Left and right circular polarization. Oh, yes, one more thing. When the circularly polarized light falls on a metallic reflective surface, the reflection reverses the sense of circular polarization. Right circular polarized light becomes left circularly polarized upon reflection and vice versa. This is the reason for the puzzling result of the "eye patch" experiment and the coin experiment described above.
This effect also seems to be the reason why the older lenticular grooved metallic screens we have long used with linear polarization are unsuitable for circular polarization.
The grooves scatter light to adjacent grooves and back to the audience. Since this doubly scattered light has suffered two reflections, it switches from right to left and back to right circular polarization, and therefore reaches the wrong eye.
Result: faint, ghostly double images. Theater 3-D screens for use with circular polarization have a shallow surface texture that distributes light to the entire audience, but prevents double reflections. The Real-D digital 3-D movie process uses a liquid crystal sheet in front of the projector, driven in synchronization with the projector so that the pictures intended for one eye are left circularly polarized, and those for the other eye are right circularly polarized.
The viewing glasses sort these out so each eye sees only the one it needs. Tilting your head, won't cause ghost images with this system, though tilting your head does cause the vertical alignment of the two images to be a bit off and the 3-D effect is somewhat compromised.
There are two opposite conventions for defining left and right circular polarization, but all we need to know here is that there are just two senses of circular polarization. This is fortunate, because we see 3-D with just two eyes. Polarizers are most effective in the middle of the optical spectrum, for yellow and green light, but not so good in the deep red and blue, and worse in the infrared and ultraviolet.
For this reason, polarizing glasses, even with "crossed" axes should never be used to look at very bright objects like the sun. Quarter wave sheets are "tuned" by controlling their composition and thickness to be most effective in the middle yellow portion of the spectrum.
You can investigate wave retardation plates easily. Place it on your computer screen and look at it through a polarizer. Or, if you don't have the appropriate computer screen, put the cellophane between two polarizers. Rotate each component. You will find that at certain angles, the cellophane shows vivid color. Multiple layers of cellophane produce different colors, which depend on the thickness.
This can be done with either linear or circular polarizers, for the circular polarizers just add another thickness of phase retardation. Layers of cellophane between parallel polarizers. The same layers of cellophane between crossed polarizers.
Note that the single layer of cellophane appears clear white when between crossed polarizers and black when between parallel polarizers. This tells us that it is acting as a quarter wave retardation sheet.
Most cellophane is, even that used in cellophane tape. You can make some colorful designs by layering cellophane tape on glass, with multiple thicknesses, parallel or crossed. Some plastics, such as clear food wrap, show very little color when placed between polarizers, for their molecules aren't well aligned. But by stretching the plastic, you bias the alignment along the direction of stretch, and then you will see colors.
Many clear hard plastics have "frozen in" stress from the rapid cooling process during manufacture. Try looking at a clear plastic tape dispenser, or the "jewel case" of a CD. Glass can show such strains, too, if not annealed properly, and this is a method for quality testing fine glassware.
The side windows of automobiles are made of glass "tempered" during annealing so that they have a tough outer layer. When shattered, they break into chunks that do not have very sharp edges. But they are under permanent stress, and that will show up as colors when placed between polarizers. It will also show when looking through polarizers at the reflected light from the window.
You may have noticed this when wearing polarizing sunglasses. A polarizing filter transmits only the component of the wave parallel to its axis, , reducing the intensity of any light not polarized parallel to its axis. Only the component of the EM wave parallel to the axis of a filter is passed.
What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by When the intensity is reduced by A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to This seems reasonable based on experimenting with polarizing films. Note that By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass.
As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter. Figure 8. Polarization by reflection. Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized.
This is akin to arrows striking on their sides bouncing off, whereas arrows striking on their tips go into the surface. Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that the reflected light is left more horizontally polarized.
The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization would be like an arrow perpendicular to the surface and would be more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and would be more likely to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized light from other sources.
Since the part of the light that is not reflected is refracted, the amount of polarization depends on the indices of refraction of the media involved. Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves often visible light that have an electric field parallel to the axis. This is accomplished with long molecules aligned perpendicular to the axis as shown in Figure 9.
Figure 9. Long molecules are aligned perpendicular to the axis of a polarizing filter. The component of the electric field in an EM wave perpendicular to these molecules passes through the filter, while the component parallel to the molecules is absorbed. Figure 10 illustrates how the component of the electric field parallel to the long molecules is absorbed. An electromagnetic wave is composed of oscillating electric and magnetic fields.
The electric field is strong compared with the magnetic field and is more effective in exerting force on charges in the molecules. The most affected charged particles are the electrons in the molecules, since electron masses are small. If the electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the fields in the wave and, hence, reduces its intensity. In long molecules, electrons can more easily oscillate parallel to the molecule than in the perpendicular direction.
The electrons are bound to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons can absorb EM waves that have a component of their electric field parallel to the molecule. The electrons are much less responsive to electric fields perpendicular to the molecule and will allow those fields to pass.
Thus the axis of the polarizing filter is perpendicular to the length of the molecule. Figure The oscillation of the electron absorbs energy and reduces the intensity of the component of the EM wave that is parallel to the molecule. All we need to solve these problems are the indices of refraction. Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Light not reflected is refracted into these media.
It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.
Polarization by scattering. Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction. If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim.
This is a clear indication that light scattered by air is partially polarized. Robert P. Bauman and Dennis R. Carr and J. Terry S. Sydney B. Jearl Walker, "7. Jearl Walker, "6. Yaakov Kraftmakher, "1. Hollis N. John H. When a third polarizer is placed between the other two with its easy axis at 45 degrees to theirs, a remarkable thing happens.
Some of the light that was blocked now gets through to the screen. The electric vector of the light coming from the first polarizer has a component that is parallel to the easy axis of the middle polarizer, so some of the light can pass through. The emerging light is now polarized at 45 degrees to its original direction and also to the easy axis of the next polarizer.
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