Answer
a. 12 cm
b. 18 cm
c. Inverted
Work Step by Step
a. The focal length is half the radius of curvature.
$$f=\frac{1}{2}r=\frac{1}{2}(24cm)=12cm$$
b. Use the mirror equation, 23–2.
$$\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}$$
Solve for the image distance.
$$d_i=\frac{d_of}{d_o-f}=\frac{(38cm)(12cm)}{38cm-12cm}$$
$$=17.54cm\approx 18cm$$
The image is located 18 cm in front of the mirror.
c. Calculate the magnification.
$$m=-\frac{d_i}{d_o}=-\frac{17.54cm}{38cm}=-0.46$$
The magnification is negative. The image is inverted.