Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 34 - Images - Problems: 22d

Answer

$p=180cm$

Work Step by Step

First, use the magnification equation $$m=-\frac{i}{p}$$ to solve for i. $$i=-pm$$ Substitute this into the lens equation. $$\frac{1}{f}=\frac{1}{p}+\frac{1}{i}$$ $$\frac{1}{f}=\frac{1}{p}-\frac{1}{pm}$$ Rearrange the equation to solve for $p$. $$\frac{1}{f}=\frac{m}{pm}-\frac{1}{pm}$$ $$\frac{1}{f}=\frac{m-1}{pm}$$ $$p=f(\frac{m-1}{m})$$ Substitute known values of $m=0.10$ and $f=20cm$ to get an object distance $p$ of $$p=(-20cm)(\frac{0.10-1.00}{0.10})=180cm$$
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