A point object is placed `60 cm` in front of a convex lens of focal length `15 cm`. A plane mirror is placed `10 cm` behind the convex lens. Where is the image formed by the system ?

Answer

At optical centre of convex lens

Explanation

The given set up is shown in Fig. For the convex lens, `f = 15 cm, u = OC = - 60 cm`
From `(1)/(v) - (1)/(u) = (1)/(f)` , `(1)/(v) = (1)/(f) + (1)/(u) = (1)/(15) + (1)/(60) = (1)/(20)`
`v = 20 cm`

If plane mirror were not there, the lens would form a real image at `I_(1)`, where `CI_(1) = v = 20 cm`. Now, `I_(1)` would act as virtual object for plane mirror, where `I_(1)M = CI_(1) - CM = 20 - 10 = 10 cm`. Therefore, it will form the image at `10 cm` in front of the plane mirror. As `MC = CM = 10 cm`, thereofre, final image will be formed at `C`, the optical centre of convex lens.