A beam of light converges to a point P. A lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm. (b) a concave lens of focal length 16 cm.

Explanation

(i) Object is virtual Focal length of convex lens `f=+20cm`
`u=+12cm`
`"Using "(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)-(1)/(12)=(1)/(20)`
`rArr" "v=(60)/(8)=7.5cm`
The image is 7.5 cm from the lens and towards the right.
(ii) Focal length of concave lens `f=-16cm`
`u=+12cm`
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)=(1)/(f)+(1)/(u)=(-1)/(16)+(1)/(12)`
`rArr" "v=48cm`
The image is 48 cm away from the lens and towards the right.