by Walter Lewin
I always carry at least one polarizer with me in my wallet—yes, always—and I urge my students to do the same.
Why am I telling you all this about polarized light? Because the light from rainbows is nearly completely polarized. The polarization occurs as the sunlight inside the water drops reflects, which, as you now know, is a necessary condition for rainbows to be formed.
I make a special kind of rainbow in my classes (using a single, though very large, water drop) and I am able to demonstrate that (1) red is on the outside of the bow, (2) blue is on the inside, (3) inside the bow the light is bright and white, which is not the case outside the bow, and (4) the light from the bow is polarized. The polarization of the bows for me is very fascinating (one reason why I always carry polarizers on me). You can see this wonderful demonstration in my lecture at http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-22/.
Beyond the Rainbow
Rainbows are the best known and most colorful atmospheric creations, but they are far from alone. There is an entire host of atmospheric phenomena, some of them really quite strange and striking, others deeply mysterious. But let’s stay with rainbows for a bit and see where they take us.
When you look carefully at a very bright rainbow, on its inner edge you may sometimes see a series of alternating bright-colored and dark bands—which are called supernumerary bows. You can see one in the insert. To explain these we must abandon Newton’s explanation of light rays. He thought that light was composed of particles, so when he imagined individual rays of light entering, bouncing around in, and exiting raindrops, he assumed that these rays acted as though they were little particles. But in order to explain supernumerary bows we need to think of light as consisting of waves. And in order to make a supernumerary bow, light waves must go through raindrops that are really small, smaller than a millimeter across.
One of the most important experiments in all of physics (generally referred to as the double-slit experiment) demonstrated that light is made of waves. In this famous experiment performed around 1801–03, the English scientist Thomas Young split a narrow beam of sunlight into two beams and observed on a screen a pattern (the sum of the two beams) that could only be explained if light consists of waves. Later in time this experiment was done differently actually using two slits (or two pinholes). I will proceed here assuming that a narrow beam of light strikes two very small pinholes (close together) made in a thin piece of cardboard. The light passes through the pinholes and then strikes a screen. If light was made of particles, a given particle would either go through one pinhole or through the other (it cannot go through both) and thus you would see two bright spots on the screen. However, the pattern observed is very different. It precisely mimics what you’d expect if two waves had hit the screen—one wave coming from one pinhole and simultaneously one identical wave coming from the other. Adding two waves is subject to what we call interference. When the crests of the waves from one pinhole line up with the valleys of waves from the other, the waves cancel each other, which is called destructive interference, and the locations on the screen where that happens (and there are several) remain dark. Isn’t that amazing—light plus light turns into darkness! On the other hand, at other locations on the screen where the two waves are in sync with one another, cresting and falling with one another, we have constructive interference and we end up with bright spots (and there will be several). Thus we will see a spread out pattern on the screen consisting of alternating dark and bright spots, and that is precisely what Young observed with his split-beam experiment.
I demonstrate this in my classes using red laser light and also with green laser light. It’s truly spectacular. Students notice that the pattern of the green light is very similar to that of the red light except that the separation between the dark and the bright spots is somewhat smaller for the green light. This separation depends on the color (thus wavelength) of light (more about wavelength in the next chapter).
Scientists had been battling for centuries over whether light consisted of particles or waves, and this experiment led to the stunning and indisputable conclusion that light is a wave. We now know that light can act both as a particle and as a wave, but that astounding conclusion had to wait another century, for the development of quantum mechanics. We don’t need to go further into that at the moment.
Going back to supernumerary bows, interference of light waves is what creates the dark and bright bands. This phenomenon is very pronounced when the diameter of the drops is near 0.5 millimeters. You can see some images of supernumerary bows at www.atoptics.co.uk/rainbows/supdrsz.htm.
The effects of interference (often called diffraction) become even more dramatic when the diameters of the droplets are smaller than about 40 microns (0.04 millimeters, or 1/635 of an inch). When that happens, the colors spread out so much that the waves of different colors completely overlap; the colors mix and the rainbow becomes white. White rainbows often show one or two dark bands (supernumerary bows). They are very rare and I have never seen one. A student of mine, Carl Wales, sent me pictures in the mid-1970s of several beautiful white rainbows. He had taken the pictures in the summer at two a.m. (yes, two a.m.) from Fletcher Ice Island, which is a large drifting iceberg (about 3 × 7 miles). At the time, it was about 300 miles from the North Pole. You can see a nice picture of a white rainbow in the insert.
These white bows can also be seen in fog, which consists of exceptionally tiny water droplets. White fogbows can be hard to spot; you may have seen them many times without realizing it. They are likely to appear whenever fog is thin enough for sunlight to shine through it. When I’m on a riverbank or in a harbor in the early morning, when the Sun is low in the sky, and where fog is common, I hunt for them and I have seen many.
Sometimes you can even create a fogbow with your car headlights. If you’re driving and the night fog rolls in around you, see if you can find a safe place to park. Or, if you’re at home and the fog comes, face your car toward the fog and turn on your headlights. Then walk away from your car and look at the fog where your headlight beams are. If you’re lucky, you might be able to see a fogbow. They make the gloom of a foggy night even spookier. You can see the results of a fellow stumbling across fogbows that he made with his car headlights at www.extremeinstability.com/08-9-9.htm. Did you notice the dark bands in the white bows?
The size of water droplets and the wave nature of light also explain another of the most beautiful phenomena that grace the skies: glories. They can best be seen when flying over clouds. Trust me, it’s worth trying to find them. In order to do so, you must, of course, be in a window seat—and not over the wings, which block your view down. You want to make certain that the Sun is on the side of the plane opposite your seat, so you’ll have to pay attention to the time of day and the direction of the flight. If you can see the Sun out your window, the experiment is over. (I have to ask you to trust me here; a convincing explanation requires a lot of very complicated math.) If these conditions are met, then try to figure out where the antisolar point is and look down at it. If you’ve hit the jackpot you may see colorful rings in the clouds and if your plane is flying not too far above the clouds, you may even see the glory circling the shadow of the plane—glories have diameters that can vary from a few degrees to about 20 degrees. The smaller the drops, the larger the glories.
I have taken many pictures of glories, including some where the shadow of my plane was clearly visible and the really fun part is that the position of my seat is at the center of the glory, which is the antisolar point. One of these pictures is in the insert.
You can find glories in all kinds of places, not just from airplanes. Hikers often see them when they have the Sun to their backs and look down into misty valleys. In these cases, a quite spooky effect happens. They see their own shadow projected onto the mist, surrounded by the glory, sometimes several colorful rings of it, and it looks positively ghostly. This phenomenon is also known as
the Brocken spectre (also called Brocken bow), named for a high peak in Germany where sightings of glories are common. In fact, glories around people’s shadows look so much like saintly halos, and the figures themselves look so otherworldly, that you will not be surprised to learn that glory is actually an old word for the circle of light around the heads of various saints. In China, glories are known as Buddha’s light.
I once took a marvelous photo of my own shadow surrounded by a glory that I refer to as the image of Saint Walter. A good many years ago I was invited by some of my Russian astronomer friends to their 6-meter telescope in the Caucasus Mountains. This was the world’s largest telescope at the time. The weather was just awful for observing. Every day I was there, at about five thirty in the afternoon a wall of fog would come rolling up out of the valley below and completely engulf the telescope. I mean totally; we couldn’t make any observations at all during my visit. A picture of the fog ascending is shown in the insert. In talking to the astronomers, I learned that the fog was very common. So I asked, “Why then was this telescope built here?” They told me that the telescope was built on that site because the wife of a Party official wanted it right there, and that was that. I almost fell off my chair.
Anyway, after a few days, I got the idea that I might be able to take a fantastic photo. The Sun was still strong in the west every day when the fog came up from the valley, which was to the east, the perfect setup for glories. So the next day I brought my camera to the observatory, and I was getting nervous that the fog might not cooperate. But sure enough, the wall of fog swelled up, and the Sun was still shining, and my back was to it. I waited and waited and then, boom, there was the glory around my shadow and I snapped. I couldn’t wait to develop the film—this was in the pre-digital age—and there it was! My shadow is long and ghostly, and the shadow of my camera is at the center of the rings of a gorgeous glory. You can see the picture in the insert.
You don’t need to be in such an exotic location to see a halo around your head. On a sunlit early morning if you look at your shadow on a patch of dewy grass (of course with the Sun right behind you), you can often see what in German is called Heiligenschein, or “holy light”: a glow around the shadow of your head. (It’s not multicolored; it’s not a glory.) Dewdrops on the grass reflect the sunlight and create this effect. If you try this—and I hope you will—they’re easier to find than glories. You will see that since it’s early morning and the Sun is low, your shadow will be quite long, and you appear much like the elongated and haloed saints of medieval art.
The many different types of bows and halos can surprise you in the most unexpected places. My favorite sighting happened one sunny day in June 2004—I remember it was the summer solstice, June 21—when I was visiting the deCordova Museum in Lincoln, Massachusetts, with Susan (who was not yet my wife at the time), my son, and his girlfriend. We were walking across the grounds toward the entrance when my son called out to me. There in front of us, on the ground, was a stunning, colorful, nearly circular bow. (Because it was the solstice, the Sun was as high as it ever gets in Boston, about 70 degrees above the horizon.) It was breathtaking!
I pulled out my camera and snapped a bunch of photos as quickly as I could. How unexpected. There were no water droplets on the ground, and I quickly realized the bow could not have been made from water drops in any event because the radius of the bow was much smaller than 42 degrees. And yet it looked just like a rainbow: the red was on the outside, the blue was on the inside, and there was bright white light inside the bow. What could have caused it? I realized that it must have been made by transparent, spherical particles of something, but what could they be?
One of my photographs of the bow, which you can see in the insert, turned out so well that it became NASA’s astronomical mystery picture of the day, posted on the web on September 13, 2004.* (This, by the way, is a terrific website, and you should look at it every day at http://apod.nasa.gov/apod/astropix.html.) I received about three thousand guesses as to what it was. My favorite response was a handwritten note from Benjamin Geisler, age four, who wrote, “I think your mystery photo is made by light, crayons, markers and colored pencils.” It’s posted on the bulletin board outside my office at MIT. Of all the answers, about thirty were on the right track, but only five were dead on.
The best clue to this puzzle is that there was a good bit of construction going on at the museum when we visited. In particular, there had been a lot of sandblasting of the museum’s walls. Markos Hankin, who was in charge of the physics demonstrations at MIT and with whom I have worked for many years, told me—I didn’t know this at the time—that some kinds of sandblasting use glass beads. And there were lots of tiny glass beads lying on the ground. I had taken a few spoonfuls of the beads home. What we had seen was a glassbow, which has now become an official category of bow, a bow formed by glass beads; it has a radius of about 28 degrees, but the exact value depends on the kind of glass.
Markos and I couldn’t wait to see if we could make one of our own for my lectures. We bought several pounds of glass beads, glued them on big sheets of black paper, and attached the paper to a blackboard in the lecture hall. Then, at the end of my lecture on rainbows, we aimed a spotlight on the paper from the back of the lecture hall. It worked! I invited the students to come, one by one, to the front of the class, where they stood before the blackboard and cast their shadow smack in the middle of their own private glassbow.
This was such a thrilling experience for the students that you might want to try it at home; making a glassbow is not too difficult. It does depend on what your objectives are. If you just want to see the colors of the bow, it’s quite easy. If you want to see the entire bow encircling your head it’s more work.
To see a small piece of the bow, all you need is a piece of black cardboard about one foot square, some clear spray adhesive (we used 3M’s Spray Mount Artist’s Adhesive, but any clear spray glue will do), and transparent spherical glass beads. They must be transparent and spherical. We used “coarse glass bead blast media,” with diameters ranging from 150 to 250 microns, which you can find here: http://tinyurl.com/glassbeads4rainbow.
Spray glue on your cardboard, and then sprinkle the beads on it. The average distance between the beads isn’t critical, but the closer the beads are, the better. Be careful with these beads—you probably want to do this outside so you don’t spill beads all over your floor. Let the glue dry, and if you have a sunny day, go outside.
Establish the imaginary line (from your head to the shadow of your head). Place the cardboard somewhere on that line; thus you will see the shadow of your head on the cardboard (if the Sun is low in the sky, you could put the cardboard on a chair; if the Sun is high in the sky you could put it on the ground—remember the glass beads at the deCordova museum were also on the ground. You may select how far away from your head you place the cardboard. Let’s assume that you place it 1.2 meters (about 4 feet) away. Then move the cardboard about 0.6 meters (2 feet) away from the imaginary line in a direction perpendicular to the line. You may do that in any direction (left, right, up, down)! You will then see the colors of the glassbow. If you prefer to place the cardboard farther away, say 1.5 meters (5 feet), then you have to move the cardboard about 0.75 meters (2.5 feet) to see the colors of the bow. You may wonder how I arrived at these numbers. The reason is simple, the radius of a glassbow is about 28 degrees.
Once you see the colors, you can move the cardboard in a circle around the imaginary line to search for other parts of the bow. By so doing, you are mapping out the entire circular bow in portions, just as you did with the garden hose.
If you want to see the entire bow around your shadow all at once, you’ll need a bigger piece of black cardboard—one full square meter will do—and with a lot more glass beads glued to it. Place the shadow of your head near the center of the cardboard. If the distance from the cardboard to your head is about 80 centimeters (about 2.5 feet), you will immediately see the entire glass bow. If you br
ing the cardboard too far out, e.g., 1.2 meters (4.0 feet), you will not be able to see the entire bow. The choice is yours; have fun!
If it’s not a sunny day, you can try the experiment indoors, as I did in lectures, by aiming a very strong light—like a spotlight—at a wall, on which you’ve taped or hung the cardboard. Position yourself so the light is behind you, and the shadow of your head is in the center of the one square meter cardboard. If you stand 80 centimeters away from the board, you should be able to see the entire bow circling your shadow. Welcome to the glass bow!
We don’t need to understand why a rainbow or fogbow or glassbow is formed in order to appreciate its beauty, of course, but understanding the physics of rainbows does give us a new set of eyes (I call this the beauty of knowledge). We become more alert to the little wonders we might just be able to spot on a foggy morning, or in the shower, or when walking by a fountain, or peeking out of an airplane window when everyone else is watching movies. I hope you will find yourself turning your back to the Sun the next time you feel a rainbow coming on, looking about 42 degrees away from the imaginary line and spotting the red upper rim of a glorious rainbow across the sky.
Here’s my prediction. The next time you see a rainbow, you’ll check to make sure that red is on the outside, blue is on the inside; you’ll try to find the secondary bow and will confirm that the colors are reversed; you’ll see that the sky is bright inside the primary bow and much darker outside of it; and if you carry a linear polarizer on you (as you always should), you will confirm that both bows are strongly polarized. You won’t be able to resist it. It’s a disease that will haunt you for the rest of your life. It’s my fault, but I will not be able to cure you, and I’m not even sorry for that, not at all!
