Question

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.

Answer 1

As a lens is placed in the path of the convergent beam, the point $P$ would lie on the right of the lens and acts as a virtual object.

Object distance, $u=12cm$

(a) Focal length, $f=20cm$ (Convex Lens)

Using the lens formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

we have,

$\frac{1}{20}=\frac{1}{v}-\frac{1}{12}$

$\frac{1}{v}=\frac{1}{20}+\frac{1}{12}=\frac{3+5}{60}=\frac{8}{60}$

$\Rightarrow v=\frac{60}{8}=7.5cm$

It is located at $7.5cm$ from the lens and it is a real image.

(b) Focal length, $f=-16cm$ (Concave Lens)

Applying lens formula, we have

$\frac{1}{-16}=\frac{1}{v}-\frac{1}{12}$

$\frac{1}{v}=\frac{-1}{16}+\frac{1}{12}=\frac{-3+4}{48}=\frac{1}{48}$

$\Rightarrow v=48cm$

It is located at $48cm$ from the lens and it is a real image.