Question

# Rainbow. above figure (a), shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflection (see above figure (b)). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation  . (a) Show that    is ,where    is the angle of incidence of the ray on the drop and    is the angle of refraction of the ray within the drop. (b) Using Snells law, substitute for    in terms of    and the index of refraction    of the water. Then, on a graphing calculator or with a computer graphing package, graph    versus    for the range of possible    values and for    for red light (at one end of the visible spectrum) and    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    curve for (c) red light and (d) blue light. (e) If these colors form the inner and outer edges of a rainbow (above figure (b)), what is the angular width of the rainbow?

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Solution
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