^ . At the second surface, the emergent ray grazes the surface, so the angle of emergence e = 90^ . Applying Snell's law at the second surface: (r₂) = 1 (90^ ) . 2 (r₂) = 1 (r₂) = 1 2 r₂ =