Concept explainers
(a)
The weakest wavelengths which are in the transmitted light.
(a)
Answer to Problem 19P
The weakest wavelengths in the transmitted light are
Explanation of Solution
Given that the index of refraction of the soap film is
The weakest wavelengths in transmitted light correspond to the strongest wavelengths in the reflected light. Rays which are found as reflected off the front of the film will be reversed in phase, since the refractive index of the air is found to be less than the refractive index of the film.
However, the rays reflected off the back of the film are not inverted and thus the reflected rays will be out of phase and the
The condition for constructive interference is used to find the strongest
Write the condition for the constructive interference.
Here,
Write the expression for the wavelength of the transmitted light.
Here,
Use equation (II) in equation (I),
Solve equation (III) for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the weakest wavelengths in the transmitted light are
(b)
Wavelengths which are strongest in the transmitted light.
(b)
Answer to Problem 19P
The wavelengths which are strongest in the transmitted light are
Explanation of Solution
The strongest wavelengths in transmitted light correspond to the weakest wavelengths in reflected light. Destructive interference in the reflected light occurs when the path difference,
Write the condition for the destructive interference.
Use equation (II) in equation (I).
Solve equation (VI) for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the wavelengths which are strongest in the transmitted light are
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Chapter 25 Solutions
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