Question

An object of height 5 cm forms its two times magnified image on a screen placed in front of a concave mirror of focal length 10 cm. find the distance at which the screen should be placed? Also find the nature of the image.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{m}=2 \\ \mathrm{f}=-10\mathrm{cm} \\ \mathrm{m}=-\frac{\mathrm{v}}{\mathrm{u}} \\ 2=-\frac{\mathrm{v}}{\mathrm{u}} \\ \mathrm{v}=-2\mathrm{u} \\ \frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\ \frac{1}{-2\mathrm{u}}+\frac{1}{\mathrm{u}}=\frac{1}{-10} \\ \frac{-1+2}{2\mathrm{u}}=-\frac{1}{10} \\ 2\mathrm{u}=-10 \\ \mathrm{u}=-5\mathrm{cm} \\ \mathrm{v}=-2\left(-5\right)=10\mathrm{cm} \\ \mathrm{Nature}\mathrm{of}\mathrm{image}\mathrm{is}\mathrm{virtual}\mathrm{and}\mathrm{erect} \end{gathered}$$