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Q.

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is 2cm. The focal lengths of the component lenses

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a

18 cm, 20cm

b

10cm, 12cm

c

12cm, 14cm

d

16cm, 18cm

answer is A.

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Detailed Solution

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For minimum spherical aberration separation, $d = f_{1} - f_{2} = 2 c m$
Resultant focal length $= F = 10 c m$
Using $\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}}$ and solving, we get $f_{1}, f_{2}$ as 18 cm and 20 cm respectively.

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