Answer
$f=3.3cm$
Work Step by Step
Use the magnification equation $$m=-\frac{i}{p}$$ to solve for $i$; $$i=-mp$$ Substitute this equation into the lens equation and simplify: $$\frac{1}{f}=\frac{1}{p}+\frac{1}{i}$$ $$\frac{1}{f}=\frac{1}{p}-\frac{1}{mp}$$ $$\frac{1}{f}=\frac{m}{mp}-\frac{1}{mp}$$ $$\frac{1}{f}=\frac{m-1}{mp}$$ $$f=\frac{mp}{m-1}$$ Substitute known values of $m=-0.50$ and $p=10cm$ to get a focal length of $$f=\frac{(-0.50)(10cm)}{-0.50-1.00}=3.3cm$$
