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Q.

A combination of two thin lenses with focal length f₁and f₂ 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 f₁ and f₂ are

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a

30 cm, –60 cm

b

20 cm, –30 cm

c

15 cm, –20 cm

d

20 cm, –15 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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A combination of two thin lenses with focal length f1 and f2 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 f1 and f2 are