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An opaque cylindrical tank with an open top has a diameter of 3.00 m and is filled with water. When the setting sun reaches an angle of $37^{o}$ above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank (in m) ?

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answer is 4.

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Detailed Solution

By Snell’s law $1 \sin 53^{o} = \frac{4}{3} \sin r$

$\frac{4}{5} = \frac{4}{3} \sin r, \sin r = \frac{3}{5} \Rightarrow r = 37^{o}$ $I n Δ O A B, \tan r = 3 / H = \tan 37^{o} \Rightarrow H = 4 m$

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