Consider a rectangular soap film placed vertically with thickness increasing linearly from top to bottom as illustrated in Fig. 6. The top portion of soap film has a negligible thickness compared to the wavelength of light. Under the illumination of white light, the top portion appears dark. A total of three sets of horizontal color fringes are observed on the soap film that has a refractive index of n = 1.4. Each fringe contains light with wavelengths ranging from violet at 400 nm to red at 700 nm. (a) Explain with the use of appropriate equations the formation of color fringes on the soap film. You should also state the phase shifts on optical reflections. (b) Explain why the top portion of the soap film is dark. (c) Within each color fringe, is the violet portion above or below that of the red portion? Explain. (d) Assuming the soap film has a vertical length that is 10000 times of its thickness at the bottom, determine the widths of the three sets of color fringes, each containing wavelengths from 400 nm to 700 nm.

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Chapter1: Units, Trigonometry. And Vectors
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Consider a rectangular soap film placed vertically with thickness increasing linearly
from top to bottom as illustrated in Fig. 6. The top portion of soap film has a negligible
thickness compared to the wavelength of light. Under the illumination of white light,
the top portion appears dark. A total of three sets of horizontal color fringes are
observed on the soap film that has a refractive index of n = 1.4. Each fringe contains
light with wavelengths ranging from violet at 400 nm to red at 700 nm.
(a) Explain with the use of appropriate equations the formation of color fringes on the
soap film. You should also state the phase shifts on optical reflections.
(b) Explain why the top portion of the soap film is dark.
(c) Within each color fringe, is the violet portion above or below that of the red portion?
Explain.
(d) Assuming the soap film has a vertical length that is 10000 times of its thickness at
the bottom, determine the widths of the three sets of color fringes, each containing
wavelengths from 400 nm to 700 nm.
(e) Determine the width of the overlap region between (i) the first and second fringes,
and (ii) the second and third fringes.
10000
Figure 6
Transcribed Image Text:Consider a rectangular soap film placed vertically with thickness increasing linearly from top to bottom as illustrated in Fig. 6. The top portion of soap film has a negligible thickness compared to the wavelength of light. Under the illumination of white light, the top portion appears dark. A total of three sets of horizontal color fringes are observed on the soap film that has a refractive index of n = 1.4. Each fringe contains light with wavelengths ranging from violet at 400 nm to red at 700 nm. (a) Explain with the use of appropriate equations the formation of color fringes on the soap film. You should also state the phase shifts on optical reflections. (b) Explain why the top portion of the soap film is dark. (c) Within each color fringe, is the violet portion above or below that of the red portion? Explain. (d) Assuming the soap film has a vertical length that is 10000 times of its thickness at the bottom, determine the widths of the three sets of color fringes, each containing wavelengths from 400 nm to 700 nm. (e) Determine the width of the overlap region between (i) the first and second fringes, and (ii) the second and third fringes. 10000 Figure 6
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