index of refraction?

Question

An underwater swimmer observes that a beam of sunlight in the water makes an angle of 17.7° with the vertical. The index of refraction for water is equal to 1.33. Assuming the surface of the water is level, determine the beam's angle as it enters the water.

Answer 1

This refraction occurs as expressed by the Snell's law equation:
n1 • sin (A1) = n2 • sin (A2)

where n1 = index of refraction value of material 1 (in this case the air, hence n1=1)

n2 = index of refraction value of material 2 (water - n2=1.33)

A1 = angle of refraction of material 1 (x)

A2 = angle of refraction of material 2 (17.7 degrees)

1 x sin(x) = 1.33 x sin(17.7)
sin(x) = 0.404
x = arcsin(x) = 23.85 degrees