77 E Rainbow. Figure 33-67 shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflec- tion (see Fig. 33-21a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation Bdev- (a) Show that 6sey is Odey = 180° + 20, – 48, where e, is the angle of incidence of the ray on the drop and 0, is the angle of refraction of the ray within the drop. (b) Using Snell's law, substitute for 6, in terms of 6, and the index of refraction n of the water. Then, on a graphing calculator or with a computer graphing package, graph Osey versus 0, for the range of possible 6; 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 color's angle of minimum de- viation is especially bright because Incident rays bunch up at that angle. Thus, the ray bright red light leaves the drop at one angle and the bright blue light leaves it at another angle. Determine the angle of mini- mum deviation from the Odey curve Water drop Figure 33-67 Problem 77.
77 E Rainbow. Figure 33-67 shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflec- tion (see Fig. 33-21a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation Bdev- (a) Show that 6sey is Odey = 180° + 20, – 48, where e, is the angle of incidence of the ray on the drop and 0, is the angle of refraction of the ray within the drop. (b) Using Snell's law, substitute for 6, in terms of 6, and the index of refraction n of the water. Then, on a graphing calculator or with a computer graphing package, graph Osey versus 0, for the range of possible 6; 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 color's angle of minimum de- viation is especially bright because Incident rays bunch up at that angle. Thus, the ray bright red light leaves the drop at one angle and the bright blue light leaves it at another angle. Determine the angle of mini- mum deviation from the Odey curve Water drop Figure 33-67 Problem 77.
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Transcribed Image Text:77 E Rainbow. Figure 33-67 shows a light ray entering and
then leaving a falling, spherical raindrop after one internal reflec-
tion (see Fig. 33-21a). The final direction of travel is deviated
(turned) from the initial direction of travel by angular deviation
Bdev- (a) Show that 6sey is
Odey = 180° + 20, – 48,
where e, is the angle of incidence of the ray on the drop and 0, is
the angle of refraction of the ray within the drop. (b) Using Snell's
law, substitute for 6, in terms of 6, and the index of refraction n of
the water. Then, on a graphing calculator or with a computer
graphing package, graph Osey versus 0, for the range of possible 6;
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 color's angle of minimum de-
viation is especially bright because Incident
rays bunch up at that angle. Thus, the ray
bright red light leaves the drop at
one angle and the bright blue light
leaves it at another angle.
Determine the angle of mini-
mum deviation from the Odey curve
Water drop
Figure 33-67 Problem 77.
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