Question

using mirror formula, compute the position of an object placed in front of a concave mirror with focal length 'f' so that the image formed is of the same size as object.

Answer 1

Given,
Size of image, h' =Size of Object,h
$$\begin{gathered} \mathrm{m}=-\frac{\mathrm{v}}{\mathrm{u}}=\frac{\mathrm{h}\text{'}}{\mathrm{h}}=1 \\ \mathrm{or}\mathrm{v}=-\mathrm{u} \\ \mathrm{Now},\mathrm{using}\mathrm{the}\mathrm{mirror}\mathrm{formula}, \\ \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}} \\ \frac{1}{(-\mathrm{f})}=\frac{1}{(-\mathrm{u})}+\frac{1}{(-\mathrm{u})}=\frac{2}{(-\mathrm{u})} \\ [\mathrm{Object}\mathrm{distance}\mathrm{is}\mathrm{always}\mathrm{taken}\mathrm{negative}\mathrm{and}\mathrm{the}\mathrm{focal}\mathrm{length}\mathrm{for}\mathrm{a}\mathrm{concave}\mathrm{mirror}\mathrm{is}\mathrm{negative}) \\ \mathrm{or}\mathrm{u}=2\mathrm{f} \\ \mathrm{Thus},\mathrm{the}\mathrm{object}\mathrm{is}\mathrm{placed}\mathrm{at}\mathrm{a}\mathrm{distance}\text{'}2\mathrm{f}\text{'}\mathrm{i}.\mathrm{e}.\mathrm{at}\mathrm{the}\mathrm{centre}\mathrm{of}\mathrm{curvature}. \end{gathered}$$