A combination of two thin lenses with focal lengths $f_{1} and f_{2}$ respectively forms an image of distant object at distance 60 cm when lenses are in contact. The position of this image shifts by 30 cm towards the combination when two lenses are separated by 10 cm. The corresponding values of $f_{1} and f_{2}$ are

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$30 cm, - 60 cm$

$20 cm, - 30 cm$

$15 cm, - 20 cm$

$12 cm, - 15 cm$

answer is B.

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Detailed Solution

$\frac{1}{60} = \frac{1}{f_{1}} + \frac{1}{f_{2}} and \frac{1}{30} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{10}{f_{1} f_{2}} On solving (i) and (ii) f_{1} f_{2} = - 600 and f_{1} + f_{2} = - 10 Hence f_{1} = 20 cm and f_{2} = - 30 cm$

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