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Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The power of the combination is -
A
$\dfrac{f_1 + f_2}{2}$
B
$\dfrac{f_1 + f_2}{f_1 f_2}$
C
$\sqrt{\dfrac{f_1}{f_2}}$
D
$\sqrt{\dfrac{f_2}{f_1}}$
Detailed Solution
Power of a lens is the reciprocal of its focal length: $P = \dfrac{1}{f}$
For thin lenses in contact the powers add: $P = P_1 + P_2$
$P = \dfrac{1}{f_1} + \dfrac{1}{f_2}$
$P = \dfrac{f_2 + f_1}{f_1 f_2}$
So the power of the combination is $\dfrac{f_1 + f_2}{f_1 f_2}$.
For thin lenses in contact the powers add: $P = P_1 + P_2$
$P = \dfrac{1}{f_1} + \dfrac{1}{f_2}$
$P = \dfrac{f_2 + f_1}{f_1 f_2}$
So the power of the combination is $\dfrac{f_1 + f_2}{f_1 f_2}$.