First slide

Ray optics

Question

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

Difficult

A

$\sqrt{π + 1}$
B

$\sqrt{\frac{π}{3} + 1}$
C

$\frac{π}{3} + 1$
D

$\frac{π}{4} + 1$

Solution

Area = 3d²; Area of base of cone
$= \frac{{πh}^{2}}{μ^{2} - 1} = \frac{{πd}^{2}}{μ^{2} - 1} 3 d^{2} = \frac{{πd}^{2}}{μ^{2} - 1}; μ^{2} - 1 = \frac{π}{3}; μ = \sqrt{\frac{π}{3} + 1}$

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