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Power of a Lens

Two thin lens...

Question

Two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are placed in contact with each other. The focal length of the combination will be given by:

A

$\frac{f_{1} + f_{2}}{2}$

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B

\sqrt{f_{1} f_{2}}

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C

$\frac{f_{1} f_{2}}{f_{1} + f_{2}}$

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D

\frac{f_{1} f_{2}}{f_{1} - f_{2}}

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Solution

The correct option is C
$\frac{f_{1} f_{2}}{f_{1} + f_{2}}$

The power of a lens is defined as the reciprocal of its focal length (in metres). When there is a combination of two lenses in contact, the effective power of the combination is the sum of the individual powers.

Total Power, $P = P_{1}$ + $P_{2}$
$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
$f = \frac{f_{1} f_{2}}{f_{1} + f_{2}}$

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