# Polarization by Reflection & Brewster's Law

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain what polarization by reflection is, give a few examples of polarization in everyday life, explain Brewster's Law descriptively and use the equation to solve problems. A short quiz will follow.

## What Is Polarization by Reflection?

One day, you and a friend are playing with a slinky. You hold one end, and your friend holds the other. While standing a few meters apart, you can send a wave down the slinky by moving your arm up and down or side to side, and the wave will travel down the slinky until it reaches your friend. It doesn't matter which way you move your arm, the wave will still travel down the length of the slinky. The only difference between moving your arm in different directions is the polarization of the wave. The polarization of a wave is the direction that a wave vibrates (or oscillates). Up and down is one polarization, side-to-side is another, and there is every diagonal in-between, too.

You can polarize a wave in a number of ways. Light from the sun is a mixture of light waves with all kinds of different polarizations, and if you shine it through a polarizing filter, which is like a series of slits, only light that is vibrating in the direction of the slits will be able to pass through. You could say that you have polarized the light.

But there's another way to polarize light, and it's called polarization by reflection. Polarization by reflection is where you bounce light off a reflective or mirrored surface, such that the light that moves away from that surface is polarized. When light hits a surface, some of it will be refracted, it will bend and go through the material, and some will be reflected, it will bounce away from the material. It turns out that light that is polarized in the direction that a reflection happens, in the same plane as the incident and reflected ray is more likely to be refracted, and light that is polarized at 90 degrees to this plane is more likely to be reflected. This means that light that bounces off surfaces towards your eyes is polarized light.

## Examples

Have you ever been hiking with polarizing sunglasses? On a sunny day, you might have noticed crystal clear reflections on a lake. Those reflections, as we talked about, are polarized. But when you put your sunglasses on, you might notice that those reflections disappear. This is because your sunglasses work by polarization. They only allow light that is polarized a certain way to go through them, so unless the reflections on the lake happen to be polarized that way, they won't go through. This allows you to see under the lake's surface.

Polarizers can also be placed on computer monitors or television screens to reduce glare, since glare is nothing more than a reflection, and those reflections are polarized.

## Brewster's Law

Reflected light is polarized, but not all of it. I said that being in the plane of a reflection makes light polarized at 90 degrees to that plane more likely to be reflected, but only more likely. In fact, the angle you shine your light at has a big impact on how polarized the reflection is. Brewster's Law helps us describe how it varies with angle.

Brewster's Law says that maximum polarization will happen when the angle between the reflected ray and refracted ray is 90 degrees. This diagram illustrates that:

The reflected ray is the light that goes into your eyes to form the reflection on the lake, and the refracted ray is the light that goes through the lake, that never makes it to your eyes. Light will be most polarized when there is 90 degrees between these two lines.

Brewster's Law can be defined mathematically by this equation, where theta-B is Brewster's angle - the angle of incidence where maximum polarization occurs, n1 is the refractive index of the material the light is passing through before it reflects and n2 is the refractive index of the material the light bounces off. A refractive index is just a number that represents how dense the material is and therefore how fast or slow light travels inside it. It's the kind of thing you can look up in a data table, or figure out by doing an experiment. For example, the refractive index of ice is 1.31, and the refractive index of Plexiglas is 1.6.

## Calculation Example

Okay, time to do an example problem. Let's go back to the hiking trip. Let's say that the light that reaches your eye after bouncing off the lake is fully polarized. Assuming the lake contains pure, fresh water, and the air has an average density, what is the angle of incidence of the light as it hits the lake?

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