The dispersive powers of crown and flint glasses are 0.2 and 0.4 respectively. A lens of crown glass and a lens of flint glass are combined to form an achromatic doublet of focal length 20cm. Then focal lengths of the two lenses are

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10 cm, 20 cm

20 cm, 10 cm

20 cm, -10 cm

10 cm, -20 cm

answer is C.

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Detailed Solution

$w_{1} = 0.2, w_{2} = 0.4 f = 20$ cm

$\frac{w_{1}}{f_{1}} = - \frac{w_{2}}{f_{2}}$

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

$o .4 f_{1} = - 0.2 f_{2} f_{2} = - 2 f_{1}$

$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$

$\frac{1}{20} = \frac{1}{f_{1}} - \frac{1}{2 f_{1}} = \frac{2 - 1}{2 f_{1}} = + \frac{1}{2 f_{1}}$

$2 f_{1} = + 20$ cm $\Rightarrow f_{1} = 10$ cm

$f_{2} = - 2 \times 10 = - 20$ cm

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