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The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/min when water is being drained out at a constant rate. The amount of water drained in cc/min is $(n_{1} = refractive indiex of air, n_{2} = refractive indiex of water)$

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$\frac{x π R^{2} n_{1}}{n_{2}}$

$π R^{2} x$

$\frac{2 π R n_{1}}{n_{2}}$

$\frac{x π R^{2} n_{2}}{n_{1}}$

answer is B.

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Detailed Solution

$d_{a p p} = \frac{d}{(n_{1} / n_{2})} ∴ d = \frac{n_{2}}{n_{1}} d_{a p p} - \frac{d}{d t} (d) = \frac{n_{2}}{n_{1}} (- \frac{d}{d t} d_{a p p}) = (\frac{n_{2}}{n_{1}}) x \frac{d v}{d t} = A [- \frac{d}{d t} d] = \frac{x π R^{2} n_{2}}{n_{1}}$

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