Q.379. Refraction of light.

Question 379.
You need to hit an underwater target lying flat on the bottom of a pool. The water is 1 m deep and you are standing so that your eyes are 3 m above the bottom of the pool. As you look at the target your gaze is 30 degrees below the horizontal. At what angle below the horizontal should you throw a spear to hit the target? (assume it travels in a straight line and that you throw at the same level as your eyes).

Answer 379.
Refer to the figure shown below.

For refraction,
sin i / sin r = 4/3
=> sin r = (3/4) sin(60°) = 3√3/8
=> tan r = tan [arcsin (3√3/8)]
=> tan r = 0.8542421962
=> AB = 0.8542421962

MB = 2cot (60°) = 3.4641016151

=> MA
= MB + BA
= 0.8542421962 + 3.4641016151
= 4.31834381

=> required angle,
θ = arctan (3/4.31834381) = 34.79°.

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