(Ill) Consider a ray of sunlight incident from air on a sphericalraindrop of radius r and index of refraction n. Defining0 to be its incident angle, the ray then follows the pathshown in Fig. 32-67, exiting the drop at a scattering angle compared with its original incoming direction, (a) Show that(f) = 180 + 20 - 4 siiT1 (sin 0/n). (b) The parallel rays ofsunlight illuminate a raindrop with rays of all possibleincident angles from 0 to 90. Plot 4> vs. 0 in the range0 < 0 < 90, in 0.5 steps, assuming n = 1.33 as is appropriatefor water at visible-light wavelengths. (c) From yourplot, you should find that a fairly large fraction of theincident angles have nearly the same scattering angle.Approximately what fraction of the possible incident anglesis within roughly 1 of (f> = 139? [This subset of incidentrays is what creates therainbow. Wavelengthdependentvariations inn cause the rainbow toform at slightly different for the various visiblecolors.]FIGURE 32-67

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