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Power and Thin Lenses in Contact

Two plano-con...

Question

Two plano-convex lenses of focal lengths $f$ and $2 f$ are coaxially separated so that the spherical aberration is minimized. The effective focal length of the combination is :

A

f

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B

\frac{3 f}{2}

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C

\frac{3 f}{4}

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D

\frac{4 f}{3}

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Solution

The correct option is B $f$
$d = f_{2} - f_{1}$ $= 2 f - f = f$

$f_{e q} = \frac{f_{1} f_{2}}{f_{1} + f_{2} - d} = \frac{2 f \times f}{f + 2 f - f} = f$

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