Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 22 - Wave Optics - Exercises and Problems - Page 650: 40

Answer

a) $9I_1$ b) $I_1$

Work Step by Step

$$\color{blue}{\bf [a]}$$ The author told us that the path-length difference is $\lambda$ which means that the interference is constructive (since we assume that the light is a monochromatic light beam). Thus, $$I_{max}=N^2I$$ where $N$ is the number of waves interfered (or the number of slits) $$I_{max}=3^2I_1$$ $$\boxed{I_{max}=9I_1}$$ $$\color{blue}{\bf [b]}$$ We have the same three slits with the seam monochromatic light and when the path length difference between any two adjacent slits is $\lambda/2$, there will be a perfect destructive interference between the first two slits, and then a full $\lambda$ remains between the first and the third slit. Thus, $$\boxed{I=I_1}$$
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