Note: those readers with a knowledge of basic physics, particularly of resonance, waves, and simple electricity and magnetism, can skip to Section 3 for explanations of the colors of rainbows, the blue sky, and the setting sun. If you are familiar with resonance and are particularly interested in WHY THE SKY IS BLUE, go to Short summary at the end of Section 4, where I present a question I used often in final exams and give the answer to it.
1. RESONANCE IN ORDINARY LIFE 1.1 Resonance between two tuning forks You probably first experienced the phenomenon of resonance as a child when you learned to pump yourself on a swing.Like most children, you imitated older children and pulled back and forth on the ropes while kicking your legs in and out.But you didn’t succeed until your back-and-forth pumping matched the natural frequency of the swing, i.e., the frequency with which you would swing back and forth if someone pulled you back and let you go.The lesson you learned is that you could swing high if your pumping rate was in resonance with the natural frequency of the swing.In slightly more technical language, you can made the swing go high if your pumping rate match the swing’s natural frequency.
All physical systems have natural frequencies of vibration.A simple system like a person on a swing, more technically known as a pendulum, has only one natural frequency.Likewise, a tuning fork has one natural frequency.(I’m avoiding a slight complication here: any physical system has a large number of “natural” frequencies, but the pendulum and tuning fork are most easily excited in just one.)A guitar string, on the other hand, has many easily excited natural frequencies, depending on where it is picked.
A tuning fork is set into vibration simply by hitting it.The same thing could be done with you on a swing, but that wouldn’t be very nice for you.It’s better to pump yourself or have someone give you a gentle push each time you swing back to your high point.Is there a more gentle way to cause a tuning fork to vibrate than hitting it?Yes, there is.The technique is illustrated in Figure 1, which shows two tuning forks.The one on the right has a fixed frequency fo, while the one on the left has a variable frequency f that can be changed gradually by sliding the small mass attached to it up or down‑ When the fork on the left is hit, it emits sound waves of frequency f, and if f is adjusted to match fo, these sound waves can pump the one on the right, i.e., some of the sound energy emitted by f is absorbed by fo.(The purpose of the sounding boxes is simply to amplify the energy emitted by f and absorbed by fo.)
It is very simple to do a tuning fork resonance experiment in a classroom, and I have done it many times. My technique is to hit the variable-frequency fork hard, let it vibrate and emit sound for a few seconds and then grab it with my hand, whereupon it stops vibrating and emitting sound. The response of the fixed-frequency fork determines how much sound can be heard coming from it when the other fork is silenced. Of course, the biggest response of fo occurs when f is as close as possible to fo, but the surprise is that moving f gradually away from fo doesn’t cause the resonance to vanish abruptly.Instead, the response of fo goes down gradually.This is depicted in Figure 2, which shows that we can still get some resonance if f is above or below fo.This “resonance curve” has a very general shape, known as a “Lorentzian” after the great late 19th and early 20th century Dutch physicist H. A. Lorentz.The Lorentzian is ubiquitous in nature, characterizing such different vibratory systems as electrical circuits and atoms.As we’ll see, it is the Lorentzian nature of the atom in its interaction with light that is responsible for the blueness of the sky!
1.2 Resonance, absorption, and scattering Technically, the resonance process between tuning forks involves three steps. First, the sound energy emitted by the variable-frequency fork is absorbed by the fixed-frequency fork. Second, the absorbed energy causes the fixed-frequency fork to vibrate. And third, the vibration re-emits the sound energy. This type of three-step process is encountered throughout the physical world and defines a "scattering" process, i.e., the energy emitted toward scattering system (in our case, the sound from the variable fork directed towards the fixed fork) is absorbed and re-emitted in a random direction. (In our case, it is re-emitted in all directions throughout the room that the demonstration is done in). So we say in this case that the sound from one fork is scattered by the other fork.
2. WAVES, ELECTROMAGNETISM, AND LIGHT 2.1 Water Waves Throw a stone as far out as you can into a still pond, and you’ll cause a disturbance where the stone hits. Because of the properties of water, the point where the stone hits bobs up and down and sends out waves in a concentric pattern, as shown schematically in Figure 3.
Figure 4 shows a profile of the wave shape of the water wave. One of the important features of a simple wave like in Figure 4 is the distance between peaks, known as the wavelength, call it L. Another important feature is the speed of the wave, v. Since in general time = distance/speed, we can say that the time needed for the wave to travel one wavelength (so the a peak in the diagram moves to the position of the next peak to the right of it) is T = L/v. Turning the equation around, we get v = L/T. But 1/T is the frequency of the wave, f. For example, if it takes 0.1 second for the wave train to move one wavelength, then the number of wave peaks passing a given point in one second, i.e., the frequency, is 1/0.1 = 10/second. So v = L/T can be written in a form commonly used in physics, called the "wave equation":
v = Lf. (1)
Normally, the wave speed is constant. For example, the speed of sound for a wide range of frequencies is 340 meters/sec (or more simply, 340 m/s), while the speed of light in a vacuum is always 300,000 km/s (186,284 mi/s). The speed of sound changes only for very high frequencies. 2.2 Resonance for Waves on a String I mentioned above that a guitar string has lots of resonances. Figure 5 shows three examples, which you can illustrate for yourself by shaking one end of a long rope tied at the other end. The resonant frequencies (and wavelengths) are determined essentially by the length of the string. In this case, the string has fixed ends, and only those frequencies which leave the ends fixed can resonate with the string. At these special resonant frequencies, the amplitude of vibration of the string becomes large and has the form of a standing wave, i.e., there are points (called nodes) of no vibration and in between, the vibrations are very large.
Please note well: as the wave equation (Eq. (1)) shows, the higher the frequency the shorter the wavelength, as demonstrated in Figure 5. This inverse relationship between wavelength and frequency is true in general, and we will use this important fact in what follows.
2.3 Light Waves Are Sort of Similar to Waves On a String All of the waves we have considered so far need some material medium made of molecules to travel through, like a string, water, or air.If there is no string, it is impossible to have a wave on a string.Light is also a form of wave, but unlike the types we just mentioned, light does not need to travel through a material medium.For example, the light from the sun travels through interplanetary space quite easily, even though there is practically no material there.There is even less material in the space between galaxies, but again light has no problem getting from one point to another.
2.4 The Electromagnetic Nature Of Light Although light doesn't need a material medium to travel through, it is, like all other waves, a disturbance that travels from one point to another.So the next question is, "A disturbance of what?" Light is a disturbance in electric and magnetic fields. In another sense, light is pure electromagnetic energy that can travel through empty space.To understand the electromagnetic nature of light, consider the electric field of a charge, conveniently represented by field lines showing the direction of the force the charge would exert on another charge situated at that point. Field lines come out in all directions from a single charge, representing the fact that another charge of the same sign (i.e., both are positive or both are negative) is repelled by the given charge.Figure 6(a) shows just a single electric field line coming out from a positive charge.You might think of the line as a string or rope hooked to the charge.This string picture turns out to be a fruitful way to analyze how charges produce light waves, because when the charge is wiggled, it is very similar to wiggling the end of a string or rope—a sinusoidal electric wave travels out along the field line, and each point of the electric line wiggles up and down.This is shown in Figure 6(b). But a wiggling charge also creates a magnetic wave, as shown in Figure 6(c). The magnetic wave is perpendicular to the E wave, and reaches its maximum value when the E wave does.The vibrating electric and magnetic fields make up what we call “light,” i.e., light is an electromagnetic (EM) wave.
A historical note is appropriate here.The great Scottish physicist James Clerk Maxwell discovered the EM nature of light in the mid-1860s.Maxwell theoretically predicted the existence of EM waves, and had a hunch that light would be a type of EM wave.The speed of EM waves depends on physical constants associated with electric attraction and repulsion between charges and a law relating magnetism to electric current.We observe electric charge effects on a dry winter day when we experience a static shock, and everyday motors use electric currents and magnets.Neither electric nor magnetic laws appear at first glance to have the remotest connection to light, but Maxwell's genius was to discover the possibility of EM waves and he expressed the speed of EM waves in terms of these physical constants.When he calculated the speed, he found it to be the same as the speed of light.What a wonderful moment it must have been to discover that light is intimately related to electricity and magnetism!
His hunch was based on the work of two other scientists, Weber and Kohlrausch, who measured electric charge in two different ways and showed that the ratio of the units appropriate to the two measurements is the speed of light.
2.5 The Varieties of EM Waves: the Electromagnetic Spectrum So far, we have been talking about light as an EM wave.When most people think of light, they think of something they can see.But there are many types of EM waves which, though they have the same nature as ordinary light, are not visible to the human eye.In fact, the human eye is, on average, able to see wavelengths of light only between 0.0000004 and 0.0000007 meters.It is more convenient to express such tiny lengths in terms of the nanometer (nm) unit, which is a billionth of a meter.Therefore, visible light covers the range of 400 to 700 nm, the red endof the range having the longer wavelength and the violet end having the shortest.
Just beyond the visible range into higher wavelengths, from about 700 to 1,000,000 nm, we have infrared (ir) radiation.Since frequency is inversely proportional to wavelength, ir radiation has a lower frequency than visible radiation.Ir radiation is emitted by all objects which possess thermal energy, i.e., by all objects above absolute zero of temperature.This is why a photograph can be taken with infrared-sensitive film in a completely dark room and yields a picture with almost as much detail as visible light.All living organisms are warm enough to emit ir radiation, and in ordinary doses, ir is not dangerous.
Just beyond the visible range towards lower wavelengths, from about 300 to 100 nm, lies the ultraviolet (uv) range. Uv radiation can be dangerous to the human body, producing cataracts and skin cancer.It also kills bacteria.Uv is emitted by very hot bodies such as the sun.This uv radiation would be a serious threat to life on Earth if it weren't for the protective ozone layer in the stratosphere which absorbs uv radiation.
Figure 7 shows the "electromagnetic spectrum," i.e., the various types of EM waves in terms of wavelength, represented by the Greek letter lambda (the funny symbol shown just to the right of the arrow tip on the wavelength scale of Figure 7). Also shown are the usual sources of the waves.Note the huge range covered by EM wavelengths: from the size of nuclei to thousands of kilometers.Many of the types are quite familiar to you, like microwaves and radio waves.The EM spectrum is a crucial part of everyday life!
2.6 The Visible Spectrum: the RGB Simplification The visible part of the EM spectrum consists of an infinite number of colors, because each frequency in the spectrum corresponds to a separate color. But traditionally, the spectrum has been arbitrarily broken down into seven colors, dependent undoubtedly by the ability of the human eye to distinguish them: violet, indigo, blue, green, yellow, orange, and red. This is more easily remembered from the first letters of each color, which spell out the name of that great alien from outer space, VIBGYOR. Most people have never heard of Vibgyor, but are familiar what that man-about-town and bon vivant Roy G. Biv (Vibgyor spelled backwards). There is an even simpler scheme using just the primary additive colors of red, green, and blue, or RGB. (When computer screens first when to color, they were known in the trade as "RGB monitors.") White light is just a mixture of all visible colors in equal proportions. Furthermore, an equal mixture of R, G, and B produces white light. Any color can be produced from the R, G, and B by mixing them in the correct proportions. In what follows, this three-color RGB simplification will suffice.
3. THE RAINBOW
Do not all charms fly At the mere touch of cold philosophy? There was an awful rainbow once in heaven: We know her woof, her texture; she is given In the dull catalogue of common things. Philosophy will clip an angel’s wings, Conquer all mysteries by rule and line, Empty the haunted air, the gnomed mine-- Unweave a rainbow.--John Keats (1795-1821)
The great English poet whose words form the introduction to this section believed that "cold philosophy," i.e., natural science, stripped nature of its charms and mysteries by providing naturalistic explanations for phenomena such as the "awful" (i.e., awe-ful) rainbow. Those who think seriously about science disagree (as I certainly do) that scientific explanations are "cold," because the fact that nature lends itself to explanation is itself a wondrous thing. As Einstein put it, "The most incomprehensible thing about the universe is that it is comprehensible." Why indeed should nature allow certain aspects of itself to be comprehended by our brains? Pondering these questions quickly raises others, such as the extent that science succeeds by ignoring the subjective aspects of nature like color and smell that concerned Keats. These issues are further discussed in four essays ("Science, art, epistemology, and values") in the Philosophy section of this web site. For now, let us investigate further how light waves behave and how they can explain the beauty of the rainbow.
As everyone knows, rainbows can occur after rain storms. But it is also possible to see a rainbow from an airplane flying above the clouds, in which case the rainbow appears on the cloud. In this case, you see a complete circular rainbow, unlike the partial arc you see when standing on Earth's surface. You can also manufacture a rainbow in your back yard on a sunny day by shooting a fine spray of water into the air. Clearly, the rainbow arises in some way from light and water droplets. This first step in understanding the rainbow was taken thousands of years ago, at least back to the time of Aristotle. Aristotle thought the rainbow resulted from a reflection of light from the raindrops, but as we'll see, this is incorrect.
Figure 8 shows a spherical raindrop suspended in the air. Also shown is sunlight hitting the top part of the raindrop. The entire raindrop is hit by sunlight, but only the small portion shown creates the rainbow. We are interested in the extremes of the rainbow, so Figure 8 shows just the red and blue ends of the visible spectrum.
When light hits the raindrop, it is bent or refracted. But the important point for the rainbow is that different colors are bent by different amounts, and this separates the colors, a phenomenon known as dispersion. We already saw an example of this different bending of different colors in the prism spectroscope. For a spherical raindrop, the amount of bending between the incoming and outgoing light differs for each color, but on average it is 42 degrees. The different bending of the red and blue creates a 1.5 degree angle between these extreme colors. Figure 8 shows that one raindrop sends red light into one person's eye and blue into another. Not shown are other people who receive orange, yellow, …etc. light from this single raindrop.
Each raindrop refracts just a tiny bit of light into a person's eye, too little for the person to notice. But "zillions" of raindrops will put enough light into the person's eye to make the rainbow visible. The situation for a single person is shown in Figure 9.
Figure 10 shows the angle the rainbow makes with the direction of the sun's rays. As seen by the person observing the rainbow, there is a 42 degree angle between the line going from the sun through the person's head to the rainbow. Furthermore, since Earth's puny gravitational field affects light very little, any raindrop 42o from the line going from the sun through the person's head produces a rainbow color. These raindrops define a circular arc with this line at the center, as shown.
4. THE BLUE SKY
4.1 A Tuning Fork Model of Earth's Atmosphere and the Sun The reason the sky is blue has much to do with the behavior of tuning forks which we discussed above, because electrons in atoms and molecules behave much like tuning forks when they emit and absorb EM radiation. To understand why, consider Figure 11(a), which roughly illustrates the frequencies of EM radiation corresponding to visible light that a typical isolated atom, say hydrogen (H), resonates strongly with. (There are many other resonant wavelengths in non-visible parts of the spectrum, but for simplicity we’ll look only at the visible frequencies that resonate strongly.) Just like an ordinary tuning fork, an atom has a few special strong resonances for a given frequency range. In fact, the famed Schrödinger equation of quantum mechanics can be transformed into a form which closely resembles the equation for a "simple harmonic oscillator," which applies to a tuning fork giving off a single tone. An atom typically has a number of resonant frequencies, so it can be thought of as a collection of tuning forks.
In Figure 11(a), the H gas is cool, e.g. like air at room temperature, and not very dense. The H atoms of the gas then absorb or resonate with only a limited number of frequencies of visible light, particularly red. In fact, the atom will also emit these same frequencies if the electron of the H atom is knocked up to a higher-energy state and falls down to the lower ones. This is true in general: any frequency emitted by an atom will also be strongly absorbed, and vice versa.
In (b), the gas is hotter and/or denser, and the sharp resonant responses of the atoms are now smeared out, so that although the frequencies shown in (a) are still most strongly absorbed, nearby frequencies are also absorbed but not as strongly as the originals.
A completely different situation arises if the hydrogen gas is extremely hot, as it is in our sun. In this case, shown in (c), we no longer have an H gas with an electron held to the atom. Instead, the electrons are stripped from the H atoms and we have a plasma and all visible frequencies are more or less equally absorbed or emitted. (The term “resonance” is not so appropriate in this case.) The sun's light is spread more or less equal emission across the visible part of the spectrum which makes the sun have an almost-white color.
We can make the tuning fork connection by re-drawing Figure 11 in terms of the resonance curve of a tuning fork in Figure 2. The re-drawing is shown in Figure 12:
In the present context, we are interested in the atoms and molecules in the atmosphere of Earth. Earth's atmosphere consists of nitrogen and oxygen molecules, and these molecules have resonances with EM radiation and like atoms can be modeled as tuning forks.
Earth’s atmosphere is neither very hot nor very dense, so the response to sunlight is more like shown in Figure 11(a), except for one important difference: the frequency most strongly absorbed is NOT in the visible region, but in the ultraviolet (uv). In fact, we will assume that this uv frequency is absorbed so strongly that the nitrogen molecules can be considered to have only one uv frequency, and likewise for oxygen. Since atoms and also molecules behave like tuning forks, we can model atmospheric molecules as tuning forks with a single frequency in the ultraviolet part of the spectrum. A "tuning fork" atmosphere is shown in a rather fanciful way in Figure 13:
The sun is a plasma, and as suggested by Figure 12(c), it emits all frequencies not just in the visible, but in all regions of the EM spectrum. Using the tuning fork model, the sun can be imagined to consist of a large number of tuning forks of all different frequencies (small forks with high frequencies and big forks with small frequencies). There is a nice analogy between the resonance of two tuning forks as shown in Figure 1 and the action of the sun's radiation on air molecules. For this purpose, think of nitrogen molecules having a resonance curve like in Figure 2, the peak of the curve being in the uv part of the EM spectrum. Similarly, oxygen molecules have a similar resonance curve with a peak also in the uv, but not quite at the same frequency as the nitrogen peak. Just as the resonant response of the fixed fork depends on how close to its resonant frequency the frequency of the variable fork is, so the resonant response of the air molecule tuning forks depends on how close the frequencies of various radiations from all the different tuning forks in the sun are to the uv peaks of the air molecule resonance curves.
Figure 14(a) is a slightly different look at figure 1, but now emphasizing the re-emission of the energy absorbed by the fixed-frequency fork. Figure 14(b) depicts, in a fanciful tuning fork model, many frequencies being radiated by the sun to Earth. Some of the radiations have frequencies that are right on the uv peaks of the air molecule resonance curves and are absorbed strongly by air molecules. Other frequencies are not on the peaks and are not absorbed as much.
The key to understanding the blue color of the sky is that the further the frequency of the visible color from the sun is from the air molecule resonance peaks, the less it is absorbed; conversely and most importantly, the closer the frequency of the visible color from the sun is from the air molecule resonance peaks, the more it is absorbed. So which color is closer to the uv? Figure 15 shows two curves (not to scale!), one for the intensity of radiation emitted by the sun, and the other the Lorentzian resonance absorption curve for nitrogen. (A separate resonance curve, almost but not quite in the same position, would apply to oxygen, but for simplicity only one curve is shown.) The first curve is a "black body" or Planck curve, named after Max Planck who discovered the equation for the curve in 1900. The other is the resonance curve for nitrogen molecules. It shows that none of the visible colors are close to resonance peak, but blue is closer than red. In fact, the resonance curve at blue, low as it is, is much higher than at red. Consequently, blue will be absorbed by air molecules much more than red. And what of uv light from the sun near or at the resonance peak? It is very strongly absorbed.
You might have noticed that the previous discussion of this section referred only to absorption of radiation and not scattering (i.e., re-emission), even though we said in Section 1.2 that absorption by the fixed-frequency fork of sound energy from the variable one is followed by re-emission, or scattering, of sound in a random direction. This is an important point. If scattering always occurred, then air molecules would be absorbing and re-emitting uv energy, which would bathe us in uv. As everyone knows, uv is dangerous. It can cause skin cancer and blindness, among other things. Thankfully, uv is not scattered. But blue light from the sun is indeed scattered, because the sky is blue in any direction you look (where there are no clouds) away from the sun. Figure 16 shows light coming straight down relative to the person at the top of Earth's curved surface. The dashed line shows the direction the person is looking. The sunlight above Earth's atmosphere (the dotted region) is shown as an equal mixture of red, green, and blue, which is close to what is actually emitted by the sun. (As mentioned earlier, the almost-equal mix is responsible for the whitish color of the sun.) The sunlight is no longer an equal mix after passing through the atmosphere, as shown by the unequal line lengths on the left. All along the viewer's line of sight, blue is being preferentially scattered in all directions, as shown by the many short blue arrows, some of which are directed toward the person's eyes and make the sky blue as seen by the person.
Completion of our the blue-sky story still requires an explanation of why uv is not scattered while blue is. There are two parts to the answer. First, any energy not close to the uv resonance peak is not held onto very long after being absorbed, but is almost immediately re-emitted in a random direction--"almost immediately" being less than a billionth of a second, too fast for a collision with another air molecule to be likely. This is certainly true of all light in the visible part of the spectrum. But uv light close to the resonance peak is held onto for a much longer time, long enough for a collision with another air molecule to occur. When a collision occurs, the energy held by the air molecule is "thermalized," i.e., it is converted to heat. In other words, the absorbed energy is released in such a way that it causes the colliding molecules to rebound with a greater relative speed than they approached each other. This same action is responsible for the tremendous absorption of uv light by ozone, whose resonance curve has a much, much higher peak in the uv than nitrogen or oxygen. So although there are not nearly as many ozone molecules in the atmosphere (actually, in the stratosphere), they suffice to absorb enough uv to keep us safe.
I taught physics for non-science majors for many years, and sky colors were an important part of the course. Given all that has gone before, it might be helpful for the reader to see a summary in terms of an answer to a question that I always gave on final exams. The question refers to the diagram in Figure 16, but minus the colored light above and below the atmosphere and the blue light scattered along the viewer's line of sight.
QUESTION ON THE BLUE SKY: The diagram shows Earth and its atmosphere when the sun is high in the sky. Also shown is a person on Earth’s surface. Use this diagram to explain why the sky is blue. Do this by the following steps. (1) Show the intensities of the red, green and blue colors in a beam of light just outside of Earth’s atmosphere. (2) Show this same beam after it is almost to the ground, again indicating the relative intensities of red, green, and blue. (3) Choose a direction for the person to be looking at the sky. (4) Show what happens to the light from the sun along the line of sight of the person. (5) Then write a narrative to explain what your diagram represents and why the sky is blue, using the concept of resonance, the tuning fork analogy, the resonant properties of the O2 and N2 molecules in the atmosphere, and conditions for the relevance of collisions between molecules. Your discussion of this last point (regarding collisions) should address what happens to the uv light compared to visible light.
ANSWER: O2 and N2 molecules in Earth's atmosphere are like little tuning forks that have resonant peaks in the uv part of the spectrum. The sun is like a collection of tuning forks which give off all frequencies of electromagnetic (EM) radiation, including visible light. Just as a tuning fork gives off a sound wave whose energy can resonate with another tuning fork, so the EM radiation given off by the sun can resonate with the O2 and N2 molecules. The only difference is that a tuning fork emits just one frequency whereas the sun gives off a range of frequencies all the time. The O2 and N2 molecules resonate with all frequencies of EM radiation from the sun, including the visible colors (i.e., r,g, and b), but the degree of resonance depends on the frequency. As mentioned, these molecules have their resonant peaks in the uv part of the EM spectrum, which means that they "like" uv photons, and when they absorb one, they will hold on to it long enough for collisions with other molecules to occur. When this happens, the uv energy is shaken loose in such a way that it makes the speed of the molecules increase. As a result, all of the original photon energy is absorbed, i.e., the photon energy disappears and is converted into thermal energy. Ozone, O3, is particularly good at absorbing uv photons and in this way it protects us from dangerous uv radiation. Visible photons, on the other hand, are not on as good "speaking terms" with O2 and N2 molecules, so the molecules get rid of these photons quickly by re-emitting or scattering them in random directions. The key to understanding the blueness of the sky is to realize that blue is closer to the O2 and N2 uv resonant peak than red and green are, and hence blue is scattered the most. It is scattered in all directions, so the sky looks blue.
5. COLORS OF THE SETTING SUN
The plural "colors" in the title of this section might come as a surprise to some, because as we have all observed, the setting sun has a reddish color. But in addition, there is a fleeting instant in which the setting sun gives off a green color--the wonderful but difficult-to-see "green flash." We'll look at both phenomena.
5.1 The Red Setting SunOne of the most beautiful sights is the red setting sun. An example is the header on each page of this web site. The explanation follows immediately from our explanation of the blue sky. As Figure 16 shows, blue is greatly removed from direct sunlight because it is scattered randomly to a great degree. Green is removed also, but not as much; and red only a bit reduced. As Figure 17 shows, when the sun is low on the horizon, it is traveling through a great thickness of air, and this removes large amounts of blue and a significant amount of green, leaving mostly red. Figure 18 shows what happens as an equal mix of red, green and blue travels through a large thickness of air. So by the time it gets to the person's eye, it is almost all red. This red light scatters and reflects from any clouds near the observer's horizon, creating spectacular patches of red and (for clouds farther away and higher up) orange.
5.2The Green FlashThe beautiful but elusive green flash can be explained by first showing the action of a prism on a beam of white light. As mentioned in the discussion of the rainbow, refraction is the bending of light when it goes from one material (e.g., air) or a vacuum into another. It is important that the beam is not coming in along the perpendicular (also called the normal) to the prism surface. The rainbow discussion also pointed out that red, green, and blue colors are bent by different amounts, i.e., they are dispersed. This is shown in Figure 19(a), where a beam of white light, i.e., an equal mix of red, green, and blue, hits a prism surface a an angle to the normal. The difference in bending for different colors is much smaller than the total bending, but the difference is exaggerated in Figure 19 for clarity. Note that blue is bent the most, red the least, and green in between. But light from the sun also comes at an angle to the normal to the top of the atmosphere when the sun is at or near the horizon . This is suggested in Figure 19(b). The net effect is that we get separate red, blue, and green images of the sun. Of course, separate color images are produced whenever the sun is not directly overhead (which is the only case where its light comes in along the normal), but the dispersion is not great enough to produce separate images unless it is near the horizon. An immediate question about Figure 19(b) arises: WHERE IS THE BLUE IMAGE OF THE SUN?? The answer is very simple. There is a blue image, but remember that sunlight travels through a great thickness of air (see Figure 17), and most of the blue is removed. Of course, a good bit of green is removed and indeed a lot of red is too, but it is mostly red and a bit of green that remain. The blue is totally negligible.
Now note that the green image is above the red one. As the sun sinks below the horizon, the red image disappears first, and what is left? The green image. This is the "green flash," the word "flash" indicating that the only thing the unaided human eye can see is a brief appearance of the color green--it lasts only for a fraction of a second if the sun comes down to the horizon at a steep angle.
The total bending of all colors in sunlight is about half a degree (much bigger than the dispersion of the colors from each other), and this is also the angular diameter of the sun. Consequently, as shown in Figure 20, the sun is actually below the horizon when we see its bottom touching the horizon. Note that on this scale, the tiny angular difference between the red and green sun images is so tiny that it is neglected.
5.3A simple demonstration of blue and red from scattering Molecules are not the only thing that can cause preferential scattering of blue light. In fact, any particle of matter whose size is smaller than a wavelength of blue light will preferentially scatter the blue. A nice everyday example is homogenized milk. Milk is homogenized when the fat particles in it are broken down into a size small enough to keep the fat suspended in the water (which makes up most of milk's substance). These fat particles are smaller than a wavelength of blue light, so you can demonstrate the mechanism of the blue sky with milk and a flashlight! This is shown in Figure 21. I have done it by starting out with a jar of clear water and then pouring bits of milk. As the amount of milk increases, the light scattered to the side appears blue while the filament of the bulb in the flashlight gets orange and then, after enough milk is poured in, it gets red.
There's an interesting phenomenon of nature that can create the most beautiful red setting sun, but the phenomenon is violent in nature: a volcanic eruptions. Volcanic eruptions throw a lot of dirt high into the atmosphere, even up to the stratosphere, and some of the dirt particles are small enough to stay suspended for long periods of time. They are also small enough to scatter blue light preferentially, so when the sun is low on the horizon, so much of the blue light is scattered out that the sun appears with a deep red color. The extremely large eruption of Indonesia's Mount Tambora in 1815 produced beautiful sunsets world-wide for several years. This eruption also cooled Earth for several years! As every climatologist knows, carbon dioxide is not the sole determinant of global temperature.
Another less comforting human activity can make sunsets red: pollution in the form of aerosols (small droplets of chemical compounds). That is about the only positive benefit of pollution!