A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens, a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coinciding with it

50 cm

For lens u = 30 cm, f = 20 cm, hence by using $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ we have

$\frac{1}{+20}=\frac{1}{v}-\frac{1}{-30}$ ⇒ v = 60 cm

The final image will coincide with the object, if light ray falls normally on convex mirror as shown.

From the figure it is clear that gap between lens and mirror is 60 – 10 = 50 cm.