A beam of light converges at a point P. Now 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, and (b) a concave lens of focal length 16 cm ?

Explanation

Here the object is virtual and the image is real `mu=+12` cm (object on right and virtual )
a) `f=+20cm`
Lens formula is `(-1)/(u)+(1)/(upsilon)=(1)/(f)`

`(1)/(upsilon)=(1)/(f)+(1)/(u)`
`=(1)/(20)+(1)/(12)=(2)/(15)`
i.e. u = 7.5 cm (image on right and real ) It is located 7.5 cm from the lens.
b) f = -16 cm

`(1)/(upsilon)=-(1)/(16)+(1)/(12)=(1)/(48)`
`upsilon = 48 cm`
Image will be located 48 cm from the lens.