A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm, at a distance 50 cm apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.

The beam incident on lens L is parallel to principal axis. Hence the lens forms an image $I_1$at its focus. i.e., at a distance $O{I}_1(=20cm)$ from the lens.

The image $I_1$ is formed in front of the mirror and hence, acts as a real source for the mirror. The concave mirror forms the image $I_2$, whose distance from the mirror can be calculated as;

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

Here : $u=-30cm$, and $f=-10cm$

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

$\Rightarrow \frac{1}{v}=-\frac{1}{10}+\frac{1}{30}$

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

$\Rightarrow v=-15cm$

Hence, the final real image is formed at a distance of 15 cm in front of the concave mirror, as shown in the following figure.