Answer
Convex; -16 m.
Work Step by Step
The mirror is convex. Concave mirrors don’t produce images that are upright and smaller than the object.
The object distance is 16.0 m. The magnification is +0.33. 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.
$$f=\frac{d_od_i}{d_o+d_i}=\frac{d_o(-md_o)}{d_o-md_o}$$
$$=\frac{(16.0m)(-(0.33)16.0m)}{16.0m-0.33(16.0m)}=-7.881m$$
The negative focal length f confirms that the mirror is indeed convex.
The radius is twice the focal length, or $r=-16m$.
