An equilateral prism of refractive index 1.6 has one face coated with a transparent material of refractive index n₂, as shown in the figure. The ray inside the prism strikes the coated face at an incidence angle of 60°. What is the maximum value of n₂ for which total internal reflection at the coated face is just possible?

Question

G1 Physics · Accepted Answer

At the limiting condition for total internal reflection, the angle of refraction in the coating is 90°. Therefore, by Snell's law, n(prism) sin i = n₂ sin90°. Given, n(prism) = 1.6, i = 60°. Hence, n₂ = 1.6 sin60° = 1.6(√3 ÷ 2) = 0.8√3 = 4√3 ÷ 5. For total internal reflection, n₂ must not exceed this limiting value. Correct option: D.