A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is :

$\begin{array}{l}\text{ Given }R=30\mathrm{cm}\\ f=R/2=+15\mathrm{cm}\end{array}$

Magnification (m) = $\pm \frac{1}{2}$

For convex mirror, virtual image is formed for real object. 

Therefore, m is +ve. 

$\begin{array}{l}\frac{1}{2}=\frac{f}{f-u}\\ u=-15\mathrm{cm}\end{array}$