A monochromatic light is incident from air on a refracting surface of a prism of angle 75° and refractive index n₀ = √3. The other refracting surface of the prism is coated by a thin film of material of refractive index n, as shown in the figure. The light suffers total internal reflection at the coated prism surface for an incidence angle θ ≤ 60°. The value of n² is:

Question

G1 Physics · Accepted Answer

At the limiting condition take θ = 60°. At the first face, Snell's law gives sin60° = √3 sin r₁, hence r₁ = 30°. Therefore the angle of incidence at the coated face is r₂ = 75° - 30° = 45°. At the limiting condition r₂ is the critical angle, so sin45° = n/√3. Hence n = √(3/2) and n² = 3/2 = 1.5. Therefore option C is correct.