A glass slab of refractive index 1·5 is cut in the shape of a parallelepiped ABCD as shown in the figure. Surface BC is polished to form a perfect reflector. Light is incident at surface AB from inside at an angle π/3. Which one of the following is the correct angle ABC (θ) such that the reflected light retraces its path?

To ensure the reflected light retraces its path, the light ray must strike the polished reflecting surface BC at a normal incidence (i.e., the angle of incidence at the mirror must be 0°, or the ray must be perpendicular to the surface).

1. The light is incident on surface AB from inside at an angle of π/3 (60°) to the normal.
2. Since the refractive index μ = 1.5, the critical angle c is sin-1(1/1.5) ≈ 41.8°. Since 60° > 41.8°, Total Internal Reflection (TIR) occurs at surface AB.
3. The angle of reflection at AB is also 60° to the normal. Consequently, the angle the reflected ray makes with the surface AB is 90° - 60° = 30° (π/6).
4. Consider the triangle formed by the vertex B, the point of incidence on AB, and the point of incidence on BC. For the ray to hit BC perpendicularly (90°), the sum of angles in the triangle must be 180°:
θ + 30° + 90° = 180° ⇒ θ = 60° = π/3.