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>> $Two plano convex lenses of focal lengths$

Question

Two plano convex lenses of focal lengths $f_{1}$ and $f_{2}$ set for minimising spherical aberration are kept apart by 2 cm. If the equivalent focal length of combination is 10 cm, the values of $f_{1}$ and $f_{2}$ are :

A

$18 c m, 16 c m$

B

$18 c m, 20 c m$

C

$20 c m, 22 c m$

D

$14 c m, 20 c m$

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Solution

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Correct option is B)

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

$\Rightarrow f_{2} - f_{1} = 2$ $\Rightarrow f_{2} = 2 + f_{1}$

$f_{e q} = \frac{f _{1} f _{2}}{f _{1} + f _{2} - d} = \frac{f _{1} f _{2}}{f _{1} + f _{2} - 2} = 10$

$\frac{( f _{1} ) ( 2 \times f _{1} )}{( 2 f _{1} )} = 10$

$2 + f_{1} = 20$

$f_{1} = 18 c m$

$f_{2} = 2 + f_{1} = 20 c m$

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