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.

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.