Consider the situation described in the previous problem. Where should a point source be placed on the principal axis so that the two images form at the same place?

Convex lens of focal length, = 15cm

Concave mirror of focal length, = 10 cm

Distance between the lens and mirror = 50cm

Two images will be formed: One due to direct transmission of light through the lens and another due to the reflection and then transmission of the rays through the lens.

Let the source be placed at a distance ‘x’ from the lens as shown, so that images formed by both coincide. By using lens formula,

For the mirror, object distance, u= 50-x

By using mirror formula,

Since, the distance between lens and mirror is 50cm, hence we can write

Solving for x, we get, x= 30cm

So, the source should be placed 30 cm from the lens.