Question

A beam of light converges to a point A. 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?

Answer 1

Given: A beam of light converges to a point A. A lens is placed in the path of the convergent beam 12 cm from P.

To find the point at which 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

Solution:

As per the given criteria,

the the object is virtual and the image is real (as the lens is placed in the path of the convergent beam)

(a) lens is a convex lens with

focal length, $f=20cm$

object distance, $u=12cm$

applying the lens formula, we get

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}⟹\frac{1}{v}=\frac{1}{f}+\frac{1}{u}⟹\frac{1}{v}=\frac{1}{20}+\frac{1}{12}⟹\frac{1}{v}=\frac{3+5}{60}⟹v=7.5cm$

Hence the image formed is real, at 7.5cm from the lens on its right side.

(b) lens is a concave lens with

focal length, $f=-16cm$

object distance, $12cm$

applying the lens formula, we get

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}⟹\frac{1}{v}=\frac{1}{f}+\frac{1}{u}⟹\frac{1}{v}=\frac{1}{-16}+\frac{1}{12}⟹\frac{1}{v}=\frac{-3+4}{48}⟹v=48m$

Hence the image formed is real, at 48 cm from the lens on the right side.