Critical angle of incidence for a pair of optical media is 45°. The refractive indices of first and second media are in the ratio:

Solution

Physics sir · 4 steps

Total internal reflection needs light going from denser to rarer, so sin C is rarer over denser.

1. Which medium is denser. A critical angle exists only when light travels from a denser medium into a rarer one. So the first medium is the denser one: n₁ > n₂.
2. Snell at critical angle. At the critical angle the refracted ray grazes the surface, so the angle of refraction is 90°. Then n₁ sin C = n₂ sin 90° = n₂.

   sin C = n₂/n₁

3. Put in C. sin 45° = 1/√2, so n₂/n₁ = 1/√2, which gives n₁/n₂ = √2/1.
4. So. The refractive indices of the first and second media are in the ratio √2 : 1, option (d).

The idea to keep. For total internal reflection, the first medium is always the denser one. Remember sin C = nᵣₐᵣₑᵣ/n_(denser), which is always less than 1.

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