Question

At 08:00hrs a 2.0- m-long vertical stick in air casts a shadow 1.8 m long. If the same stick is placed at 08:00hrs in air in a flat bottomed pool of salt water half the height of the stick, how long is the shadow on the floor of the pool? (For this pool, n = 1.56.)

Answer 1

Use the length of the stick and the air shadow length to get the angle of incidence. It appears to me to be arctan 1.8/2.0 = 42.0 degrees Call that angle I

Next use Snell's law to get the angle of refraction (R) in the salt water.

sin I = N sin R

Solve for the angle R. N = 1.56. (That must be VERY salty water).

You can get the length of the shadow on the bottom of the pool (X) from the pool depth (D) and the refraction angle.

X/D = tan R

Answer 2

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