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There is a small source of light at some depth below the surface of water (refractive index = 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 2πrh]

1. 21 %
2. 34 %
3. 50 %
4. 17 %

Correct answer: 17 %

Solution

The percentage of light emerging from the water surface can be calculated using Snell's law and the critical angle for total internal reflection. Given the refractive index of water, the critical angle is approximately 48.6 degrees, which allows only a fraction of the light to escape, resulting in about 17% of the light emerging from the surface.

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