Unformatted text preview: 31. The wave reﬂected from the front surface suﬀers a phase change of π rad since it is incident in air on a medium of higher index of refraction. The phase of the wave reﬂected from the back surface does not change on reﬂection since the medium beyond the soap ﬁlm is air and has a lower index of refraction than the ﬁlm. If L is the thickness of the ﬁlm, this wave travels a distance 2L farther than the wave reﬂected from the front surface. The phase diﬀerence of the two waves is 2L(2π/λf ) − π , where λf is the wavelength in the ﬁlm. If λ is the wavelength in vacuum and n is the index of refraction of the soap ﬁlm, then λf = λ/n and the phase diﬀerence is 2nL 2π λ − π = 2(1.33)(1.21 × 10−6 m) 2π 585 × 10−9 m − π = 10π rad . Since the phase diﬀerence is an even multiple of π , the interference is completely constructive. ...
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- Fall '08