The radius of curvature of a convex mirror is 30 cm. It forms an image of an object which is half the size of the object. Find the separation between…

$\displaystyle m=-\frac{v}{u}=\frac{h_{I}}{h_{O}}=\frac{1}{2}$ $\displaystyle u=-2 v$ $\displaystyle \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ $\displaystyle \frac{1}{15}=\frac{1}{v}-\frac{1}{2 v}$ On solving: $\displaystyle v=7.5 \mathrm{~cm}$ $\displaystyle u=+15.0 \mathrm{~cm}$ Separation $\displaystyle =15.0+7.5=22.5 \mathrm{~cm}$