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 the refraction at the convex lens, we have
u = -12cm,v = ? f = +10 cm
Using leens formula
`1/v -1/(-12) =1/10`
or, v=+60cm
Thus, in the absence of the convex mirror, convex lens will form the image, at a distance of 60 cm behind the lens. As the mirror is at a distance of 10 cm from the lens, it will be at a distance of (60 - 10) = 50 cm from the mirror. Now, as the final image is formed at the object itself, the rays after reflection from the mirror retraces its path, i.e., the rays on the mirror are incident normally
R=+50cm and `f=R/2=50/2=+25cm`