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What is the focal length of the combination of a convex lens of focal length 30 cm in contact with a concave lens of focal length 10 cm? [Ignore thickness of lens]

Asked in GUJCET 2022 · Combinations and silvered lenses

Answer: (1) -15 cm

Step-by-step solution

Given: convex lens f₁=+30 cm, concave lens f₂=-10 cm, held in contact.

Idea: thin lenses in contact add their powers, 1/F=1/(f₁)+1/(f₂). Only the concave lens carries a negative focal length.

1/F=1/(30)-1/(10)=(1-3)/(30)=-2/(30).

So F=-15 cm.

The concave lens is the stronger of the two, so the pair as a whole diverges light.

Why the other options are wrong

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