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Topic: Magnification, power of lens, combination of thin lenses· Optics

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 F_1. When the space between the two lenses is filled with glycerin (which has the same refract…

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 \(F_1\). When the space between the two lenses is filled with glycerin (which has the same refractive index (\(\mu = 1.5\)) as that of glass) then the equivalent focal length is \(F_2\). The ratio \(F_1 : F_2\) will be :

1. 2 : 1

2. 1 : 2

3. 2 : 3

4. 3 : 4

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Answer: 2. 1 : 2

Two thin lenses in contact: \(\dfrac1{F_1}=\dfrac1f+\dfrac1f\), so \(F_1=\dfrac f2\).

When the gap is filled with glycerin of the same index as glass, the glass-glycerin surfaces do not bend light at all. The system acts as a single equi-convex lens made of the two outer surfaces.

Each outer surface has radius \(R\), and \(\dfrac1f=(1.5-1)\dfrac2R\) gives \(f=R\). The combined lens has the two outer surfaces, so \(F_2=f\).

\(F_1:F_2=\dfrac f2:f=1:2\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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