Answer
(a) concave
(b) $7.34m$
(c) $16.4m$
Work Step by Step
(a) We know that the image formed by the concave mirror is upright and enlarged. Moreover, the image is virtual, since it is on the same side of the lens as the object. Thus, the mirror must be concave.
(b) We know that
$d_i=-(\frac{h_i}{h_{\circ}})d_{\circ}$
$d_i=-(\frac{2.74m}{0.50m})(3.0m)=-16.4m$
As $\frac{1}{f}=\frac{1}{d_{\circ}}+\frac{1}{d_i}$
$\frac{2}{R}=\frac{1}{d_{\circ}}+\frac{1}{d_i}$
We plug in the known values to obtain:
$\frac{2}{R}=\frac{1}{3.0m}+\frac{1}{-16.4m}$
This simplifies to:
$R=7.34m$
(c) We know that
$d_i=-(\frac{h_i}{h_{\circ}})d_{\circ}$
We plug in the known values to obtain:
$d_i=-(\frac{2.74m}{0.50m})(3.0m)=-16.4m$
The negative sign shows that the image is formed behind the mirror.
