A point object is placed at a distance of 12 cm on the axis of 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. What is the focal length of convex mirror?

For convex lens, $\frac{1}{\mathrm{v}}-\frac{1}{-12}=\frac{1}{10}\text{; i.e., }\mathrm{v}=60\mathrm{cm}$
i.e., in the absence of convex mirror, convex lens will form the image I₁ at a distance of 60 cm behind the lens. Since, the mirror is at a distance of 10 cm from the lens, I₁ will be at a distance of 60 – 10 = 50 cm from the mirror, i.e., MI₁ = 50 cm.

Now as the final image I₂ 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., I₁ is the centre of the mirror, so that
R = MI₁ = 50 cm and hence F = (R/2) = (50/2) = 25 cm