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.

Solution

Physics sir · 4 steps

Find the apex angle from A = r₁ + r₂, then let the triangle's angle sum hand you θ.

1. Angle of incidence. The first face makes 45° with the base, so its normal makes 90° - 45° = 45° with the horizontal. The incident ray is horizontal, so i = 45°.
2. First refraction. Snell's law gives sin r₁ = (sin 45°)/√2 = 1/2, so r₁ = 30°.
3. Grazing emergence. The ray grazes the second face, so it meets that face at the critical angle. sin C = 1/√2, so r₂ = C = 45°.

   A = r₁ + r₂ = 30° + 45° = 75°

4. So. The three angles of the prism add up to 180°: θ = 180° - 45° - 75° = 60°. That is option (c).

The idea to keep. Grazing emergence means r₂ equals the critical angle. Inside any prism r₁ + r₂ = A, and the apex angle with the base angles closes the triangle.

Answer from the NTA final answer key. Solution by PrepWiser.