The figure below shows the positions of a point object 0, two lenses, a plane mirror and the final image I which coincides with the object. The focal length of the convex lens is 20 cm. Calculate the focal length of the concave lens.

Explanation

For convex lenses `(1)/(f)=(1)/(v)-(1)/(u)`
`(1)/(20)=(1)/(v)+(1)/(45)`
`(1)/(v)=(1)/(20)-(1)/(15)`
`v=(20xx45)/(25)=36 cm`
So .u. for concave lens = 36-16 = 20 cm
For concave lens `(1)/(f)=(1)/(v)-(1)/(u)`
`(1)/(f)=(1)/(oo)-(1)/(20)`
`f=-20 cm`
So, focal length of concave lens =--20 cm.