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.

For pure lens,  1f1=(1.5−1)(−120+110)=12(−1+220)=140 ∴P1=140and   For pure mirror,  Pm=1fm=1−5  Combination of lens and mirror ∴P=Pm − 2P1=−15−120=−1−420 = −14 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