Fig. shows a plane mirror `M` placed at a distance of `10 cm` from a concave lens `L`. A point object is placed at a distance of `60 cm` from the lens. The image formed due to refraction by the lens and reflection by the mirror is `30 cm` behind th mirror. What is the focal length of this lens ?
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Answer

`- 30 cm`

Explanation

The given set up is shown in Fig. Here
`CM = 10 cm. u = CO = - 60 cm , f = ?`

The ray starting from `O`, diverge on passing through concave lens, get reflected from the mirror, would form image at `I_(1)`, where `MI_(1) = 30 cm`. The corresponding position of object from the mirror will be at `I` where `MI = MI_(1) = 30 cm`. Therefore, `CI = MI - MC = 30 - 10 = 20 cm`. `I` is the position of object for plane mirror. This must also be position of virtual image of object formed by concave lens alone. Therefore, for lens,
`v = CI = - 20 cm`.
From `(1)/(f) = (1)/(v) - (1)/(u)` ,
`(1)/(f) = (1)/(-20) + (1)/(60) = -(2)/(60) = -(1)/(30)`
`:. f = - 30 cm`.