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>> $Two plano - convex lenses of focal lengt$

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

$f$

B

$\frac{3 f}{2}$

C

$\frac{3 f}{4}$

D

$\frac{4 f}{3}$

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Solution

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Correct option is A)

$d = f_{2} - f_{1}$ $= 2 f - f = f$

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

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