Polarization of Light
A light beam which has all of the wave oscillations in a single plane of space is said to have total plane polarization. Light with an equal amount of oscillations in all directions is unpolarized. The “in-between” case is one where there is partially polarized light.
Most sources of light in nature to not emit polarized light. To do so would require the oscillating electric charges that produce it to move in unison in the same direction.
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For a plane polarized beam. We can always subdivide the amplitude as the vector sum of two perpendicular components. We will see that this is useful, because we can usually choose how to do the subdivision to solve a particular problem. If we could “see” the amplitudes for a beam coming directly toward us, it might look like this. |
Similarly, an unpolarized beam could be represented this way |
Note that the unpolarized beam can be thought of as a large number of plane polarized beams, each of which can be decomposed into xy components.
Now, any such beam can be decomposed into a net oscillation in the x and y directions.
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This in turn can be thought of as the sum of a completely (100%) polarized beam and an unpolarized beam! Mathematically, they are equivalent. |
Now, for some more “fun”, it should be stated that this sort of decomposition into two orthogonal (perpendicular) waves works if the waves have the same wavelength and phase. That is, the crests are lined up so that they hit a target together. It is also possible to have light where the two components are 1/4 wave out of phase, so the electric field traces out a helix in space!
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Such a beam, shown here, would not be plane polarized, but circularly polarized. An observer would see the tip of the net electric vector trace out a circle instead of a line as it arrived. |
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And
of course, light can even be a mixture of circular and plane polarized elliptically polarized (totally or partially).
For now we will stick to linearly polarized light.
We can produce and alter the polarization of a beam in many ways. We will deal with 4 methods: transmission, reflection, refraction, and scattering.
Transmission
Polarizing filters, such as those in Polaroid sunglasses, are designed to allow only one plane of light through (although they are not 100% effective, they can be pretty close to that value).
If we then put another polarizing filter in the beam, we can get some interesting results!
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In each case shown, the second filter allows only that component that lies in the “transmission direction” though. In (a), all of the amplitude is in the transmission direction, so it all gets through. In (b), none of the amplitude is in the transmission direction, so none gets through. In (c), the transmission direction is rotated 45° to the direction of the amplitude, so some of the light gets through.
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Mathematically, J is the component of K in the transmission direction. By definition, J/K is the cosine of the angle between the two, so J = K cos (angle JK). For a 45° angle, we get
Because the intensity is proportional to the square of the amplitude, the second filter transmits 1/2 of the light reaching it. If you would like to see this “in action” see the following: 2 filter polarization and 3 filter polarization demonstrations.
PDF-ers:
http://micro.magnet.fsu.edu/primer/java/polarizedlight/filters/index.html
http://lectureonline.cl.msu.edu/~mmp/kap24/polarizers/Polarizer.htm
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Reflection
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Light striking a surface, such as a piece of glass, the surface of water, etc., can be both transmitted through the surface and reflected from it. The amount that is transmitted or reflected, and its polarization, depends on the angle of incidence and the material it is hitting.
Parallel component: the amplitude runs along the plane of the surface as it hits
Perpendicular component: the amplitude is in the plane of incidence (strictly speaking, it is the plane of incidence and reflection
The important angle here is the angle of
incidence,
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If we decompose the incident beam into two perpendicular (sometimes called “orthogonal”) components, we can follow each individually. And they behave differently! We will call the two components by the following terms:
For the parallel component, there is always some
reflection, even when the angle of incidence
The perpendicular component has a more complex
behavior. It begins at the same reflectance as the parallel beam at
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Refraction
Some materials, such as the mineral calcite, have the interesting property of refracting the two planes of polarized light at slightly different angles! This birefringence is useful in the design of optical devices that need to measure both components simultaneously (such as optical polarimeters used in astronomy and other fields).
Many plastic materials become birefringent when physically stressed. Likewise, safety glass in cars has built-in stress that is visible when viewed through a Polaroid filter (see later in these notes)
Scattering
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Sunlight scattering off molecules in the air produces polarized light. The degree of polarization depends on the scattering angle, becoming a maximum near 90 degrees. This phenomenon seems to be utilized by animals whose eyes are sensitive to the polarization direction. The human eye has its own weak sensitivity to polarized light that give rise to Hadinger’s Brush, a yellowish patch that can actually become annoying once you become aware of it!
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Optical Activity
Some crystals and organic materials have a twisted molecular structure that produces another interesting effect: “optical activity”. Here, the plane of polarization rotates as the beam passes through the material, and it can rotate different amounts for different wavelengths. This phenomenon is useful for analyzing mineral crystals and organic pharmaceuticals.
Polarized Light in the Environment
Due to the optical properties of various natural and artificial materials, the effects of polarized light are all around us. In addition to Haidinger’s Brush, we often use polarized filters in the form of sunglasses to cut glare due to reflected sunlight. It is also used to darken the sky in photography, remove glare from subjects behind windows, etc.
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A SIMPLE POLARIMETER DESIGN
As we saw before, many materials (such as calcite) have an index of refraction that depends on the orientation of the polarization component. Effectively, they separate them. These can be combined in clever ways to make an effective polarimeter. One example uses a Wollaston prism:
This can be combined with a rotating half-wave plate that has the effect of rotating the plane of polarization (it’s optically active) by an amount that depends on the orientation of the plate to the plane of polarization. For every 1/2 turn of the plate, the plane of polarization rotates 360°. Inserted in front of a Wollaston prism causes a polarized input beam to be redirected in one exit beam, and then the other.
Polarimetry in Astronomy
Interstellar Polarization
Light from distant stars in the Galaxy is polarized by interstellar dust grains (acting like little Polaroid filters!):
The polarization reaches a maximum at visible wavelengths, suggesting that the grains responsible must be about 1μm in size:
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It is thought that elongated silicate grains, pinning end-over-end and aligned by the galactic magnetic field are responsible.
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Left: model of a spinning grain. Right: An interstellar grain. |
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Circumstellar Dust
Jets in Active Galaxies:
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The jet in the elliptical galaxy M87, thought to be powered by a supermassive black hole |
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Polarization
map of the jet. The polarization and spectrum indicates the jet emission is
due to synchrotron emission |
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Stellar (& Solar) Magnetic Fields
Planetary Surfaces
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