## Fundamentals of Physics Extended (10th Edition)

Published by Wiley

# Chapter 34 - Images - Problems: 11b

#### Answer

$i=-4.4cm$

#### Work Step by Step

"The distance between the focal point and the mirror" is defined as the focal length. Since the mirror is convex, the value of the focal length is negative. Therefore, the focal length is $-10cm$. To find the image distance, use the formula $$\frac{1}{f}=\frac{1}{p}+\frac{1}{i}$$ Solving for $i$ yields $$\frac{p}{pf}-\frac{f}{pf}=\frac{1}{i}$$ $$\frac{p-f}{pf}=\frac{1}{i}$$ $$i=\frac{pf}{p-f}$$ Substituting values of $f=-10cm$ and $p=+8.0cm$ yields $$i=\frac{(8.0cm)(-10cm)}{8.0cm+10cm}=-4.4cm$$

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