Answer
The focal length is 2.677 cm and the radius is 5.3 m.
Work Step by Step
The object distance is 2.00 cm. The magnification is +4. Find the image distance, then the focal length.
$$m=-\frac{d_i}{d_o}$$
$$d_i=-md_o$$
Use the mirror equation, 23–2.
$$\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}$$
Solve for the focal length.
$$f=\frac{d_od_i}{d_o+d_i}=\frac{d_o(-md_o)}{d_o-md_o}$$
$$=\frac{(2.0cm)(-(4)2.0cm)}{2.0cm-4(2.0cm)}=2.677cm$$
The radius is twice the focal length, or 5.3 cm.
The focal length is positive, so the mirror is concave, aka a converging mirror.
