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Question

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 glycerine (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 :

A
$$1 : 2$$
B
$$2 : 1$$
C
$$2 : 3$$
D
$$3 : 4$$
Solution
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Correct option is B. $$1 : 2$$
Equivalent focal length in air,
$$\dfrac{1}{F_1} = \dfrac{1}{f} + \dfrac{1}{f} = \dfrac{2}{f}$$
When glycerin is filled inside, glycerin lens behaves like a diverging lens of focal length (-f)
$$\implies \dfrac{1}{F_2} = \dfrac{1}{f} + \dfrac{1}{f} - \dfrac{1}{f}$$
$$ = \dfrac{1}{f}$$
$$\implies \dfrac{F_1}{F_2} = \dfrac{1}{2}$$

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