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 θ of prism is.

Question

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 θ of prism is.

G1 Physics · Accepted Answer

The incident ray is parallel to the base. The left base angle of the prism is 45°, so the angle of incidence at the first surface is i = 45°. Apply Snell's law at the first surface: 1 × sin45° = √2 sin r₁. Since sin45° = 1/√2, we get 1/√2 = √2 sin r₁. Thus, sin r₁ = 1/2, so r₁ = 30°. At the second surface, the emergent ray grazes the surface. Therefore the refracted angle outside is 90° and the internal angle r₂ is the critical angle. Hence, sin r₂ = 1/√2, so r₂ = 45°. For a prism, A = r₁ + r₂…