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

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

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Answer 1 · 2017-03-02T13:45:43

Focal length of the lens $L_{2}$ $L_2$ is $34.286$ $34.286$ $c m$ $cm$ .

Explanation:

When we use two lenses of focal length $f_{1}$ $f_1$ and $f_{2}$ $f_2$ in conjunction, combined focal length $f$ $f$ is given by $\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$ $1/f=1/(f_1)+1/(f_2)$ . Further, if $f$ $f$ is the focal length of the lens, $u$ $u$ is the distance of object and $v$ $v$ is the distance of image from lenses, the relation between them is $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ $1/f=1/u+1/v$

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

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

but $\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$ $1/f=1/(f_1)+1/(f_2)$ i.e. $\frac{1}{f} = \frac{1}{20} + \frac{1}{f_{2}}$ $1/f=1/20+1/(f_2)$ , as focal length of first lens is $20$ $20$

and hence $\frac{1}{15} + \frac{1}{80} = \frac{1}{20} + \frac{1}{f_{2}}$ $1/15+1/80=1/20+1/(f_2)$ and

$\frac{1}{f_{2}} = \frac{1}{15} + \frac{1}{80} - \frac{1}{20} = \frac{16 + 3 - 12}{2407} / 240$ $1/(f_2)=1/15+1/80-1/20=(16+3-12)/2407/240$

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

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

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Two lenses kept together form image of an object placed at a distance of 15cm15cm from lenses at a distance of 80cm.80cm.. If focal length of one lens is 20cm.20cm., what is the focal length of other lens?

1 Answer

Explanation:

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