Question

A diverging lens of focal length 20 cm and a converging mirror of focal length 10 cm are placed coaxially at a separation of 5 cm. Where should an object be placed so that a real image is formed at the object itself?

Answer 1

Let the object to placed at a distance x from the lens further away from the mirror.
For the concave lens (1st refraction)

So, the virtual image due to fist refraction lies on the same side as that of object. (A'B') This image becomes the object for the concave mirror. For the mirror,

So, this image is formed towards left of the mirror.
Again forsecond refraction in concave lens,

(assuming that image of mirror is formed between the lens and mirro)

v = +x (Since, the final image is produced on the object)
Using lens formula,

The object should be placed at a distance 60 cm from the lens further away from the mirror.
So that the final image is formedon itself.