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

1. 18 cm, 20 cm
2. 10 cm, 12 cm
3. 12 cm, 14 cm
4. 16 cm, 18 cm

Correct answer: 18 cm, 20 cm

Solution

For separated lenses, 1/F = 1/f1 + 1/f2 - d/(f1*f2). Testing f1=18, f2=20 cm with d=2: 1/18 + 1/20 - 2/360 = 0.1000, giving F = 10 cm. So the component focal lengths are 18 cm and 20 cm.

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