posted by alex giroux on .
On a sunny day, a 1.20 m long vertical stick in air casts a shadow 1.20 m long. If the same stick is held vertically and touching the flat bottom of a pool of salt water (n=1.71) half the height of the stick, how long is the shadow on the floor of the pool?
The angle of incidence above the water is 45 degrees, because of the equal stick and shadow lengths above the water.
Then with half the stick above the water, the top of the stick's shadow hits the water 0.60 m from the stick. Then it proceeds below the water at a smaller angle of refraction given by Snell's law.
0.60 m times the tangent of the refraction angle (added to 0.60 m) will tell you where it hits the bottom of the pool.
The index of refraction (1.71) that they tell you to use for saltwater is much too high, but they probably expect you to use it anyway.