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A convex lens of focal length 63 cm and dispersive power 0.21 is kept in contact with another lens of dispersive power 0.50 in order to make an achromatic doublet. The focal length of second lens is

A

50cm

B

63 cm

C

-126cm

D

-150 cm

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Solution

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Correct option is D)

For achromatic doublet:

$\frac{w _{1}}{f _{1}} + \frac{w _{2}}{f _{2}} = 0$

$\frac{0 . 2 1}{6 3} + \frac{0 . 5 0}{f _{2}} = 0$

$f_{2} = - \frac{0 . 5 0 \times 6 3}{0 . 2 1}$

$= - 150 c m$

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