A lobster fisherman looks just over the edge of a pierand spots a lobster restin

Question

A lobster fisherman looks just over the edge of a pierand spots a lobster resting at the bottom of the lake (n=1.33). Thefishing spot is 3.5m deep. Judging from the angle at which he spotsthe lobster, the fisherman thinks the lobster is at a horizontaldistance of 6.0m from the shore, but when he drops his trap at thelocation he does not catch the lobster. What is the true horizontaldistance of the lobster from the shore? A lobster fisherman looks just over the edge of a pierand spots a lobster resting at the bottom of the lake (n=1.33). Thefishing spot is 3.5m deep. Judging from the angle at which he spotsthe lobster, the fisherman thinks the lobster is at a horizontaldistance of 6.0m from the shore, but when he drops his trap at thelocation he does not catch the lobster. What is the true horizontaldistance of the lobster from the shore?

Explanation / Answer

By using Snell's law and simple geometry it can be shownthat Aparent depth = Actual depth * (Refractive index ofair/Refractive index of water) or Actual depth = Aparent depth * (Refractive index ofwater/Refractive index of air) Aparent depth = 6.0 Refractive index of water = 1.33 Refractive index of air = 1 or Actual depth = 6.0 * (1.33/1) = 8.0 m the true horizontal distance of the lobster from theshore d = (82 - (3.5)2)1/2 =7.2 m

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