Question

Two lenses kept together form image of an object placed at a distance of `15cm` from lenses at a distance of `80cm.`. If focal length of one lens is `20cm.`, what is the focal length of other lens?

Answer 1

Focal length of the lens `L_2` is `34.286` `cm`.

Explanation:

When we use two lenses of focal length `f_1` and `f_2` in conjunction, combined focal length `f` is given by `1/f=1/(f_1)+1/(f_2)`. Further, if `f` is the focal length of the lens, `u` is the distance of object and `v` is the distance of image from lenses, the relation between them is `1/f=1/u+1/v`

As the object is at a distance of `15` `cm` and image is at a distance of `80` `cm`, we have

`1/15+1/80=1/f`,

but `1/f=1/(f_1)+1/(f_2)` i.e. `1/f=1/20+1/(f_2)`, as focal length of first lens is `20`

and hence `1/15+1/80=1/20+1/(f_2)` and

`1/(f_2)=1/15+1/80-1/20=(16+3-12)/2407/240`

i.e. `f=240/7=34.286` `cm.`