A convex lens of focal length 10cm is placed 30 cm in front of a second convex lens also of th esame focal length. A plane mirror is placed after the two lenses. Where should a point object be placed in front of the first lens so that it imagees on to itself?

Explanation

The convex lenses and the plane mirror as shown in figure.
The combination behaves like a concave mirror.
Let the distance of the object from the first lens be x.
For the ray to retrace its path, it should be incident normally on the plane mirror.
Form the diagrm, we see that for lens `L_(2)`
`v=oo, f=+10cm, u=?`
Form the lens equation, we get
`(1)/(v)-(1)/(u)=(1)/(f)` or `u=-10cm`
From the diagram, we see that for lens `L_(1)`
`v=30-10=20cm, f=+10cm, u=-x`
From the lens equation, we get
`(1)/(v)-(1)/(u)=(1)/(f)` or `(1)/(20)-(1)/(-x)=(1)/(10)` or `x=20cm`