A spotlight is mounted on a pole at the end of a fishing pie

A spotlight is mounted on a pole at the end of a fishing pier as shown below. If the light is mounted a distance of y = 2.90 m above the water, and the light strikes the water at a point that is x = 6.70 m horizontally from the end of the pier, determine the distance from the end of the pier to the point where the light strikes the bottom of the lake if the water is 3.00 m deep.

___________ m

Solution

for incident angle i,

tani = x/y = 6.70 / 2.90

i = tan^-1(6.70/2.9) = 66.6 deg

using snell\'s law to find refraction angle,

ni sini =nr sinr

1 * sin66.6 = 1.33 sinr

r = 43.6 deg

now for triangle inside the water,

tanr = (d - x)/3

d - 6.70 = 3 tan43.6

d = 6.70 + 2.86 = 9.56 m