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: 32

Answer

$7.6\;\rm mm$

Work Step by Step

Since we have two mediums, we need to use the formula of $$\dfrac{n_1}{s}+\dfrac{n_2}{s'}=\dfrac{n_2-n_1}{R}$$ where $n_1=n_{\rm air}=1$, and $n_2=n_{\rm aqueous~ humor}=1.34$. The author asks for the radius of curvature so we need to solve for $R$. $$R=\dfrac{n_2-n_1}{\left[\dfrac{n_1}{s}+\dfrac{n_2}{s'}\right]}$$ Now we can assume that $s=\infty$ when we are dealing with parallel rays coming. And since we need to focus these ryas in the humor, $s'=f$. $$R=\dfrac{n_2-n_1}{\left[\dfrac{n_1}{\infty}+\dfrac{n_2}{f}\right]}$$ Plugging the known; $$R=\dfrac{1.34-1}{\left[0+\dfrac{1.34}{3}\right]}=\bf 0.76\;\rm cm$$ $$R=\color{red}{\bf 7.6}\;\rm mm$$
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