Answer
12 cm
Work Step by Step
The magnification is -0.5.
Use the magnification to find the image distance. It is real so it is a positive number.
$$m=-0.5 = -\frac{d_i}{d_o}= -\frac{d_i}{18cm}$$
$$d_i=9.0cm$$
Use the mirror equation, 23–2.
$$\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}$$
Solve for the focal length.
$$f=\frac{d_od_i}{d_o+d_i}$$
$$=\frac{(18cm)(9.0cm)}{18cm+9.0cm}=6.0cm$$
The radius is twice the focal length, so r = 12 cm.
