Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 35 - Interference - Questions - Page 1072: 1b

Answer

Decreases.

Work Step by Step

The formula for double slit interference patterns is given by $dsin \theta=m \lambda$. For small angles, $sin \theta \approx tan \theta \approx \theta$. Therefore, $sin \theta$ can be rewritten as $\frac{y}{L}$. This leaves $$\frac{dy}{L}=m \lambda$$ Assume $m$ (order number) is one and use $y$ as the distance from the center to the next area of maximum brightness. This leaves $$y=\frac{\lambda L}{d}$$ If the color is changed from red to blue, the wavelength decreases. Therefore, as $\lambda$ decreases, the distance between fringes $y$ decreases too.
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