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Unformatted text preview: 35. Light reﬂected from the front surface of the coating suﬀers a phase change of π rad while light reﬂected
from the back surface does not change phase. If L is the thickness of the coating, light reﬂected from the
back surface travels a distance 2L farther than light reﬂected from the front surface. The diﬀerence in
phase of the two waves is 2L(2π/λc ) − π , where λc is the wavelength in the coating. If λ is the wavelength
in vacuum, then λc = λ/n, where n is the index of refraction of the coating. Thus, the phase diﬀerence
is 2nL(2π/λ) − π . For fully constructive interference, this should be a multiple of 2π . We solve
λ − π = 2mπ for L. Here m is an integer. The solution is
L= (2m + 1)λ
4n To ﬁnd the smallest coating thickness, we take m = 0. Then,
560 × 10−9 m
= 7.00 × 10−8 m .
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