Answer
5.7 m
Work Step by Step
The object distance is 1.9m. The magnification is +3. 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.
$$f=\frac{d_od_i}{d_o+d_i}=\frac{d_o(-md_o)}{d_o-md_o}$$
$$=\frac{(1.9m)(-(3)1.9m)}{1.9m-3(1.9m)}=2.85m$$
The radius is twice the focal length, or $r = 5.7 m$.