## Fundamentals of Physics Extended (10th Edition)

$p=180cm$
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 $$p=(-20cm)(\frac{0.10-1.00}{0.10})=180cm$$