Answered: A thin film having an index of…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Wave Optics

Section: Chapter Questions

Problem 63P: Both sides of a uniform film that has index of refraction n and thickness d are in contact with air....

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Question

A thin film having an index of refraction of 1.50 is surrounded by air. It is illuminated normally by white light. Analysis of the reflected light shows that the wavelengths 360, 450, and 602 are the only missing wavelengths in or near the visible portion of the spectrum. That is, for those wavelengths, there is destructive interference. What is the thickness of the film? (Give your answer in nm.)

Expert Solution

Step 1

Given that,

The refractive index of the film n=1.50

The destructive interference is found for the wavelength

$λ_{1} = 360 n m = 360 n m \times \frac{1 m}{10^{9} n m} = 360 \times 10^{- 9} m$

The destructive wavelength for the second wavelength

$λ_{2} = 450 n m = 450 n m \times \frac{1 m}{10^{9} n m} = 450 \times 10^{- 9} m$

The destructive interference for the third wavelength

$λ_{3} = 602 n m = 602 n m \times \frac{1 m}{10^{9} n m} = 602 \times 10^{- 9} m$

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