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NEET PHYSICSMedium

Two similar thin equi-convex lenses, of focal length ff each, are kept coaxially in contact with each other such that the focal length of the combination is F1F_1. When the space between the two lenses is filled with glycerine (which has the same refractive index (μ=1.5\mu = 1.5) as that of glass) then the equivalent focal length is F2F_2. The ratio F1:F2F_1 : F_2 will be :

1

2:12 : 1

2

1:21 : 2

3

2:32 : 3

4

3:43 : 4

Step-by-Step Solution

For two lenses in contact, 1F1=1f+1f=2f  ⟹  F1=f2\frac{1}{F_1} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f} \implies F_1 = \frac{f}{2}. When glycerine is filled, the combination acts as a single lens of focal length F2=fF_2 = f. Thus F1:F2=f2:f=1:2F_1 : F_2 = \frac{f}{2} : f = 1 : 2.

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