A concave mirror of radius of curvature $\displaystyle 16$ cm produces two-times enlarged real image of an object kept in front of it. Find the position of the object.

Given: $\displaystyle \mathrm{R}=-16 \mathrm{~cm}$ (concave mirror) \[\begin{aligned} m & =-\frac{\mathrm{v}}{\mathrm{u}}=-2 \\ \mathrm{v} & =2 \mathrm{u} \end{aligned} \] Now for concave mirror, \[\begin{aligned} & \mathrm{f}=-8 \mathrm{~cm}, \mathrm{v}=2 \mathrm{u}, \mathrm{u}=? \\ & \frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \end{aligned} \] \[\begin{aligned} & \frac{1}{2 \mathrm{u}}+\frac{1}{\mathrm{u}}=\frac{1}{-8} \\ & \frac{1+2}{2 \mathrm{u}}=\frac{1}{-8} \\ & \frac{2 \mathrm{u}}{3}=-8 \\ & \mathrm{u}=-\frac{24}{2}=-12 \mathrm{~cm} \\ & \therefore \mathrm{u}=-12 \mathrm{~cm} \end{aligned} \]