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 23 - Ray Optics - Exercises and Problems - Page 692: 55

Answer

$2$

Work Step by Step

As we see in the figure below, the focal length is twice the radius of the sphere. Hence, $s'=2R$ And since the paraxial light rays are parallel, $s=\infty$. Recalling that $$\dfrac{n_1}{s}+\dfrac{n_2}{s'}=\dfrac{n_2-n_1}{R}$$ where $n_1=n_{air}=1$, and $n_2=n_{sphere}$ Plugging the known, $$\dfrac{1}{\infty}+\dfrac{n_{sphere}}{2R}=\dfrac{n_{sphere}-1}{R}$$ $$0+\dfrac{n_{sphere}}{2 \color{red}{\bf\not} R}=\dfrac{n_{sphere}-1}{ \color{red}{\bf\not} R}$$ $$n_{sphere}=2n_{sphere}-2$$ $$n_{sphere}=\color{red}{\bf 2}$$
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