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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

Asked in JEE Main Online 2018 · Combinations and silvered lenses

• (1) 18 cm, 20 cm
• (2) 12 cm, 14 cm
• (3) 16 cm, 18 cm
• (4) 10 cm, 12 cm

Step-by-step solution

Why the other options are wrong

• (2) Only checks f₂ - f₁ = d; these give F = (12 × 14)/(24) = 7 cm, not 10 cm.
• (3) Only checks f₂ - f₁ = d; these give F = (16 × 18)/(32) = 9 cm.
• (4) Only checks f₂ - f₁ = d; these give F = (10 × 12)/(20) = 6 cm.

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