Polarization
Polarized light is light that has its electric field propagating in a plane. Most light is not like this and is comprised of many waves which all propagate in separate planes while all sharing a common wave velocity.
In the animation, the green field is the electric field which we tend to focus on when we discuss polarization. Notice that this electric field is confined to the green plane. What most natural light would look like is lots of these waves with their respective green planes all different. While we won't focus on it, the red wave is the magnetic field component of light.
Brewster's Law
When light is reflected off a surface, it will become at least partially polarized. The extent of the polarization depends upon the specifics of the incidence angle and the refractive indices of the media forming the interface.
In order for the light to become 100% polarized, the angle between the reflected and refracted rays must be . This will only happen at one incidence angle given the indices of refraction. This can be calculated as follows: Using Snell's law we write: . Notice that the refracted angle . We can substitute this back into Snell's law and get . Next we can rewrite this as . This leads to . This particular angle of incidence is named Brewster's angle for the scientist who discovered the relation. Thus it is common to call it . So we get
Please note here that the order of and matters! The light is coming from material and bouncing off of material .
How Else Does Light Become Polarized?
There are a few common ways that light waves become polarized besides via reflection. Among them are:
- Scattering: Light scattering is the process that makes the sky blue. While it's a different process than reflection, it also ends up polarizing light. Light most strongly polarized via scattering is seen at angles where your line of sight is at right angles to the incident sunlight. The sky can be as much as 80% polarized at those angles. Don't expect much effect when looking toward the sun.
- Polarizers: Certain materials have molecules arranged such that they will absorb light energy preferentially along certain planes more so than others. If the absorption plane is only singular, then all other planes will pass unaffected. Polaroid corporation was the first producer of commercial polarizers in 1929. It was called the J-sheet. They were too opaque for widespread use due to scattering of light. Their second version, available by 1938, which is still used today is made of PVA (poly-vinyl alcohol) with an Iodine dopant to make the polymer chains conducting in order to allow the electric field component of the light to do work on electrons in the long polymer chains of the material, and thus get absorbed. The generic term for these is the H-sheet. These common H-sheet polarizers transmit around 90% of light along their transmission axes, and only 0.1% in the orthogonal plane.It is worth looking at that process of light absorption in more detail for a moment. We have discussed that light is an electromagnetic wave. Generally speaking, the electric field component is more effective than the magnetic one for transferring of energy to materials. The electric field is analogous to gravity. While gravity exerts force on mass, electric fields exert force on charge. The two equations have identical form: , and , where is charge. When light waves meet matter, they attempt to shake the charges back and forth. Recall from our studies of mechanics that a force only transfers energy to something if it manages to move the object, or . So in the context of polarizing materials, it must be possible for charges to only move along one direction and not orthogonal to that. Imagine beads on parallel wires. The beads are the charge. If the light tries to move the beads along the wires length-wise, there is a large displacement and a lot of work is done. So the beads gain energy at the expense of light intensity. On the other hand, trying to move the beads orthogonal to the wires - even if the force is equal - will result in no displacement and no work or transfer of energy. In this decent analogy the wires are the long polymer molecules which have become conducting due to the iodine dopant. The mobile charges are the beads. It is clear then that light perpendicular to the molecular chains is the light that makes it through, or is transmitted. Some tutorials about polarization online make it look like light is slipping through the gaps between the molecular chains. They are simply wrong.
![[url=https://commons.wikimedia.org/wiki/File:Wire-grid-polarizer.svg]"Wire Polarizer"[/url] by Fffred is licensed under [url=http://creativecommons.org/licenses/by-sa/3.0]CC BY-SA 3.0[/url]
A wire grid polarizer for microwaves. Notice that the plane of polarization that gets transmitted is perpendicular to the wires in the grid.](https://www.geogebra.org/resource/g7mh5CKV/OwWi3IJpuTuwArML/material-g7mh5CKV.png)
Uses for Polarizers
Polarizers are useful for reducing what we often call glare off of objects. Think of the refection of sunlight off the rear window glass of the car in front of you, or off of a lake while fishing, or off of the road while driving. Reflected light is polarized at least partially as described above. The plane of polarization for the reflected rays is parallel to the surface off of which it reflected. So when light reflects off of the road, the electric field of the reflected light coming at you is going left to right (parallel to the road surface), not up to down. Wearing polarizing sunglasses with a transmission axis oriented vertically will filter out that reflected "glare" off the road. Such glasses are nice for driving or fishing, etc.
Since the blue sky is polarized by a consistent scattering angle and white clouds are not, photographers can take advantage of this by using polarizing filters to filter out the blue sky and make it darker colored in contrast with the clouds. This can produce dramatic effects. See this link: Video of polarizing filters in photography
The ability to reduce the intensity of light with two polarizers oriented with non-parallel transmission axes is used by photographers to increase the shutter time, or the time the shutter remains open. Generally short shutter times are preferred to avoid blurred images, but suppose you want blurring. For instance, if you want a daytime view of the Golden Gate Bridge without cars appearing, you either need friends to block traffic, or some clever solution. By forcing your camera to keep its shutter open for many seconds, the cars will effectively be blurred into the road as if you wiped chalk with your finger. If they aren't driving with lights on they will often be invisible in the final photograph. Likewise, to take pictures of a mountain stream that have unrealistically looking soft, misty water, it also requires long shutter times.
There are actually many types of polarized light besides the type we have mentioned here. The type we are discussing here should really be specified as linearly polarized light. While I don't intend to discuss details of elliptically or circularly polarized light, and right versus left handed polarization in these contexts, please realize that you will come across these topics regularly in conjunction with technology using polarizers. If you feel like doing some self study you will find plenty of information on these topics online.
![[url=https://pixabay.com/en/creek-falls-flow-flowing-green-21749/]"This work"[/url] is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]
The mystical look of the water in this photo requires a long shutter time. In daylight a long shutter time will over-expose a picture so it looks all white. To avoid this, crossed polarizers can be used to lower the light intensity.](https://www.geogebra.org/resource/YwBwwaag/Q4mcIgdPlfUKqOiR/material-YwBwwaag.png)