Concept explainers
(a)
The first three smallest thicknesses of the film for the constructive interference when wavelength of the wave in vacuum is
(a)
Answer to Problem 32SP
Solution:
Explanation of Solution
Given data:
The wavelength of the wave in vacuum is
The refractive index of the film is
Formula used:
The expression for the path length difference for the constructive interference of the waves is
Here, the values of
Explanation:
Refer to the Fig. 40-2 provided in the textbook:
Write the expression for the path length difference of the reflected waves, from upper and the lower surface of the film, for the constructive interference:
The wave reflected by the lower and the upper surface of the film has the path difference, which is equals to
Substitute
Here,
Rearrange for
Substitute
For
For
For
Conclusion:
The thicknesses of the film for the constructive interference are
(b)
The first three smallest thicknesses of the film for the destructive interference when the refractive index of the film is given.
(b)
Answer to Problem 32SP
Solution:
Explanation of Solution
Formula used:
The expression for the path length difference for the destructive interference of the waves is
Here, the values of
Explanation:
Write the expression for the path length difference of the reflected waves, from upper and the lower surface of the film, for the destructive interferences:
The wave reflected by the lower and upper surface of the film has the optical path length difference of
Substitute
Rearrange for
Substitute
For
For
For
Conclusion:
The thicknesses of the film for the constructive interference are
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Chapter 40 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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