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 24 - Optical Instruments - Exercises and Problems - Page 714: 30

Answer

$\approx 3.6^\circ$

Work Step by Step

We are given that the angle subtended by the image is 8$\times$ the angle subtended by the object. $$\theta_{\rm image}=8\theta_{\rm object}$$ where, for small angle approximation, $\theta_{\rm object}=\dfrac{h}{s}$ Hence, $$\theta_{\rm image}=\dfrac{8h}{s}$$ We need it in degrees, so $$\theta_{\rm image}=\dfrac{8h}{s}\;\rm rad\cdot\dfrac{180^\circ}{\pi\;\rm rad}$$ Plugging the known; $$\theta_{\rm image}=\dfrac{8(0.14)(180)}{18\pi}=\color{red}{\bf 3.565^\circ}$$
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