Concept explainers
Figure CQ37.2 shows an unbroken soap film in a circular frame. The film thickness increases from lop to bottom, slowly at first and then rapidly. As a simpler model, consider a soap film (n = 1.33) contained within a rectangular wire frame. The frame is held vertically so that the film drains downward and forms a wedge with flat faces. The thickness of the film at the top is essentially zero. The film is viewed in reflected white light with near-normal incidence, and the first violet (λ = 420 nm) interference band is observed 3.00 cm from the top edge of the film, (a) Locate the first red (λ = 680 nm) interference band, (b) Determine the film thickness at the positions of the violet and red bands, (c) What is the wedge angle of the film?
(a)
The position of the first red interference band.
Answer to Problem 37.70AP
The position of the first red interference band is
Explanation of Solution
Given info: The index of refraction of the soap film is
The diagram of thin film in rectangular wire frame is,
Figure (1)
From figure (1), the formula of tangent of angle is,
Here,
Rearrange the above equation for
The condition for constructive interference for red band in a thin soap film is,
Here,
The condition for constructive interference for violet in a thin soap film is,
Here,
Divide equation (3) by (4) on both sides.
Substitute
Substitute
Substitute
Conclusion:
Therefore, the position of the first red interference band is
(b)
The film thickness at the position of red and violet bands.
Answer to Problem 37.70AP
The film thickness at the position of red band is
Explanation of Solution
Given info: The index of refraction of the soap film is
From equation (3), the condition for constructive interference is,
Substitute
From equation (4), the condition for constructive interference is,
Substitute
Conclusion:
Therefore, the film thickness at the position of red band is
(c)
The wedge angle of the film.
Answer to Problem 37.70AP
The wedge angle of the film is
Explanation of Solution
Given info: The index of refraction of the soap film is
From figure (1), the formula of tangent of angle is,
Substitute
Conclusion:
Therefore, the wedge angle of the film is
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Chapter 37 Solutions
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