Experiments With Polarized Light.

by Donald E. Simanek

Screwy Light.

So you've just seen a 3-d movie. I hope you saved those glasses you paid for. If not, ask at the box office if you could have a few that have been used and will be discarded. The Real-D 3-d movie process uses circular polarization, unlike the 3-d movies of the 50s that were presented using linear polarization. If you are into 3-d photography and project your pictures on a screen, you probably have used linear polarizing glasses of the older kind. Both types of glasses also have other uses, as we shall see.

Experiments.

Let's first demonstrate some of the curious effects of polarizing glasses.

Which picture represents
what you will see when you
look in a mirror?

The spooky eye-patch. Put on the Real-D glasses. Look at your reflection in a mirror. Now close one eye. Your image in the mirror shows one of the polarizers black—the one over your open eye. You can clearly see your closed eye in the mirror. Think about it. How can your open eye see through the darkened polarizing filter? Go ahead, open both eyes, then close the other one, but predict what will happen before you do it.

Place a shiny object, such as a coin, on the table, and look at it through the circularly polarizing glasses. Looks normal, doesn't it. Then remove the glasses and place one of the circular polarizers directly upon the coin. Now it looks dark, black or maybe purple. lay one side of the circularly polarizing glasses on it. Why? We'll tell you later, but for now, play around and experiment with different orientations of the coin and glasses.

Predict what you'd see if, while wearing the glasses, you looked at another person also wearing glasses. Then what if you closed your right eye? Would you then see the other person's left, or right eye?

Why is the 50 cent coin (top) dark when seen
through the circular polarizer, but
the 25 cent coin (bottom) isn't?

If you have a pair of linear polarizing glasses, try the same experiment. The results are different. We'll explain why a bit later.

The light from your computer screen is a bit strange. And it's not just because of the websites you visit. If you have a computer with a flat screen liquid crystal display, turn it on. Open your word processor to display the "writer's block" screen (pure white). Now hold the polarizing glasses with earpieces toward the screen. Rotate the glasses, and you will find one position where the screen appears black when seen through the glasses. The glasses will probably be at 45° to the vertical, as shown in the figure. The results will depend on your brand of computer. Try various models. Try high definition TV display screens.

Creating colors. Obtain some cellophane from product wrappers, such as CDs or DVDs. While wearing your polarizing glasses, place the cellophane over the computer screen, and rotate it to different positions. In two orientations it will show strong color. Several layers show different colors, that are more pastel. Crumpled cellophane may produce an abstract work of color art. Rotate the polarizing glasses (take them off, first) and each color shifts to its complementary color.

Glasses block light. Glasses transmit light.

Color everywhere. Look at samples of transparent hard plastic in the same way. Abstract patterns of all colors may be seen. Try a plastic comb, or a clear plastic container from cellophane tape. Try the cellophane tape itself, applied onto a glass sheet in various patterns and different number of layers. (Don't stick the tape to your computer screen.)

Tape dispenser between
crossed polarizers.
Plastic comb between
crossed polarizers.

Why?

Passage of light through materials is, on the quantum level, a process of atomic and molecular absorption and re-emission of photons. (Light doesn't just "slip through between the atoms and molecules".) Time delays in this process result in apparent bending of light (refraction) through transparent materials), and for reflection from shiny materials, as well as for the selective effects that depend on wavelength, producing colors from white light. This isn't the best place to go into this deeply, so we will content ourselves with an older "classical" model of light that does a pretty good job describing the phenomena at hand.

Classical model of light.
K is the direction of propagation.
E and B are the electric and magnetic field vectors.

A Unpolarized light; wave packets have unbiased polarization angles.
B, C, D, electric vectors of light polarized at various angles.
Seen looking along the direction of propagation.

Difference between plane
and circular polarization.
Circularly polarized light. Two oscillating electric fields,
one retarded by 1/4 wavelength, combine to produce a wave in which
the electric vector traces a helical path.
Diagrams from the HyperPhysics web site, by Rod Nave. Used with permission.

Think of light as an electromagnetic wave phenomenon of the same character as radio waves, only of much shorter wavelength. Electromagnetic radiation can be thought of as wave fluctuations of electric and magnetic fields, the two fields being directed at right angles to each other and also at right angle to the direction of the wave's propagation. For light, we need only look at the electric field, for it is responsible for most of the effects that allow us to detect light, including our own eyes. So the magnetic field isn't shown in diagrams.

Think of light from common sources, such as sunlight and incandescent lamps as short bursts (wave packets) of radiation, each with its electric vector along a certain direction. Call this its direction of polarization. But these wave packets have no preferred direction, and the polarization takes many directions, each packet's polarization direction uncorrelated with the others. We call such light "unpolarized" because, averaged over many wave packets, many possible directions of individual packet polarization are represented nearly equally without bias.

An even simpler, but useful, model treats polarized light as represented by a vector lying in the polarization direction, whose length is proportional to the light intensity. (This vector is chosen to be the direction of the electric field of the light wave.) When such light passes through another polarizer with its axis aligned differently than the polarization direction of the light incident upon it, the emergent light is polarized along the new direction, along the polarizer's axis. It emerges with reduced intensity, which can be calculated by finding the projection of the incident intensity vector onto the new axis, as shown in the figure. If this light then passes through another polarizer, the only light that gets through is polarized along that polarizer's axis, with intensity again reduced by the projection construction. In the figure the first and last polarizers are at right angles, yet because of the second polarizer in between, the light has not been completely blocked. This surprising result can be easily demonstrated with three polarizing sheets, as shown below.

Polarizing sheets at different relative orientation.

Think of the plastic material of your polarizing glasses as being made of long chain molecules, aligned during manufacture to be predominately along one direction. Call this direction the "easy" axis of the polarizer. If a light wave packet comes along with its polarization parallel to the polarizer's axis, it will be absorbed easily by a molecule, which then emits another photon traveling in the same direction and with the same polarization angle. If a wave packet's polarization direction is perpendicular to that of the polarizer (and to its long molecules) it will be absorbed, and no photon will be emitted. At other angles, the probability of absorption has intermediate values, but emitted wave packets are predominantly polarized parallel to the molecules. Ideally, the emitted light should have about 50% the intensity of the incident light, but in real materials it is somewhat less. This is how a polarizing sheet produces linearly polarized light.

Some transparent materials have a similar selective effect on wave packets, but the re-emitted light is nearly as intense as the incident light. Many clear plastics do this, but we do not notice anything unusual going on until we deliberately investigate it, and our polarizing movie glasses are a good tool for doing that. In these materials light polarized in one direction (along the "easy" axis) suffers few absorptions and re-emissions. But along the perpendicular axis (the "slow" axis) there are many, and each re-emission has a time delay. On emergence, this wave, along the "slow" axis, has its phase retarded due to these accumulated delays.

Nearly everyone has a computer with a plasma screen display. Those screens emit polarized light, usually at 45° to the vertical. Some brands are 45° to the left, some to the right. It doesn't matter to the user. Open your word processor to display the blank white screen (pure white). If you have a pair of polarizing sunglasses (linear polarizers), hold them over the screen and rotate them. When the polarizer axis is perpendicular to the polarization of the light from the screen, the screen will appear black. When parallel to the screen polarization, it will let light through. The sunglasses' polarization axis is horizontal, so that it blocks reflected light from horizontal surfaces, such as bodies of water, or light reflected from a shiny roadway.

Linear polarizing glasses from 50s movies had their polarizers at 45° to the vertical, and perpendicular to each other. The two projectors had similarly oriented polarizers. So your right eye saw only the picture intended for it, and your left eye saw the other picture. (If you have any of these, you can check what I'm saying with your computer screen.) But, if you tilt your head during a 3-d movie or slide show, the polarizer alignment will be incorrect, and each eye will see some ghost image of the wrong picture, inducing the "3-d headache".


3-D projection using linear polarization.
Polarizers (2, 4) in front of
the projector lenses have their
polarization axes at 45°
to the vertical. Polarizers
(54, 56) in the viewing glasses
are also polarized at matching
angles (58, 60).

Ordinary matte screens are unsuitable for polarized light, for the scattered light from them doesn't preserve the polarization. Metallic surfaced screens are required.

Circular polarizing glasses from today's 3-D movies consist of a polarizing sheet (nearest the eyes) and a retardation sheet (nearest the screen). If the retardation sheet is just thick enough to retard the wave packets aligned along its "slow" axis so that they emerge displaced one quarter wavelength behind the wave packets aligned along the fast axis, this combination is called a quarter wave plate or a "circular polarizer". It can be thought of as producing a classical wave with its electric vector rotating around the direction of propagation, tracing a corkscrew path through space.

Of course, there are two possible senses of rotation of circularly polarized light: right and left. If the slow axis of the quarter wave sheet is at -45° to the axis of the polarizer you get circular polarization of the opposite sense compared to what you get if it's oriented at +45°. The two kinds of circular polarization are mirror images of each other as illustrated below.

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. Obtain some cellophane from product wrappers, such as that from CDs or DVDs. 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. Whatever color you see, rotating one of the polarizers 90° changes its color to its complementary color. 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.
Cellophane axis at 45° to the polarizers.
The same layers of cellophane
between crossed polarizers.
One polarizer has been rotated 90° but the cellophane
axis is still at 45° to the polarizers.
These pictures were taken with polarized light from a computer screen
polarized at 45°to the vertical, and a linear polarizer in front of the camera lens.

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. Two equal thickness retardation sheets, with axes at 90°, will effectively cancel each other's effect.

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.

Inexpensive polarizers for your digital camera.

Circular polarizers are required for use with digital cameras because plane polarized light passing through the mirrors of the auto-exposure system would cause incorrect readings that depend on the polarizer's orientation. But, rather than pay $30 and up for a glass mounted circular polarizer at a camera store, you can get the same results with the circular polarizing material from a pair of Real-D 3-D cinema glasses. Remember, that for this application the quarter wave plate must be nearest the camera, while it must be nearest the screen for viewing 3-D movies. If you have it on correctly, a clear sky will darken as you rotate the polarizer. If it is incorrectly placed, you will see no change in the viewfinder scene when rotating the polarizer. Photographers use polarization control to eliminate reflections from shiny surfaces, darken skies, and reduce reflections from leaves, for more saturated color in foliage. This is a good way to experiment with polarization before you spend money on a professional glass-mounted polarizer for your camera.

You can find out more about polarization, with experiments you can easily do, at:
http://www.lhup.edu/~dsimanek/scenario/labman3/polarize.htm.

For a mathematical treatment of the theory, and lots of good experiments you can do at home, see http://instructor.physics.lsa.umich.edu/int-labs/Chapter4.pdf.