Chapter 30, Problem 56P

(a) Differentiate the result of Problem 55 to show that the maximum value of ϕ occurs when the incidence angle θ is given by cos²θ = $\frac{1}{3}$(n² − 1). (b) Use this result and that of Problem 55 to find the maximum ϕ in a raindrop with n = 1.333. The is the angle at which the rainbow appears, as shown in the Application on pages 573-574.

57. Figure 30.24 shows the approximate path of a light ray that undergoes internal reflection twice in a

FIGURE30.24 Problems 57