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Power and Thin Lenses in Contact

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Question

The following figure shows different arrangements of two identical pieces of thin Plano-convex lenses. The refractive index of the liquid used is less than that of the glass. The effective focal lengths in the three cases are related as :

A

f_{1} = f_{2} > f_{3}

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B

f_{1} \neq f_{2} \neq f_{3}

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C

f_{1} = f_{2} < f_{3}

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D

f_{1} = f_{2} = f_{3}

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Solution

The correct option is B $f_{1} = f_{2} < f_{3}$
Let the focal length of each piece be, $f$

Then, the focal length of the combination will be,

$\frac{1}{F} = \frac{1}{f} + \frac{1}{f}$

So, $F = \frac{f}{2}$

Now, in the third case, the presence of water between the two surfaces, acts as a diverging mirror and thereby increases the focal length of the combination

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