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Find the equivalent focal length of a combination of two convex lenses in contact, the focal length of each of them being 30 cm.

Asked in GUJCET 2021 · Combinations and silvered lenses

• (1) 15 cm
• (2) 30 cm
• (3) 20 cm
• (4) 40 cm

Step-by-step solution

Why the other options are wrong

• (2) comes from leaves one lens's focal length unchanged. Two lenses in contact carry twice the power, P=2×1/(0.30)=6.67 D, so the pair is stronger and its focal length is shorter than 30 cm.
• (3) No route gives 20 cm. Sanity check: 1/F=1/(30)+1/(30)=1/(15).
• (4) 40 cm is longer than either lens, so the pair would be weaker than one lens alone — the opposite of what contact does. Even the common wrong route F=f₁+f₂ gives 60 cm.

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