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Two plano-convex lenses of same material and of focal lengths $f$ and $2 f$ are coaxially separated by a suitable distace to minimize chromatic aberration. The equivalent focal length of the combination is

A

$f$

B

$3 f / 2$

C

$3 f / 4$

D

$4 f / 3$

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Solution

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Correct option is D)

$d = \frac{f _{2} + f _{1}}{2} = \frac{2 f + f}{2} = \frac{3 f}{2}$

$f_{e q} = \frac{f \times 2 f}{\frac{- 3 f}{2} + 2 f + f} = \frac{2 f ^{2}}{\frac{3 f}{2}} = \frac{4 f}{3}$

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