Question

A convex lens of focal length 20cm is placed 10cm in front of a convex mirror or radius of curvature 15cm. Where should a point object be placed in front of the lens so that it images on to itself?

Answer 1

The convex lens and the convex mirror are shown in Figure.
The combination behaves like a concave mirror.
Let the distance of the object from the lens be x.
For the ray to retrace its path, it should be incident normally on the convex mirror, or in other words the rays shold pass through the center of curvature of the mirror.
From the diagram, we see that for the lens
`u=-x, f=+20cm, v=+10+15=+25 cm`
From the lens equation, we get
`(1)/(v)-(1)/(u)=(1)/(f)` or `(1)/(25)-(1)/(-x)=(1)/(20)` or `x=100 cm`