## Fundamentals of Physics Extended (10th Edition)

$i=-72cm$
"The distance between the focal point and the mirror" is defined as the focal length. Since the mirror is concave, the value of the focal length is positive. Therefore, the focal length is $36cm$. 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 $f=36cm$ and $p=+24cm$ yields $$i=\frac{(24cm)(36cm)}{24cm-36cm}=-72cm$$