Two similar thin equi-convex lenses, of focal length f each, are kept… | NEET 2019

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Combination of Lenses

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 ( $\mu$ = 1.5) as that of glass) then the equivalent focal length is F2. The ratio F1: F2 will be:

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Answer: (a)

Equiconvex, $\mu = 1.5$ : $\frac{1}{f} = 0.5 \cdot \frac{2}{R} \Rightarrow f = R$ . In contact: $F_1 = \frac{f}{2}$ .
Glycerin forms a biconcave lens of same $\mu$ and $R$ : focal length $-f$ .
$\frac{1}{F_2} = \frac{2}{f} - \frac{1}{f} = \frac{1}{f} \Rightarrow F_2 = f$
So the answer is (a) $F_1 : F_2 = 1 : 2$ .

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