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A point light source is submerged inside water (refractive index n = 4/3). When the source is at depth H below the surface, the fraction of total light energy that escapes out of the water is 'a'. When the same source is placed at depth 2H, the fraction that escapes is 'b'. Which of the following correctly relates a and b?

1. b = a/2
2. a = b
3. b = a/4
4. b = a/pi

Correct answer: a = b

Solution

Total internal reflection occurs for rays beyond the critical angle C (where sin C = 1/n = 3/4). The escape cone half-angle is C, and the fraction of emitted light that exits = (1 - cos C)/2, which depends only on n. Since n is the same at both depths H and 2H, the fraction of escaping light is the same: a = b.

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