Halliday, Resnick & Walker — Electromagnetic Waves: Problem 56

56 In Fig. 33-49, light from ray A refracts from material 1 ($n_1 = 1.50$) into a thin layer of material 2 ($n_2 = 1.80$), crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3 ($n_3 = 1.30$). (a) What is the value of incident angle $\theta_A$? (b) If $\theta_A$ is decreased, does part of the light refract into material 3? Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3 ($n_3 = 1.30$). (c) What is the value of incident angle $\theta_B$? (d) If $\theta_B$ is decreased, does part of the light refract into material 3?