A glass slab of thickness 3cm and refractive index 1.5 is placed in front of a concave mirror of focal length 20cm. Where should a point object be placed if it is to image on to itself?

Explanation

The glass slab and the concave mirror are shown in Figure.
Let the distance of the object from the mirror be x.
We known that the slabe simply shifts the object. The shift being equal to `s=t[1-(1)/(mu)]=1cm`
The direction of shift is toward the concave mirror.
Therefore, the apparent distance of the object from the mirror is `x-1`
It the rays are to retrace their paths, the object should appear to be at the center of curvature of the mirror.
Therefore, `x-1=2f=40cm ` or `x=41 cm ` from the mirror.