# 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?

Mar 2, 2017

Focal length of the lens ${L}_{2}$ is $34.286$ $c m$.

#### Explanation:

When we use two lenses of focal length ${f}_{1}$ and ${f}_{2}$ in conjunction, combined focal length $f$ is given by $\frac{1}{f} = \frac{1}{{f}_{1}} + \frac{1}{{f}_{2}}$. 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 $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

As the object is at a distance of $15$ $c m$ and image is at a distance of $80$ $c m$, we have

$\frac{1}{15} + \frac{1}{80} = \frac{1}{f}$,

but $\frac{1}{f} = \frac{1}{{f}_{1}} + \frac{1}{{f}_{2}}$ i.e. $\frac{1}{f} = \frac{1}{20} + \frac{1}{{f}_{2}}$, as focal length of first lens is $20$

and hence $\frac{1}{15} + \frac{1}{80} = \frac{1}{20} + \frac{1}{{f}_{2}}$ and

$\frac{1}{{f}_{2}} = \frac{1}{15} + \frac{1}{80} - \frac{1}{20} = \frac{16 + 3 - 12}{2407} / 240$

i.e. $f = \frac{240}{7} = 34.286$ $c m .$