by Walter Lewin
So how can you go rainbow hunting? First of all, trust your instincts about when a rainbow might form. Most of us tend to have a good intuitive sense of that: those times when the Sun is shining just before a rainstorm, or when it comes out right after one. Or when there’s a light shower and the sunlight can still reach the raindrops.
When you feel one coming on, here’s what you do. First, turn your back to the Sun. Then locate the shadow of your head, and look about 42 degrees in any direction away from the imaginary line. If there’s enough sunlight, and if there are enough raindrops, the collaboration will work and you will see a colorful bow.
Suppose you cannot see the Sun at all—it’s somehow hidden by clouds or buildings, but it’s clearly shining. As long as there are no clouds between the Sun and the raindrops, you still ought to be able to see a rainbow. I can see rainbows in the late afternoon from my living room facing east when I cannot see the Sun that is in the west. Indeed, most of the time you don’t need the imaginary line and the 42-degree trick to spot a rainbow, but there is one situation where paying attention to both can make a big difference. I love to walk on the beaches of Plum Island off the Massachusetts coast. Late in the afternoon the sun is in the west and the ocean is to the east. If the waves are high enough and if they make lots of small water drops, these droplets act like raindrops and you can see two small pieces of the rainbow: one piece at about 42 degrees to the left of the imaginary line and a second piece about 42 degrees to the right. These rainbows only last for a split second, so it’s a huge help in spotting them if you know where to look in advance. Since there are always more waves coming, you will always succeed if you can be patient enough. More about this later in this chapter.
Here is another thing you can try to look for, the next time you spot a rainbow. Remember our discussion of the maximum angle at which certain light can refract out of the raindrop? Well, even though you will see blue, or red, or green from certain raindrops, raindrops themselves cannot be so choosy: they refract, reflect, and refract lots of light at less than a 40-degree angle too. This light is a mixture of all the different colors at roughly equal intensities, which we see as white light. That’s why, inside the blue band of a rainbow, the sky is very bright and white. At the same time, none of the light that refracts, reflects, and refracts again can exit raindrops beyond the 42-degree angle, so the sky just outside the bow is darker than inside the bow. This effect is most visible if you compare the brightness of the sky on either side of the rainbow. If you’re not specifically looking for it, you probably won’t even notice it. There are excellent images of rainbows in which you can see this effect on the Atmospheric Optics website, at www.atoptics.co.uk.
Once I began explaining rainbows to my students, I realized just how rich a subject they are—and how much more I had to learn. Take double rainbows, which you’ve probably seen from time to time. In fact, there are almost always two rainbows in the sky: the so-called primary bow, the one I’ve been discussing, and what we call the secondary bow.
If you’ve seen a double rainbow, you’ve probably noticed that the secondary bow is much fainter than the primary bow. You probably haven’t noticed, though, that the order of colors in the secondary bow is blue on the outside and red on the inside, the reverse of that in the primary. There is an excellent photograph of a double rainbow in this book’s photo insert.
In order to understand the origin of the secondary bow, we have to go back to our ideal raindrop—remember, of course, that it actually takes zillions of drops to make up a secondary rainbow as well. Some of the light rays entering the drops reflect just once; others reflect twice before exiting. While light rays entering any given raindrop can reflect many times inside it, the primary bow is only created by those that reflect once. The secondary bow, on the other hand, is created only by those that reflect twice inside before refracting on the way out. This extra bounce inside the raindrop is the reason the colors are reversed in the secondary bow.
The reason the secondary bow is in a different position from the primary bow—always outside it—is that twice-reflected red rays exit the drop at angles always larger (yes, larger) than about 50 degrees, and the twice-reflected blue rays come out at angles always larger than about 53 degrees. You therefore need to look for the secondary bow about 10 degrees outside the primary bow. The reason that the secondary bow is much fainter is that so much less light reflects inside the raindrops twice than reflects once, so there’s less light to make the bow. This is, of course, why it can be hard to see the secondary bow, but now that you know they often accompany primary rainbows, and where to look for them, I’m confident you’ll see lots more. I also suggest that you spend a few minutes on the Atmospheric Optics website.
Now that you know what makes rainbows, you can perform a little optical magic in your own backyard or on your driveway or even on the sidewalk, with just a garden hose. But because you can manipulate the raindrops, and they are physically close to you, there are a couple of big differences. For one thing, you can make a rainbow even when the Sun is high in the sky. Why? Because you can make raindrops between you and your shadow on the ground, something that rarely happens naturally. As long as there are raindrops that the sunlight can reach, there can be rainbows. You may have done this already, but perhaps not as purposefully.
If you have a nozzle on the end of the hose, adjust it to a fine spray, so the droplets are quite small, and when the Sun is high in the sky, point the nozzle toward the ground and start spraying. You cannot see the entire circle all at once, but you will see pieces of the rainbow. As you continue moving the nozzle in a circle, piece by piece you will see the entire circle of the rainbow. Why do you have to do it this way? Because you don’t have eyes in the back of your head!
You will see red at about 42 degrees from the imaginary line, the inside edge of the circular bow will be blue, and inside the bow you will see white light. I love performing this little act of creation while watering my garden, and it’s especially satisfying to be able to turn all the way around and make a complete 360-degree rainbow. (The Sun, of course, will then not always be behind you.)
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.)
