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Critical Angle

A point sourc...

Question

A point source of light is placed at distance h below the surface of a large and deep lake. What fraction of light will escape through the surface of water?

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Solution

Due to TIR, light will be reflected back into the water if i > θ_c. So only that portion of incident light will escape which passes through the cone of angle θ = 2θ_c.
So, the fraction of light escaping
$f = \frac{a r e a A C B}{t o t a l a r e a o f s p h e r e} = \frac{2 π R^{2} (1 - c o s θ_{c})}{4 π R^{2}} = \frac{1 - {c o s θ}_{c}}{c}$

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