The radius of concave surface is 20 cm and radius of convex surface is 10 cm. The refractive index of material of lens is 1.5. If image of point object P coincides with it. Find the distance (in cm) between object and lens.

$\begin{array}{l}For pure lens, \\ \frac{1}{f_1}=(1.5-1)(-\frac{1}{20}+\frac{1}{10})=\frac{1}{2}\left(\frac{-1+2}{20}\right)=\frac{1}{40}\\ \therefore P_1=\frac{1}{40}\\ and \\ For pure mirror, \\ P_m=\frac{1}{f_m}=\frac{1}{-5}\\ Combination of lens and mirror\\ \therefore P=P_m - 2P_1=-\frac{1}{5}-\frac{1}{20}=\frac{-1-4}{20} = \frac{-1}{4}\\ So, equivalent mirror is concave mirror of focal length 4 cm.\\ Hence, object should be at the centre of curvature of equivalent concave mirror i.e 8 cm\\ \end{array}$