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A combination of two thin lenses with focal length $f_{1}$ and $f_{2}$ respectively forms an image of distant object at distane 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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20 cm, –30 cm

15 cm, –20 cm

20 cm, –15 cm

30 cm, –60 cm

answer is B.

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Detailed Solution

$\frac{1}{60} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$ ...(i)

$\frac{1}{30} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{10}{f_{1} f_{2}}$ ...(ii)

on solving (i) and (ii)

$f_{1} = 20 cm and f_{2} = - 30 cm$

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