Snell's law: An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for the oil is 1.15, and for water it is 1.33.)

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Quizplus · Accepted Answer

To find the angle of refraction in the water, we first use Snell's law to find the angle of refraction in the oil, then use it again to find the angle in the water. Snell's law is $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the indices of refraction, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively. For air to oil, $n_1 = 1$ (for air), $n_2 = 1.15$ (for oil), and $\theta_1 = 45^\circ$. Solving for $\theta_2$ gives the angle of refraction in the oil. Then, using this angle as the angle of incidence from oil to water, with $n_1 = 1.15$ and $n_2 = 1.33$, we find the angle of refraction in the water, which is approximately 32°.

Snell's Law: an Oil Layer That Is 5