A thick layer of oil is floating on the surface of water in a tank. A beam of light traveling in the oil is incident on the water interface at an angle of 33.0° from the normal. The refracted beam travels in the water at an angle of 47.5° from the normal.
What is the refractive index of the oil?

Refractive index of oil will be equal to 1.802    

Explanation:

We have given light is incident on water surface at an angle of

Let the refractive index of oil is

Light is refracted in the water at an angle of

Refractive index of water is

We have to find the refractive index oil

From law of refraction

So refractive index will be equal to 1.802

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y