A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.

Explanation

`(1)/(f_1)=(1)/(30)-(1)/(-15)=(1+2)/(30)`
`f_1=10cm`
`(1)/(F)=(1)/(60)-(1)/(-15)=(1+4)/(60)`
`F=12cm`
`(1)/(f_1)+(1)/(f_2)=(1)/(F)`
`(1)/(10)+(1)/(f_2)=(1)/(12)implies(1)/(f_2)-(1)/(10)=(5-6)/(60)`
`f_2=-60cm`
Focal length of concave lens `=60cm`