Concept explainers
An oil film (n = 1.45) floating on water is illuminated by white light at normal incidence. The film is 280 nm thick. Find (a) the wavelength and color of the light in the visible spectrum most strongly reflected and (b) the wavelength and color of the light in the spectrum most strongly transmitted. Explain your reasoning.
(a)
Answer to Problem 22P
Explanation of Solution
Given Information: The refractive index of the oil film is
It is given that an oil film floating on water is illuminated by white light at normal incidence as shown in figure given below.
Figure (1)
For most strongly reflected waves:
Write the expression for the constructive interference in thin film.
Here,
From equation (1), formula to calculate the value of wavelength of the light is,
From equation (2), formula to calculate the value of wavelength of the light for
Here,
Substitute
The range for the wavelength of the visible light is
Thus, the value of wavelength of the light for
From equation (2), formula to calculate the value of wavelength of the light for
Here,
Substitute
Thus, the value of wavelength of the light for
From equation (2), formula to calculate the value of wavelength of the light for
Here,
Substitute
Thus, the value of wavelength of the light for
Conclusion:
Therefore, the value of wavelength of the light for
(b)
Answer to Problem 22P
Explanation of Solution
Given Information: The refractive index of the oil film is
For most strongly transmitted waves:
Write the expression for the destructive interference in thin film.
From equation (5), formula to calculate the value of wavelength of the light is,
From equation (6), formula to calculate the value of wavelength of the light for
Here,
Substitute
Thus, the value of wavelength of the light for
From equation (6), formula to calculate the value of wavelength of the light for
Here,
Substitute
Thus, the value of wavelength of the light for
From equation (6), formula to calculate the value of wavelength of the light for
Here,
Substitute
Thus, the value of wavelength of the light for
Conclusion:
Therefore, the value of wavelength of the light for
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Chapter 36 Solutions
Physics for Scientists and Engineers
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- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning