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The focal length of the field lens (which is an achromatic combination of two lenses) of telescope is 90 cm. The dispersive powers of the two lenses in the combination are 0.024 and 0.036. The focal lengths of two lenses are

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30 cm and -45 cm

15 cm and 45 cm

30 cm and 60 cm

45 cm and 90 cm

answer is B.

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Detailed Solution

For achromatic combination

$\begin{array}{l} \frac{f_{1}}{f_{2}} = - \frac{ω_{1}}{ω_{2}} = - \frac{0 .036}{0 .024} = - \frac{3}{2} and \frac{1}{f_{1}} - \frac{1}{f_{2}} = \frac{1}{90} \\ Solving above equations we get f_{1} = 30 cm, f_{2} = - 45 cm \end{array}$

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