Answered: A thin film having an index of…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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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