Answer
-6.8 m
Work Step by Step
The object distance is 3.4 m. The magnification is +0.5. 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.
$$f=\frac{d_od_i}{d_o+d_i}=\frac{d_o(-md_o)}{d_o-md_o}$$
$$=\frac{(3.4m)(-(0.5)3.4m)}{3.4m-0.5(3.4m)}=-3.4m$$
The radius is twice the focal length, or -6.8m.
