Question

An object is placed infront of a concave mirror of focal length 30 cm. The virtual image of the object is obtained at a distance 20 cm from the mirror. Calculate the position of the object.

Answer 1

$$\begin{gathered} \mathrm{Mirror}\mathrm{formula}: \\ \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}} \\ \mathrm{Here},\mathrm{u}\mathrm{is}\mathrm{object}\mathrm{distance},\mathrm{v}\mathrm{is}\mathrm{image}\mathrm{distance},\mathrm{and}\mathrm{f}\mathrm{is}\mathrm{focal}\mathrm{length} \\ \mathrm{Hence}, \\ \frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}-\frac{1}{\mathrm{v}} \\ =\frac{1}{-30}-\frac{1}{20} \\ =\frac{-50}{600} \\ =-\frac{1}{12} \\ \mathrm{So}, \\ \mathrm{Object}\mathrm{distance},\left|\mathrm{u}\right|=12\mathrm{cm} \\ \mathrm{Position}\mathrm{of}\mathrm{the}\mathrm{object}:12\mathrm{cm}\mathrm{from}\mathrm{the}\mathrm{mirror} \end{gathered}$$