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, at a distance of 60 cm behind the lens. Since, the mirror is at a distance of 10 cm from the lens, I 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` is formed at the object O itself, the rays after reflection from the mirror retraces its path, i.e., rays on the mirror are incident normally, i.e., I, is the centre of the mirror, so that `R=MI_1 = 50 `cm and hence `F=(R//2) = (50//2) = 25 `cm