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Two identical thin biconvex lenses of focal length $15 c m$ and refractive index $1.5$ are in contact with each other. The space between the lenses in filled with a liquid of refractive index $1.25$ . The focal length of the combination is ______ $c m$ .

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-10

+15

+10

-20

answer is D.

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Detailed Solution

$f = \frac{R}{2 (μ - 1)} \Rightarrow R = 15 \times 2 \times (1.5 - 1) c m = 15 c m$

$focal length of the medium which is enclosed within the two lens is f_{l} = \frac{- R}{2 (μ_{l} - 1)} = - 30 cm$

$\frac{1}{F_{combination}} = \frac{1}{15} + \frac{1}{15} - \frac{1}{30} = \frac{2 + 2 - 1}{30}$

$\Rightarrow F_{combo} = + 10 cm$

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