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A point source of light is placed at the bottom of a water lake. If the area of the illuminated circle on the surface is equal to 3 times the square of the depth of the lake. The refractive index of water is

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$\sqrt{π + 1}$

$\sqrt{\frac{π}{3} + 1}$

$\frac{π}{3} + 1$

$\frac{π}{4} + 1$

answer is B.

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Detailed Solution

$\begin{array}{l} Area = 3 d^{2}; Area of base of cone \\ = \frac{π h^{2}}{μ^{2} - 1} = \frac{π d^{2}}{μ^{2} - 1} \\ 3 d^{2} = \frac{π d^{2}}{μ^{2} - 1}; μ^{2} - 1 = \frac{π}{3}; μ = \sqrt{\frac{π}{3} + 1} \end{array}$

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