For the Love of Physics (16 page)

One cold winter day in 1972 I was so determined to get some good photos of these homemade rainbows for my class that I made my poor daughter Emma, who was just seven, hold the hose in my yard, squirting the water high in the air, while I snapped away with the camera. But I guess when you’re the daughter of a scientist you have to suffer a little bit for the sake of science. And I did get some great pictures; I even managed to photograph the secondary bow, using my contrasting blacktop driveway as the background. You can see the picture of Emma in the insert.

I hope you’ll try this experiment—but do it in the summer. And don’t be too disappointed if you don’t see the secondary bow—it may be too faint to show up if your driveway isn’t dark enough.

From now on, with this understanding of how to spot rainbows, you’ll find yourself compelled to look for them more and more. I often can’t help myself. The other day as Susan and I were driving home, it started to rain, but we were driving directly west, into the Sun. So I pulled over, even though there was a good deal of traffic; I got out of the car and turned around, and there it was, a real beauty!

I confess that whenever I walk by a fountain when the sun is shining, I position myself so I can search for the rainbow I know will be there. If you’re passing by a fountain on a sunny day, give it a try. Stand between the Sun and the fountain with your back to the Sun, and remember that the spray of a fountain works just like raindrops suspended in the sky. Find the shadow of your head—that establishes the imaginary line. Then look 42 degrees away from that line. If there are enough raindrops in that direction, you’ll spy the red band of the rainbow and then the rest of the bow will come immediately into view. It’s rare that you see a full semicircular arc in a fountain—the only way you can see one is to be very close to the fountain—but the sight is so beautiful, it’s always worth trying.

Once you’ve found it, I warn you that you may just feel the urge to let your fellow pedestrians know it’s there. I often point these fountain rainbows out to passersby, and I’m sure some of them think I’m weird. But as far as I’m concerned, why should I be the only one to enjoy such hidden
wonders? Of
course
I show them to people. If you know a rainbow could be right in front of you, why not look for it, and why not make sure others see it too? They are just so beautiful.

Students often ask me whether there is also a tertiary bow. The answer is yes and no. The tertiary bow results, as you might have guessed, from three reflections inside the raindrop. This bow is centered on the Sun and, like the primary bow, which is centered on the antisolar point, it also has a radius of about 42 degrees and red is on the outside. Thus you have to look toward the Sun to see it and it has to rain between you and the Sun. But when that is the case, you will almost never see the Sun. There are additional problems: a lot of sunlight will go through the raindrops without reflecting at all and that produces a very bright and very large glow around the Sun which makes it effectively impossible to see the tertiary bow. The tertiary bow is even fainter than the secondary. It is also much broader than the primary and the secondary bow; thus the already faint light of the bow is spread out even more over the sky and that makes it even more difficult to see it. As far as I know, no pictures of tertiary bows exist, and I do not know of anyone who has ever seen a tertiary bow. Yet there are some reports of sightings.

Inevitably, people want to know if rainbows are real. Maybe they’re mirages, they wonder, receding endlessly as we approach them. After all, why can’t we see the end of the rainbow? If this thought has been at the back of your mind, breathe easy. Rainbows are real, the result of real sunlight interacting with real raindrops and your real eyes. But since they result from a precise collaboration between your eyes, the Sun, and the raindrops, you will see a different rainbow from the person across the street. Equally real, but different.

The reasons we usually cannot see the end of the rainbow touching the Earth are not because it doesn’t exist, but because it’s too far away, or hidden by buildings or trees or mountains, or because there are fewer raindrops in the air there and the bow is too faint. But if you can get close enough to a rainbow, you can even touch it, which you should be able to do with the rainbow you make with your garden hose.

I have even taken to holding rainbows in my hand while I shower. I accidentally discovered this one day. When I faced the shower spray, I suddenly saw two (yes two!) bright primary rainbows inside my shower, each one about a foot long and an inch wide. This was so exciting, so beautiful; it was like a dream. I reached out and held them in my hands. Such a feeling! I’d been lecturing on rainbows for forty years, and never before had I seen two primary rainbows within arm’s reach.

Here’s what had happened. A sliver of sunlight had shone into my shower through the bathroom window. In a way, it was as though I was standing not in front of a fountain, but inside the fountain. Since the water was so close to me and since my eyes are about three inches apart, each eye had its own, distinct imaginary line. The angles were just right, the amount of water was just right, and each of my eyes saw its own primary rainbow. When I closed one eye, one of the rainbows would disappear; when I closed the other eye, the other bow vanished. I would have loved to photograph this astonishing sight, but I couldn’t because my camera has only one “eye.”

Being so close to those rainbows that day made me appreciate in a new way just how real they were. When I moved my head, they too moved, but as long as my head stayed where it was, so did they.

Occasionally I time my morning showers whenever possible to catch these rainbows. The Sun has to be at the right location in the sky to peek through my bathroom window at the right angle and this only happens between mid-May and mid-July. You probably know that the Sun rises earlier and goes higher in the sky in certain months, and that in the Northern Hemisphere it rises more to the south (of east) than in the winter months, and more to the north (of east) in summer.

My bathroom window faces south, and there’s a building on the south side, making sure that light can never enter from due south. So sunlight only comes in roughly from the southeast. The time I first saw the shower bows was while I was taking a very late shower, around ten o’clock. In order to see rainbows in your own shower you will need a
bathroom window through which sunlight can reach the spray. In fact, if you can never see the Sun by looking out your bathroom window, there’s no point in looking for shower bows—there just won’t be any. The sunlight must be able to actually reach your shower. And even if it does come directly in, that’s no guarantee, because many water drops have to be present at 42 degrees from your imaginary line, and that may not be the case.

These are probably difficult conditions to meet, but why not try? And if you discover that the Sun enters your shower just right late in the afternoon, well, then, you could always think about changing your shower schedule.

Why Sailors Wear Sunglasses

Whenever you do decide to go rainbow hunting, be sure to take off your sunglasses if they are the kind we call polarized, or you might miss out on the show. I had a funny experience with this one day. As I said, I love to take walks along the beaches of Plum Island. And I’ve explained how you can see little bows in the spray of the waves. Years ago I was walking along the beach. The sun was bright and the wind was blowing, and when the waves rolled over as they got close to the beach, there was lots of spray—so I was frequently seeing small pieces of bows as I mentioned earlier in this chapter. I started pointing them out to my friend, who said he couldn’t see what I was talking about. We must have gone back and forth half a dozen times like this. “There’s one,” I would shout, somewhat annoyed. “I don’t see anything!” he would shout back. But then I had a bright moment and I asked him to take off his sunglasses, which I looked at—sure enough, they were polarized sunglasses. Without his sunglasses he did see the bows, and he even started to point them out to me! What was going on?

Rainbows are something of an oddity in nature because almost all of their light is polarized. Now you probably know the term “polarized” as
a description of sunglasses. The term is not quite technically correct, but let me explain about polarized light—then we’ll get to the sunglasses and rainbows.

Waves are produced by vibrations of “something.” A vibrating tuning fork or violin string produces sound waves, which I talk about in the next chapter. Light waves are produced by vibrating electrons. Now, when the vibrations are all in one direction and are perpendicular to the direction of the wave’s propagation, we call the waves linearly polarized. For simplicity I will drop the term “linearly” in what follows as I am only talking in this chapter about this kind of polarized light.

Sound waves can never be polarized, because they always propagate in the same direction as the oscillating air molecules in the pressure waves; like the waves you can generate in a Slinky. Light, however, can be polarized. Sunlight or light from lightbulbs in your home is not polarized. However, we can easily convert nonpolarized light into polarized light. One way is to buy what are known as polarized sunglasses. You now know why their name isn’t quite right. They are really polarizing sunglasses. Another is to buy a linear polarizer (invented by Edwin Land, founder of the Polaroid Corporation) and look at the world through it. Land’s polarizers are typically 1 millimeter thick and they come in all sizes. Almost all the light that passes through such a polarizer (including polarizing sunglasses) has become polarized.

If you put two rectangular polarizers on top of each other (I hand out two of them to each of my students, so they can experiment with them at home) and you turn them 90 degrees to each other, no light will pass through.

Nature produces lots of polarized light without the help of one of Land’s polarizers. Light from the blue sky 90 degrees away from the direction of the Sun is nearly completely polarized. How can we tell? You look at the blue sky (anywhere at 90 degrees away from the Sun) through one linear polarizer and rotate it slowly while looking through it. You will notice that the brightness of the sky will change. When the sky becomes almost completely dark, the light from that part of the sky
is nearly completely polarized. Thus, to recognize polarized light, all you need is one polarizer (but it’s much more fun to have two).

In the first chapter I described how in class I “create” blue light by scattering white light off cigarette smoke. I arrange this in such a way that the blue light that scatters into the lecture hall has scattered over an angle of about 90 degrees; it too is nearly completely polarized. The students can see this with their own polarizers, which they always bring with them to lectures.

Sunlight that has been reflected off water or glass can also become nearly completely polarized if the sunlight (or light from a lightbulb) strikes the water or glass surface at just the right angle, which we call the Brewster angle. That’s why boaters and sailors wear polarizing sunglasses—they block much of the light reflecting off the water’s surface. (David Brewster was a nineteenth-century Scottish physicist who did a lot of research in optics.)

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.