Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 24 - The Wave Nature of Light - Problems - Page 709: 31

Answer

$\sin\theta=D\sin\theta_i-\dfrac{m\lambda}{D}\tag{$m=\pm1,\pm2,..$}$

Work Step by Step

First of all, to find the central maxima, we need to find the net path difference which is given by $$\Delta r=D\sin\theta_i-D\sin\theta$$ where $D\sin\theta_i$ is the path difference between the top and the bottom ends of the slit for the incident wave and $D\sin\theta$ is the path difference between the top and the bottom ends of the slit for the diffracted wave. When $\theta_i=\theta$, the net path difference is zero which means that a constructive interference is created there. Now we can be sure that the central maximum is laying at the position in which $\theta=28^\circ$. Thus, the path difference equal to $$\Delta r=D\sin\theta_i-D\sin\theta=m\lambda$$ where $m=\pm1,\pm2,\pm3,...$ And hence, the angle of minima $\theta$ is given by $$\sin\theta=D\sin\theta_i-\dfrac{m\lambda}{D}\tag{$m=\pm1,\pm2,..$}$$ Therefore, and from all the above, at an initial angle of $\theta_i=28^\circ$, the first minimum fringe will be surrounding the central maximum fringe symmetrically at $28^\circ$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.