EARTH 520
Plate Tectonics and People

Snell's Law

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Now that we are experts on how light is refracted as it passes from air to water, we can extend what we know to generalized waves passing through any medium. As long as we know the index of refraction, we should be able to describe the path a wave takes through some complicated layered structures. (See where we are going here? The Earth can be thought of as a big piece of material consisting of layers through which seismic waves pass.)

Snell's law describes the refraction of a wave passing through two materials that transmit the wave at different velocities:

snell's law. the sine of the angle of incidence divided by the sine of the angle of refraction is equal to the ratio of transmission velocities between the the two materials

In words, the formula above says that if a wave passes from material 1 to material 2, the ratio of the sines of the angles of incidence and refraction (θ1 and θ2) will be a constant number and this constant number is equal to the ratio of the transmitting velocities of the two materials (v1 and v2) as well as the inverse ratio of the indices of refraction of the two materials (n1 and n2).

A diagram of what this formula means graphically is shown below.

snell's law demonstrated graphically
In the figure above, a ray of light passes from air to water. It enters the water with an angle of incidence θ1 and is bent toward the normal (dotted line) so that the angle of refraction is θ2. The ratio of the sines of the angles is equal to the ratio of the transmitting velocities of the two materials (v1 and v2) and to the inverse ratio of their indices of refraction.

Hopefully this rings a bell from the lab experiment we just did! In our experiment, our two materials were air and water just like in the diagram above. Air has an index of refraction of 1 (n1 = 1) and water has an index of refraction of 1.33 (n2 = 1.33).

Nitpicker Alert

Okay, actually a vacuum has an index of refraction of 1. Air at room temperature, pressure, and humidity has an index of refraction of about 1.0003. You'd have to design an experimental setup with a little more precision than what we did to resolve this discrepancy.

This means that we can use Snell's Law and calculate that the sine of the angle of incidence sin(θ1) divided by the sine of the angle of refraction sin(θ2) will always be equal to the ratio of the two indices of refraction, 1.33/1. This is what we confirmed in our experiment. Yay! Science works!

This also means we know that the ratio of the velocity of light through air to the velocity of light through water is equal to 1.33.

Quiz Yourself!

The velocity of light through air is 3 x 108 m/s. What is the velocity of light through water?

Try it yourself and then click here to see my answer

ANSWER:

The velocity of light through water is about 2.26 x 10^8 m/s. I got that answer by dividing 3 x 10^8 by 1.33.