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

Here the object is virtual.
Given, object distance, `u=+12cm` (object is one the right side of the lens)
(a) For lens of focal length, `f=+20cm`
Using lens formula, we get
`(1)/(v)-(1)/(u)=(1)/(f)`

`(1)/(v)=(1)/(f)+(1)/(u)`
`=(1)/(20)+(1)/(12)=(2)/(15)`
`rArr v=7.5cm`, i.e. the image on the right side of the lens and is real. It is located 7.5 cm from the lens.
(b) For lens of focal length, `f=-16cm`

`(1)/(v)=-(1)/(16)+(1)/(12)`
`=(1)/(48)`
`rArr v=48cm`, i.e. image on the right side of the lens and is real. It is located 48 cm from the lens.