Question

The diagram below shows the path of a blue ray through the prism:

1. Calculate the critical angle of the material of the prism for blue colour.
2. What is the measure of the angle of this prism (A)?
3. Which colour should replace the blue ray, for the ray to undergo Total Internal Reflection?
   

Answer 1

1. Here, the refracted ray PQ is normal to the surface AB of the prism (i.e., ∠r = 0°), so the incident ray at the point P should also be normal to the surface AB so that ∠i = 0°. At point Q, the angle of incidence for the ray PQ is 133° - 90° = 43°.

Now this angle should be equal to the critical angle because ray PQ is refracted at 90°, i.e., it is refracted along QC.

Hence, the critical angle of the prism is 43°.

2. In ΔAPQ

∠APQ + ∠PQA + ∠PAQ = 180°

90° + 47° + ∠PAQ = 180°

∠PAQ = 180° - 90° - 47°

∠PAQ = 43°

∴ ∠A = 43°

3. The light used and its wavelength determine the angle of deviation. With a decrease in the light wavelength, the angle of deviation increases.
Accordingly, the beam will experience total internal reflection if we swap out the blue light for intense light, sometimes known as indigo light.