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 693: 75

Answer

$13.3\;\rm cm$

Work Step by Step

We know, for thin lenses, that $$\dfrac{1}{s}+\dfrac{1}{s'}=\dfrac{1}{f}$$ where $f=R/2$ $$\dfrac{1}{s}+\dfrac{1}{s'}=\dfrac{2}{R}\tag 1$$ We are given that the image is 3 times the object and an upright one, so $$m=-\dfrac{s'}{s}=3$$ Hence, $$s'=-3s$$ Plugging into (1), $$\dfrac{1}{s}+\dfrac{1}{-3s}=\dfrac{2}{R} $$ $$ \dfrac{-3+1}{-3s}=\dfrac{2}{3s}=\dfrac{2}{R} $$ Thus, $$s=\dfrac{R}{3}=\dfrac{40}{3}$$ $$s=\color{red}{\bf 13.3}\;\rm cm$$
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