Question

An object placed 50 cm from a lens produces a virtual image at a distance of 10 cm from the lens. Find the focal length of the lens and also state the type of the lens used.

Answer 1

Given,
$$\begin{gathered} \mathrm{Object}\mathrm{distance},\mathrm{u}=-50\mathrm{cm} \\ \mathrm{Image}\mathrm{distance},\mathrm{v}=-10\mathrm{cm}(\mathrm{virtual}\mathrm{image}\mathrm{is}\mathrm{formed}\mathrm{on}\mathrm{the}\mathrm{left}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{lens}) \\ \mathrm{Now},\mathrm{using}\mathrm{the}\mathrm{lens}\mathrm{formula}, \\ \frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\ \frac{1}{\mathrm{f}}=\frac{1}{(-10)}-\frac{1}{(-50)}=\frac{1}{-10}+\frac{1}{50}=\frac{-5+1}{50}=\frac{-4}{50} \\ \mathrm{or}\mathrm{f}=-\frac{50}{4}=-12.5\mathrm{cm} \\ \mathrm{Since}\mathrm{the}\mathrm{focal}\mathrm{length}\mathrm{is}\mathrm{negative},\mathrm{it}\mathrm{will}\mathrm{be}\mathrm{a}\mathrm{concave}\mathrm{lens}. \end{gathered}$$