Find the two possible positions of an object kept in front of a lens of +5.0 D, so that the image formed in both cases is four times magnified.

Power of lens = +$\displaystyle 5$ D Focal length of lens $\displaystyle =\frac{100}{5}=20 \mathrm{~cm}$ Magnification , $\displaystyle \mathrm{m}= \pm 4$ Case $\displaystyle \mathbf{I}, \mathrm{m}=4=\frac{\mathrm{v}}{\mathrm{u}} \quad \therefore \mathrm{v}=4 \mathrm{u}$ $$\begin{aligned} & \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ & \frac{1}{20}=\frac{1}{4 u}-\frac{1}{u} \\ & u=-15 \mathrm{~cm} \end{aligned} $$ Case II, $\displaystyle \mathrm{m}=-4=\frac{\mathrm{v}}{\mathrm{u}} \quad \therefore \mathrm{v}=-4 \mathrm{u}$ $$\begin{aligned} & \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ & \frac{1}{20}=\frac{1}{-4 u}-\frac{1}{u} \\ & u=-25 c m \end{aligned} $$