Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure.
The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is :

Solution

Physics sir · 3 steps

Every ray meets PR at 45°, so only a colour whose critical angle is bigger than 45° can get out.

1. No bending at PQ. All three rays hit face PQ along the normal, so they enter the glass without bending. Each ray then reaches face PR at an angle of incidence equal to the prism angle at P, which is 45°.
2. Condition to emerge. A ray leaves PR only if its angle of incidence is less than the critical angle C, where sin C = 1/μ. So we need sin 45° < 1/μ, which means μ < √2.

   μ < 1/(sin 45°) = √2 ≈ 1.414

   Colour	μ	Critical angle C	At PR
   Red	1.27	≈ 51.9°	45° < C, emerges
   Green	1.42	≈ 44.8°	45° > C, totally reflected
   Blue	1.49	≈ 42.2°	45° > C, totally reflected

3. So. Only red has μ below 1.414, so only the red ray comes out of face PR. Green and blue undergo total internal reflection, so the answer is (d).

The idea to keep. Inside glass, compare the angle of incidence with the critical angle. At 45° the cut-off is μ = √2 ≈ 1.414: below it the ray escapes, above it the ray is totally reflected.

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