There is a small source of light at some depth below the surface of… | JEE Main 2020 (9 Jan, Shift 2)

Q39JEE Main 2020 · 9 JAN · SHIFT 2Medium

Total Internal Reflection

There is a small source of light at some depth below the surface of water (refractive index = $\frac{4}{3}$ ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly): [Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2 $\pi$ rh]:

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Answer: (a)

Only light inside the cone of half-angle $C$ escapes: $\sin C = \frac{3}{4}$ , $\cos C = \frac{\sqrt{7}}{4} \approx 0.661$ .
On a sphere of radius $r$ about the source, this cone cuts a cap of height $h = r(1-\cos C)$ .
Fraction $= \frac{2\pi r h}{4\pi r^2} = \frac{1-\cos C}{2} = \frac{1-0.661}{2} \approx 0.17$ .
So the answer is (a) 17%.

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Total Internal Reflection question from JEE Main 2020 (9 Jan, Shift 2)

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