# Light and Polarization

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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## Refraction

The behavior of light in materials is governed by Snell's Law. Any material that transmits light has an index of refraction, usually symbolized n. The velocity of light in the material is v = c/n, where c is the speed of light in a vacuum.

 When light passes from a material where it has refractive index ni (i for incident) into a material where it has index nr (r for refracted), its path bends. The relationship between the incident and refracted angles (i and r) is given by: ni sin i = nr sin r. Also note that light is reflected at angle i.We also see that sin i = (nr/ni)sin r. If sin r is greater than ni/nr, then sin i is greater than 1, an impossibility. In that case, there is total reflection at the interface.

## Polarized Light

Light consists of oscillating electrical fields, denoted by E, and magnetic fields, denoted by B. We will concentrate on the electric field component and ignore the magnetic field; however, we could just as well describe light and its effects in terms of the magnetic field component. We don't do it because the interaction of magnetic fields with charged particles is more complex than electric fields, but we could.

Light whose electric field oscillates in a particular way is said to be polarized. If the oscillation is in a plane, the light is said to be plane polarized (top right). Plane polarized light can be polarized in different directions. Light can also be circularly polarized, with its electric field direction spiraling in a screw pattern. Circularly polarized light can be right- or left-handed (bottom). Light can consist of a combination of plane and circular polarization as well; its electric field spirals in a screw fashion with an elliptical cross-section. Such light is called elliptically polarized.

Although we often speak of "unpolarized" light, every photon of light is polarized in some manner. "Unpolarized" light is a random mixture of light of all polarizations. When light has an easily observed dominant polarization, we refer to it as polarized.

### Natural Polarization

When light strikes an electron, it causes it to vibrate and emit its own radiation. Only oscillations perpendicular to your line of sight result in emitted radiation. Thus, the excited electron at the top left emits radiation in a plane perpendicular to its vibration direction, but not along it. This basic fact leads to two common natural sources of polarized light.

Skylight is polarized (top right). For light oscillating in the plane of the diagram, electrons in a direction 90 degrees from the Sun vibrate mostly along your line of sight. For light oscillating perpendicular to the diagram, all light oscillates perpendicular to the line of sight. Thus skylight 90 degrees from the Sun is polarized, with the effect diminishing at greater and smaller angles. Photographers make use of this effect to increase the contrast between sky and clouds. Repeated scattering, however, re-randomizes the light, so light from clouds is unpolarized. Skylight is not perfectly polarized because there is some multiple scattering from particles in the air.

Light reflected from non-metallic surfaces is polarized (bottom). The incident light causes electrons in the material to vibrate. Vibrations parallel to the surface emit radiation. Vibrations perpendicular to the surface have a large component in the direction of the reflected light and emit much less radiation. There is one angle where reflected light is 100 percent polarized, but it's not 45 degrees. It depends on the index of refraction of the material but is typically about 30 degrees.

This is how polarizing sunglasses work. Most glare is from horizontal surfaces, so the polarizers are oriented to block that radiation.

### Polarizing Filters

Imagine a material where electrons can move freely in one direction but not another. Intuitively, you might think light polarized parallel to the direction of freedom might be able to "slip through". In fact, the opposite is the case.

Light polarized parallel to the easy direction moves the electrons back and forth. In the process it does work and is absorbed. Light oriented perpendicular to that direction cannot move the electrons very much, does no work, and passes through. A grid of parallel wires will polarize radio waves. For light, long polymers doped with ions are the most common way to produce polarizing filters. Before this technique was invented, polarizing filters were very hard to make and extremely expensive.

Recall that electric fields are vectors. Light polarized obliquely to the easy direction is resolved into vector components parallel and perpendicular to that direction. The parallel component is absorbed and the perpendicular component is transmitted.

Some minerals are natural polarizers. Tourmaline is one such mineral. Before polarizing microscopes were developed, mineralogists used to examine minerals with "tourmaline tongs", with two slices of tourmaline serving as the polarizing filters.

Created 15 Sep 1997, Last Update 7 Oct. 1997

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