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A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ₁ and μ₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

Asked in NEET 2013 · Combinations and silvered lenses

• (1) R/(2(μ₁+μ₂))
• (2) R/(2(μ₁-μ₂))
• (3) R/(μ₁-μ₂)
• (4) (2R)/(μ₂-μ₁)

Step-by-step solution

Why the other options are wrong

• (1) comes from adds the two indices where the powers subtract, and halves as well; it is the difference that survives, because the two -1 terms cancel
• (2) comes from has the right difference but an extra factor of 2; each lens brings one curved surface to the pair, not two
• (4) comes from inverts the difference and doubles R; the order of μ₁ and μ₂ decides whether the pair converges or diverges, so it cannot be swapped

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