Two thin lenses of focal length $f_{1}$ and $f_{2}$ are in contact and coaxial. The power of the combination is __________.

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

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

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

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

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Solution

The correct option is D $\frac{f_{1} + f_{2}}{f_{1} f_{2}}$
Power of the lens is given by $P = \frac{1}{f}$
where $f$ is the focal length of the lens.
Thus we get $P_{1} = \frac{1}{f_{1}}$ and $P_{2} = \frac{1}{f_{2}}$
Power of combination of lenses $P = P_{1} + P_{2}$
$⟹ P = \frac{1}{f_{1}} + \frac{1}{f_{2}} = \frac{f_{1} + f_{2}}{f_{1} f_{2}}$
Correct answer is option D.

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