ABOUT POLAGE® ART:

THE PHYSICS OF POLAGE

The Light Fantastic

by Donald H. Lyons,Department of Physics,University of Massachusetts/Boston March 1987

The title of my talk is “The Light Fantastic.” It might have been something like “Fascinating Physics,” or “Why I Love Physics,” or maybe, more deeply, something like “The Explanatory Power of Physics,” or, dressing it up, “Modern Paradigms for Light.” But really, it’s mainly going to be a kind of magic show.

Let me tell you a bit of how I got into this. Lexington, where I live, has an art gallery called “Gallery on the Green.” [Editor’s note: No longer in business. Contact the studio for list of places you might see Austine's Polage Artwork in real life.] One day I wandered into the gallery and saw these things called Polages. I have one here on exhibit 1. If you look at it carefully, you’ll see that the colors in it continually shift and change. The first question for me was, how does it work? By the way, the artist who makes these Polages is in the audience. Her name is Austine Wood-Comarow, and she is here with her husband to supervise the mounting of a huge 25 foot by 27 foot permanent exhibit of Polages in the Boston Museum of Science.

When I shine light through this Polage, you don’t see much of anything, just some nearly colorless plastic. Now, if I put this other piece of colorless plastic in front of the Polage, suddenly I get intense colors which shift and change as I rotate the plastic. They also change if I tilt the plastic or you view it at a different angle. If I take away the plastic and you look at the Polage in reflection, using an ordinary mirror, again you don’t see much of anything, nothing unexpected. But if I substitute a shiny piece of black plastic for the mirror, you’ll see colors again. The image formed by reflection is colored, but the object which is reflected is not! There are a lot of little mysteries here!

To help explain what we have seen, I’ll run through a brief history of optics. The first thing we note is the stellar galaxy of people who contributed to the science of optics of thought about light. We can go back to Euclid, who contributed the idea that there are rays of something which travel in straight lines. According to Euclid, however, that something traveled outward from the eye – a common theory in earlier times. One didn’t receive light or anything else, rather the eye actively sought out objects by emitting something. After Euclid, we come to another famous figure, Claudius Ptolemy, who lived in Alexandria. Ptolemy made a table of angles of incidence vs. angles of refraction for a light beam passing from air to water. This data is perhaps the oldest recorded table of physical measurements. Ptolemy, of course, is much better known for his theories of how the sun and planets move around the Earth; He was also the leading astrologer of the day. Kepler, known chiefly for his immortal three laws of planetary motion – for example that planets move in elliptical orbits – in addition laid the foundation for geometrical optics. Descartes was the first to give a proper explanation for the formation of rainbows; here we again have colorless material, water droplets, making colors. He also said, supposedly, “I think, therefore I am.” By thinking about rainbows, he proved his own existence. Newton’s experiments with prisms were famous. Newton not only showed that light could be dispersed by a prism into a spectrum of colors; he showed that a second prism could recombine the light of different colors into white light. That demonstrated that the colors were not manufactured in the prism itself but were actually present in the white light.

Bartholinus, a Danish physicist not now generally known, discovered double refraction. Double refraction, also called birefringence, is at the heart of our story, the heart of how a Polage works.

Here I show an arrow, and now I put a calcite crystal over it and you see two arrows instead of one. When I rotate the crystal, you notice that one arrow stays fixed while the other one rotates. We’ll get back to this after the next bit of history, which is Huygens discovery of polarization. Huygens, known today mostly for his principle of secondary wavlets which contributed a lot to the development of the wave theory of light, also discovered the phenomenon of polarization. Before explaining polarization, I want to show you what effect it has. I have here something called a Polaroid filter, which polarizes light. If I lay it on top of the calcite crystal and orient the polaroid one way, we see only one arrow . If I rotate it by 90 degrees, we see only the other arrow. This proves that the light in one arrow is polarized one way and the light in the other arrow is polarized along the perpendicular direction. Birefringence and polarization are the two phenomena required to explain how a Polage works. A complete Polage is a sandwich of two polaroids with birefringent material in the middle (Fig. 2). So we have three elements: polaroid. birefringent material, another polaroid. When we understand how these work together, we’ll understand Polages.

Goethe (a brief history of optics), not a famous name in science (although he wrote something like fourteen volumes on science) wrote a huge tome of some fifteen hundred pages on the theory of colors, part of which is still useful; not an equation in it, no mathematics at all. The first part is an immense compendium of all the phenomena that have to do with color, the next part is a polemical attack on Newton’s theory of light, and then there is a final historical part. Up to the time of the early nineteenth century there was a dispute as to whether light consisted of waves or particles. The great authority Newton maintained that light consisted of particles despite the fact that many of his own experiments could be easily explained with the wave theory. The wave theory triumphed in the nineteenth century as a result of the experiments of Young and Fresnel, who demonstrated that light exhibits the properties of a particular kind of wave, namely transverse waves. The only kind of wave that can be polarized is a transverse wave.

The next name, Brewster, is not very well known but Brewster comes into our story because he studied how reflected light is polarized. When light is reflected by a non-metallic surface, the reflected light is partially or completely polarized even if the incident light is unpolarized. That is why we saw a colored image of the Polage when we saw it as a reflection in the black plastic sheet. We didn’t see colors in the image formed by the mirror because the reflecting surface, the film of silver, was metallic. In the course of his studies of reflection, Brewster invented the kaleidoscope, which became a rage throughout Europe and a principal form of home entertainment. This should have made Brewster rich but, unfortunately for him, the market quickly became captured by a flood of cheap, inferior kaleidoscopes. I have something here which looks like a kaleidoscope, called a “Karascope”. Designed by Judith Karelitz and sold through the Museum of Modern Art, it works on the same principles as Polages; if you look through it and rotate it, you see various shifting colors made by polarizers and birefringent plastic.

The next, and very important, figure is James Maxwell, who added to and unified the existing theories of electricity and magnetism. Here is a T-shirt on which are printed the celebrated Maxwell equations of electromagnetism. Such shirts are commonly owned by physics students who study these equations at length and learn that most of the properties of light can be predicted from them. From his equations, Maxwell inferred the existence of electromagnetic waves which travel with the known speed of light, and concluded that light consisted of such waves. Light waves, because they are electromagnetic waves, exert forces on the charged particles of matter.

Einstein also had a little bit to do with light. According to Einstein, light travels at the same speed, with respect to an observer, no matter how fast the observer is moving. That‘s screwy! But not really – that idea led to the special theory of relativity! Still, Einstein didn’t get a Nobel prize for that or for his general theory of relativity; he got it for explaining certain features of the photoelectric effect. To do that, he invented the photon concept, in which light is modeled as a stream of particles. So, is light a particle or a wave? I could say a lot about that, but I won’t. For us, it’s a wave: it acts like a wave. The other, final bit of history which made Polages possible was the invention of a cheap, simple and convenient polarizer. In 1928, when he was an undergraduate at Harvard University, Edwin Land invented something called J-sheet. In 1938 he invented H-sheet, which is what we’re using today. He called the material “polaroid” and went on to found the Polaroid Corporation. As I’ve said, two polaroid sheets make up the front and back of a complete Polage.

I want to turn now to what polarized light is and how polaroid’s work, how they polarize light. When light is incident on or passing through a medium, the charged particles (nuclei, electrons) experience a force. I want to focus on the force. (Fig. 3) Let the little black dot in the center of the screen represent a charged particle, and suppose there is a light wave traveling from the screen toward you. There will be a force on the particle. The arrow represents the force, the length of the arrow being proportional to the size of force and the direction of the arrow being the direction of the force, which lies parallel to the screen. I can resolve the force into components, one horizontal component and one vertical component. Together, the two components make up a force that is at an angle to the horizontal. The picture shows the force at one instant of time. As time passes, the two components rapidly change their size, and go back and forth from positive to negative. For visible light, these fluctuations are extremely fast – on the order of one million, billion times each second. By definition, when the light is Iinearly polarized, the two components will fluctuate together and the resultant force will always be parallel (or, anti-parallel) to the direction shown on the screen. The two components, in this case, are precisely correlated and we say they are in phase. On the other hand, for unpolarized light, the two components are uncorrelated and the tip of the arrow will move all around the center of the diagram, and at any Instant might be pointing in any direction. If unpolarized light passes through a polarizer, it emerges linearly polarized.

How does a polarizer change unpolarized light to polarized light? The polarizers I’m going to talk about are called dichroic polarizers. They absorb or reflect the energy from one component and let the other component through. Now imagine a lot of wires like this, vertical, and light incident on the wires (Fig. 4). The force on the electrons in the wire at one instant of time is represented by the arrow. One can break the arrow into two components, one that fluctuates vertically, parallel to the wires, and the other component that fluctuates horizontally. The vertical component causes the electrons to move up and down in the wire, which results in the energy in that component of the light being partly reflected and partly turned into heat in the wire. The other component of the light exerts a horizontal force on the electrons, but they are confined to the wire and cannot move horizontally. As a result, the horizontal component passes through the wire grid and the light that emerges is horizontally polarized – the force that it exerts on a charged particle is horizontal. That’s how a wire grid polarizer works. To make one, the wires must be much closer than the wavelength of the light, which means there has to be a lot of wires very close together. Someone succeeded in making one with fifty thousand wires per inch, so that in one one-thousandth of an inch, there are fifty wires. How do you make something like that? You rule a diffraction grating. That is, you have a machine which scratches a straight line on a metal plate with a diamond point. The point is attached to a very fine screw which can be advanced 1/50,000 of an inch between scratches. Then, you use the plate to form a transparent plastic sheet imprinted with the scratched lines. Having done all that, you evaporate gold atoms so that they are incident on the plastic at a very shallow angle. The gold gets plated on the edges of the ridges as shown by the black dots in the diagram. You end up with a wire grid, 50,000 wires per inch that polarizes light. This little trick was accomplished in 1960.

Edwin Land had a better idea in 1938, when he invented H-sheet (Fig.5). It consists of polyvinyl alcohol (PVA) plastic sheet which has been stretched and mounted on cellulose acetate. Before you stretch it, the molecules are all twisted every which way, but when you stretch it out, the long molecules line up in the direction of the stretch. Iodine atoms are attached to the PVA molecules which make the molecules conducting. The PVA sheet is attached to the cellulose acetate to keep it from shrinking back to its original size. So now you have microscopic wires all lined up and the system acts just like a wire grid polarizer.

Now let’s see polaroid in action. I have two large pieces here. If you want some, what you do is call up the Polaroid company and ask them to send you a price list and some samples. They send you these big sheets. The second time you do it, they send you these little tiny sheets. Unfortunately, the process converges rapidly and you only get a finite amount of polaroid out of them. Now, I put a polaroid on the projector and a second polaroid on top of it. You don’t see anything much, just two ordinary pieces of gray plastic. But if I turn the top polaroid 90 degrees, it blocks out almost all the light. The first polaroid passes only the horizontal component of the unpolarized light, and the second polaroid blocks it now because it allows only a vertical component to pass. But now watch this. I insert a piece of glass between the polaroids and you see that nothing changes. Now, I put a piece of tape on the glass – Tuck tape which is cellulose tape – and insert it between the polaroids. Now light passes through where the tape is If I rotate the top polaroid, light passes everywhere except where the tape is. Now cross the first tape with a second piece and you see that the second piece cancels out the effect of the first where they cross, so that the center is light, but the rest of the tape is dark. Rotating the top polaroid again reverses that. On the other hand, the tape does nothing if it is lined up with the edges of the polaroids. Tuck tape can do all this because, like calcite, it is birefringent. You can see that now we have all kinds of possibilities. Before explaining how polaroids combined with birefringent material can exhibit colors, let me show you some more examples of the phenomenon. Brewster, who made the first study of polarization, also invented two new applied fields. One is called optical mineralogy, the study of minerals, generally under a microscope, while being sandwiched between polarizers. Here’s an example, a large piece of mica, and you see I can make a “Polage” out of it . If I place the mica between polaroids, it becomes iridescent because it’s birefringent. If I replace the mica with a folded and crumpled sheet of cellophane, it appears very similar to the mica. We can learn a lot about minerals by using polarized light. The second field created by Brewster is called photoelasticity. This piece of Plexiglass plastic is only weakly birefringent, but if I stress it, the birefringence increases and you can see intense and varied colors appear in the regions of maximum stress. If you’re clever enough, before you build a bridge, you build a model of the bridge out of plastic, illuminate the model with polarized light and examine it through a polaroid. You can deduce a lot, even quantitatively, about the stresses. When you have a complex problem in stress analysis, that’s a way to do it.

Now let’s talk about how light passing through calcite produces two images and how the polarization of light is changed when it passes through cellophane; both effects are consequences of birefringence. When a ray of unpolarized light is incident on the calcite from the direction shown, it divides into two rays, each one linearly polarized (Fig. 6). The ray which goes straight through is the ordinary ray, so-called because it obeys Snell’s law of refraction. The X’s and 0’s represent arrows into and out of the plane of the figure, respectively, and give the direction of the force field at their locations. Thus, the ordinary ray is linearly polarized perpendicular to the figure. The lower ray, the extraordinary ray, so-called because instead of going straight through, it goes through in a crazy direction, creates a second image. The arrows indicate that this ray is polarized in the plane of the figure. The two rays with different polarizations – and this fact is crucially important for the following – go through in different directions because they travel at different speeds.

Cellophane is a little different from calcite, but the principle involved is very similar (Fig. 7). There are two perpendicular axes in the plane of the cellophane, which I’ll call the fast axis and the slow axis. Light which is polarized along the fast axis travels faster through the cellophane than light which is polarized along the slow axis. The diagram shows incident light which is linearly polarized in a direction between the fast and slow axes. This is equivalent to a combination of light polarized along the fast axis plus light polarized along the slow axis, whose force fields are in phase, as illustrated by placing the arrows directly under the X’s and 0’s. The two components have been displaced vertically in the diagram in order to more clearly illustrate what happens. In the cellophane, the light travels more slowly, as can be inferred by the shorter wavelengths, given by the distance between vertical arrows, for example. (Incidentally, this slower travel is in contradiction to Newton’s theory of light particles which he thought must travel faster in material.) Note that the wavelength of light polarized in the plane is slightly shorter than the wavelength of light polarized perpendicular to the figure, when the light is in the cellophane. Hence, when the light emerges from the cellophane, the two components are no longer in phase. Here’s a second diagram (Fig. 8) which is slightly different. Instead of representing the force field by arrows, it shows graphs of the two components of the field. As before, the two components have been displaced vertically in the diagram in order to more clearly illustrate what happens. The height of the peaks of both components is equal, implying that the components are equal in magnitude. This means that the resultant force field makes equal angles, 45 degrees, with the fast and slow axes. You see that two and a quarter slow waves fit in the material, whereas only two waves of the fast wave fit inside. Consequently, when the peaks of the two waves emerge, they are separated in space by a quarter of a wavelength. Now a quarter of a wavelength in space translates to a quarter of a cycle in time. A full cycle is 360 degrees; one-quarter is 90 degrees, so the two emergent waves are ~g0 out of phase, whereas they were in phase before entering. As a result, the birefringent material has altered the polarization; what went in as linearly polarized light comes out circularly polarized.

“Circular (I) polarization- you never mentioned that before,” I hear you cry. Well, there’s not only linear and circular polarization, there’s elliptical polarization. When two perpendicular vectors oscillate with the same frequency, the tip of the resultant vector traces out an ellipse (or line segment or circle, special cases of ellipses). Figure 9 shows some of the possibilities. The shape and size of the ellipse depends on the amplitudes and phases of the oscillations of the component vectors. When the phase difference of the oscillations is zero, the ellipse flattens to a line segment and the tip of the resultant vector moves back and forth along a straight line. For a phase difference of 60~, the tip moves along a skinny ellipse. If the phase difference is 900, and the amplitudes are equal, the tip moves in a circle. I can demonstrate this concept with the aid of a ball on a string. As I swing the ball in a vertical circle, you see it moving up and down, while at the same time it moves left and right. Note that the maximum vertical displacement from the center occurs when the horizontal displacement is zero; the horizontal displacement is one quarter of a cycle, or 90 degrees , out of phase with the vertical displacement Now imagine a strong light illuminating this ball from some arbitrary direction, with a shadow of the ball cast upon some screen. The shadow would trace out an ellipse on the screen. The motion of the shadow could be resolved into two simultaneous oscillations of generally different amplitudes and phases, the oscillations being along different axes in the plane of the screen. Returning now to Figure 8, you can see that the phase difference, and hence the ellipse of polarization, clearly depends on both the wavelength of the light and on the thickness of the material; the thicker the material, the greater the phase difference. The two amplitudes and the phase difference depend also on the orientation of the fast and slow axes relative to the direction of polarization of the incident light.

Now we can put it all together, lets return to Figure 2 which shows light traversing the three elements of a complete Polage. The amplitude of light of a given wavelength which emerges from the Polage depends on the polarization ellipse, which in turn depends on the wavelength. Hence, the Polage alters the proportions of the various colors which compose the incident white light and the eye will generally perceive color. In addition, the ellipse depends on the orientation and thickness of the cellophane, both of which differ in different regions of the Polage which then will exhibit different colors. Finally, rotating either polaroid also alters the spectrum of the light which emerges so that the colors change. Figure 10 illustrates how the position of the second polaroid affects the spectrum. When the pass direction is vertical as shown, the emergent light is mainly blue light; when the pass direction is horizontal, the emergent light is mainly red light. The artist, Austine Wood-Comarow, takes full advantage of all these possibilities to create beautiful and exciting effects in her work.

The formal talk ended here. Figure 11 illustrates a demonstration that was exhibited informally to some of the members of the audience.

Notes:

1. The Polage art exhibited pictured Leda and the Swan. It was a complete Polage, i.e., could be viewed without adding another polarizing filter. Mounted in a light box, its rear polarizer rotated slowly.

2. A Polage of hummingbirds was illuminated from behind. When a square of polarizer was held in front, the area behind the polarizer became iridescent.

3. A plate on which there was a transparent arrow surrounded by black was placed on the projector.

Bibliography:

Sabra, Theories of Light from Descartes to Newton – Cambridge University Press 1981.

Goethe, Farbenlehre, “Didactic Part,” trans. Charles Eastlake in 1820. Reprint Van Nostrand Reinhold, 1971.

Shurcliff and Ballard, Polarized Light . D. Van Nostrand 1964.