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

In the given situation, the object is virtual and the image formed is real.
Object distance, u=`+12cm`.
a) Focal length of the convex lens, f=20cm
Image distance = v
According to the lens formula, we have the relation:
`1/v-1/u=1/f`
`1/v-1/12=1/20`
`1/v=1/20+ 1/12=(3+5)/(60)= 8/60`
`therefore v=60/8=7.5 cm`
Hence, the image is formed 7.5 cm away from the lens, towards its right.
b) Focal length of the concave lens, f=`-16cm`
Image distance=v
According to the lens formula, we have the relation:
`1/v-1/u=1/f`
`1/v=-1/16+1/12=(-3+4)/(48) = 1/48`
`therefore v=48cm`
Hence, the image is formed 48 cm away from the lens, towards its right.