Walker, Halliday & Resnick — Electromagnetic Waves: Problem 23

23 In Fig. 33-39, light is incident at angle $\theta_1 = 40.1^\circ$ on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If $n_1 = 1.30, n_2 = 1.40, n_3 = 1.32, \text{ and } n_4 = 1.75$, what is the value of (a) $\theta_5$ in the air and (b) $\theta_4$ in the bottom material?