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Power of a Lens

Two thin lens...

Question

Two thin lenses of focal lengths, $f_{1}$ and $f_{2}$ are in contact and coaxial. The combination is equivalent to a single lens of power:

A

f_{1} + f_{2}

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B

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

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C

\frac{1}{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 D $\frac{f_{1} + f_{2}}{f_{1} f_{2}}$
The effective power of two lenses in contact is the sum of their individual powers.
$P = P_{1} + P_{2}$

Now, power is equal to the inverse of the focal length. So,
$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
$f = \frac{f_{1} f_{2}}{f_{1} + f_{2}}$

Power of lens is:
$P = \frac{1}{f}$
$P = \frac{f_{1} + f_{2}}{f_{1} f_{2}}$

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