Rainbow. Figure 33-67 shows a light ray entering and then leaving a falling, spherical

Chapter 33, Problem 77

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Rainbow. Figure 33-67 shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflection (see Fig. 33-21a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation udev. (a) Show that udev is udev 180 2ui 4ur, where ui is the angle of incidence of the ray on the drop and ur is the angle of refraction of the ray within the drop. (b) Using Snells law, substitute for ur in terms of ui and the index of refraction n of the water. Then, on a graphing calculator or with a computer graphing package, graph udev versus ui for the range of possible ui values and for n 1.331 for red light (at one end of the visible spectrum) and n 1.333 for blue light (at the other end). The red-light curve and the blue-light curve have different minima, which means that there is a different angle of minimum deviation for each color. The light of any given color that leaves the drop at that colors angle of minimum deviation is especially bright because rays bunch up at that angle.Thus, the bright red light leaves the drop at one angle and the bright blue light leaves it at another angle. Determine the angle of minimum deviation from the udev curve 75 for (c) red light and (d) blue light. (e) If these colors form the inner and outer edges of a rainbow (Fig. 33-21a), what is the angular width of the rainbow? Water dropIncidentray i rFigure 33-67 77.