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Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F₁. When the space between the two lenses is filled with glycerin (which has the same refractive index (1.5) as that of glass) then the equivalent focal length is F₂. The ratio F₁ : F₂ will be:

1. 2:1
2. 1:2
3. 2:3
4. 3:4

Correct answer: 2:1

Solution

When two identical lenses are in contact, the combined focal length is given by F₁ = f/2. When the space between the lenses is filled with glycerin (same refractive index as glass), the lenses effectively lose their refractive power, and the combination behaves as a single lens with focal length F₂ = f. Thus, the ratio F₁ : F₂ = (f/2) : f = 1:2.

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