Question

A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

Answer 1

Let us first locate the image of the point object $O$ formed by the convex lens.

Here : $u=-60$ cm and $f=20$cm

From the lens formula, we have :

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

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

=$\frac{1}{20}+\frac{1}{-60}=\frac{3-1}{60}=\frac{2}{60}=\frac{1}{30}$

$v=+30$ cm

The positive sign indicates that the image is formed at the right of the lens.


The image $I_1$ is formed behind the mirror and acts as a virtual source for the mirror. The convex mirror forms the image $I_2$, whose distance from the mirror can be determined as :

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

Here,

$u=15$ cm

and, $f=\frac{R}{2}=10$cm

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

$\Rightarrow \frac{1}{v}=\frac{1}{10}-\frac{1}{15}$

$\Rightarrow \frac{1}{v}=\frac{3-2}{30}=\frac{1}{30}$

$\Rightarrow v=30$ cm

Hence, the final virtual image is formed at a distance of 30 cm from the convex mirror.