Answer
$f=3.2cm$
Work Step by Step
Use the magnification equation $$m=-\frac{i}{p}$$ to solve for $i$: $$i=-mp$$ Substitute this expression into the lens equation: $$\frac{1}{f}=\frac{1}{i}+\frac{1}{p}$$ $$\frac{1}{f}=\frac{1}{p}-\frac{1}{mp}$$ Solve for $f$: $$\frac{1}{f}=\frac{m}{mp}-\frac{1}{mp}$$ $$\frac{1}{f}=\frac{m-1}{mp}$$ $$f=\frac{mp}{m-1}$$ Substituting known values of $m=-0.25cm$ and $p=16cm$ yields a focal length of: $$f=\frac{(-0.25)(16cm)}{-0.25-1}=3.2cm$$
