Question

​A concave mirror of 10 m radius is to be used in solar cooker. How far must the cooker be placed from the optical centre of the mirror for it to receive maximum solar energy?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{To}\mathrm{receive}\mathrm{maximum}\mathrm{solar}\mathrm{energy},\mathrm{the}\mathrm{cooker}\mathrm{must}\mathrm{be}\mathrm{placed}\mathrm{at}\mathrm{the}\mathrm{focal} \\ \mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{mirror}. \\ \mathrm{Object}\mathrm{distance},\mathrm{u}=-\infty \\ \mathrm{Image}\mathrm{distance},\mathrm{v}=? \\ \mathrm{focal}\mathrm{length},\mathrm{f}=\frac{\mathrm{R}}{2},\mathrm{where}\mathrm{R}=\mathrm{radius}\mathrm{of}\mathrm{curvature} \\ \Rightarrow \mathrm{f}=\frac{10}{2}=5\mathrm{m} \\ \mathrm{From}\mathrm{mirror}\mathrm{formula}, \\ \frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\ \frac{1}{\mathrm{v}}+\frac{1}{\left(-\infty \right)}=\frac{1}{5} \\ \frac{1}{\mathrm{v}}=\frac{1}{5} \\ \mathrm{v}=5\mathrm{m} \\ \mathrm{The}\mathrm{cooker}\mathrm{must}\mathrm{be}\mathrm{placed}\mathrm{at}5\mathrm{m}\mathrm{from}\mathrm{the}\mathrm{optical}\mathrm{centre}\mathrm{of}\mathrm{the}\mathrm{mirror}. \end{gathered}$$