Two similar thin equiconvex lenses, of focal length f each, are kept coaxially in contact so that focal length of combination is F₁. When the space between the two lenses is filled with glycerine, having the same refractive index (μ = 1.5) as the glass, equivalent focal length is F₂. Ratio F₁ : F₂ will be:
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Question

Two similar thin equiconvex lenses, of focal length f each, are kept coaxially in contact so that focal length of combination is F₁. When the space between the two lenses is filled with glycerine, having the same refractive index (μ = 1.5) as the glass, equivalent focal length is F₂. Ratio F₁ : F₂ will be:

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G1 Physics · Accepted Answer

Step 1: Initially two identical lenses in air in contact: powers add 1/F₁ = 1/f + 1/f = 2/f ⇒ F₁ = f/2. Step 2: Filling the gap with glycerine having exactly the same index as the glass removes optical refraction at the two facing surfaces. The two outside curved surfaces then act as one equiconvex lens with focal length f. Hence F₂ = f. Step 3: F₁ : F₂ = (f/2) : f = 1 : 2. Final answer: (A) 1 : 2.