A point object is placed at a distance of `12 cm` from a convex lens of focal length `10 cm.` On the other side of the lens, a convex mirror is placed at a distance of `10 cm` from the lens such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is

Explanation

For convex lens `1/v-1/(-12)=1/10`
i.e., v=60 cm i.e., in the absence of convex mirror. Convex lens will form the image `I_1` at a distance of 60cm behind the lens. Since the mirror is at a distance of 10cm from the lens `I_1` will be at a distance of 60-10=50 cm from the mirror, i.e., `MI_1=50 cm`

Now as the final image `I_2` s formed at the object O itself, the rays after reflection from the mirror retraces its path i.e., rays on the mirror are incident normallly i.e., `I_1` is the centre of the mirror , so that `R=MI_1=50 cm and ` hence `F=(R//2)=(50//2)=25 cm`