An oil film floats on a water surface.The indices of refraction for water and oil,respectively,are 1.333 and 1.466.If a ray of light is incident on the air-to-oil surface at an angle of 25.4° with the normal,what is the incident angle at the oil-to-water surface?
A) 18.8°
B) 17.0°
C) 23.0°
D) 25.4°
E) 20.8°

Question

An oil film floats on a water surface.The indices of refraction for water and oil,respectively,are 1.333 and 1.466.If a ray of light is incident on the air-to-oil surface at an angle of 25.4° with the normal,what is the incident angle at the oil-to-water surface?
A) 18.8°
B) 17.0°
C) 23.0°
D) 25.4°
E) ​20.8°

Quizplus · Accepted Answer

Using Snell's law, we can find the refracted angle at the air-to-oil interface to be:

n1 sin(theta1) = n2 sin(theta2)
(1.000) sin(25.4°) = (1.466) sin(theta2)
sin(theta2) = (1.000/1.466) sin(25.4°) = 0.562

Therefore, the refracted angle at the oil-to-water interface is:

n1 sin(theta1) = n2 sin(theta2)
(1.466) sin(theta1) = (1.333) sin(90° - theta2)
sin(theta1) = (1.333/1.466) sin(90° - sin^-1(0.562))
sin(theta1) = 0.444
theta1 = sin^-1(0.444) = 25.4° - 17.0° = 8.4°

So the incident angle at the oil-to-water surface is 17.0°. Therefore, the answer is B.

An Oil Film Floats on a Water Surface