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 649: 13

Answer

$ 7.94\;\rm \mu m$

Work Step by Step

In a diffraction grating experiment, we know that the bright fringes are given by $$d\sin\theta_m=m\lambda$$ And at $m=1$, $$d\sin\theta_1=\lambda$$ So, $$d=\dfrac{\lambda}{\sin\theta_1}\tag 1$$ Now we need to find $\theta_1$, as we see in the figure below, [see the yellosih right-triangle below], $$\theta_1=\tan^{-1}\left[ \dfrac{16}{200} \right]=\bf 4.57^\circ$$ Plugging the known into (1); $$d=\dfrac{633\times 10^{-9}}{\sin4.57^\circ}=\bf 7.94\times 10^{-6}\;\rm m$$ $$d=\color{red}{\bf 7.94}\;\rm \mu m$$
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