THE COLORS OF THE SKY during daylight and twilight have been notoriously hard to explain even though they have been scrutinized scientifically for well over a century. Why is a clear daytime sky mostly blue but white near the horizon? Why is the setting sun normally red and the sky just above it a tapestry of colors? At twilight why does a curved shadow with a rosy border rise in the eastern sky? Why does a purple patch sometimes appear and then fade in the western sky soon after sunset, and why does another purple patch sometimes appear as much as two hours later? These questions call for studies of how light interacts with molecules and airborne particles. For some of the questions definitive answers are still being sought.

There has been no shortage of explanations for why a clear sky is largely blue. Many popular schemes involve the scattering of sunlight from such airborne materials as dust, aerosols, ice crystals and water droplets; others depend on absorption of the red end of the visible spectrum by the water and ozone in the atmosphere. The inadequacies of these accounts were reviewed in 1985 by Craig F. Bohren and Alistair B. Fraser of Pennsylvania State University, who also pinpointed the correct explanation, one that was introduced in 1899 by Lord Rayleigh.

Rayleigh had been slow to accept his own explanation, in part because of findings published in 1869 by John Tyndall, the British physicist who is remembered for his skill at making science accessible to nonscientists. Tyndall demonstrated how artificially produced smog took on "a colour rivalling that of the purest Italian sky" when it was illuminated with a beam of white light and viewed at an angle to the beam. For years thereafter many investigators, including Rayleigh, believed the scatter of light from particles produced the blue of the sky. Moreover, they concluded that a pure gas such as air cleansed of all particles would not be able to scatter light and break it up into different colors.

In his publication of 1899 Rayleigh finally stated that the scattering and color separation were due to the air molecules themselves-that "even in the absence of foreign particles we should still have a blue sky." By then he had constructed an elegant model of how a molecule scatters light. To understand his model, consider an air molecule (it makes no difference which kind) illuminated by white sunlight. The light is a composite of all the colors in the visible spectrum; a wavelength is associated with each tint. The wavelength increases from blue to green, yellow and red; the wavelength associated with red light is about 1.68 times the wavelength associated with blue light.

Each color component in the sunlight is scattered from the molecule in all directions but not with uniform intensity. The brightest scatter is in the forward direction (as if the light passed directly through the molecule) and in the backward direction (back toward the sun). Light scattered at a right angle to the sunlight's initial path is only half as bright. All the colors scatter in this pattern, but the intensity scattered in any particular direction is different for each color. Rayleigh found that the intensity depends on the inverse fourth power of the wavelength. Therefore short-wave-length light (say blue) is more strongly scattered than, say, red light, which has a long wavelength. Since the ratio of their wavelengths is about 1.68, the blue scattered light is 1.684 (or about eight) times as bright as the red scattered light.

Suppose you intercept the light that is scattered to the side at an angle of about 90 degrees to the initial direction of the sunlight. If you could perceive the light from a single molecule, it would be bluish, because the blue end of the spectrum would be brightest. The picture is more realistic when abundant molecules scatter light to you, so that the light and its color are perceptible. That is the case when you look up at an area of the sky away from the sun. All the molecules along your line of sight scatter light to you that is dominated in intensity by blue; that part of the sky appears to be bluish-not pure blue, because you also intercept the other, fainter colors.

The fact that the blue end of the spectrum is strongly scattered out of the initial beam of light means the beam continuing through the atmosphere gradually becomes dominated by the red end of the spectrum. If you look toward the sun when it is high, the light reaching you has traversed too little of the atmosphere to be appreciably reddened. When the sun is low and the sunlight takes a longer path through the atmosphere to reach you, the light is noticeably reddened, and so sunsets are dominated by the red end of the spectrum.

You may detect an apparent contradiction in this argument. Blue light is always more strongly scattered than red light-in any direction. The statement even applies to the light that is scattered forward and continues in the initial direction of the beam. If blue light is more strongly scattered forward than red light, why does the continuing beam redden?

James A. Lock, a colleague of mine at Cleveland State University, turns to a particulate description of light to show there is no contradiction. Suppose the initial beam of light has 1,000 red and 1,000 blue photons. When the beam reaches a group of molecules, the number of blue photons that scatter in all directions (or in any particular direction) is eight times the number of red photons. Suppose a total of 80 blue and 10 red photons are scattered in all directions, of which eight blue photons and one red photon are scattered forward. In the continuing beam, then, there are 991 red photons but only 928 blue ones, and so the beam has reddened.

You might also question how it is that light can be scattered through a molecule in the forward direction. A molecule is not a solid barrier like a wall; rather it is largely empty, with electrons in various orbits around a remarkably small nucleus. In a classical description of scattering, the electric field of the passing light forces the electrons to oscillate, and energy is transferred from the light to the oscillations. When a charged particle such as an electron is forced to oscillate, it radiates light in all directions except directly along the line on which it oscillates. This newly emitted light is the "scattered" light, and of course some of it is emitted in the forward direction.

Bohren and Fraser raised and then removed a possible objection to the Rayleigh explanation of the blue sky. The very shortest wavelengths in the visible spectrum correspond to violet rather than blue. Why then is the sky not violet? Bohren and Fraser gave two reasons. One minor reason is that because the initial sunlight is somewhat weaker in violet than in blue, less violet than blue is scattered to you. A more important reason is that the human eye is much less sensitive to violet than to blue.

People occasionally attribute the blueness of the sky to the water vapor in the atmosphere, perhaps because bodies of water are often bluish. One reason a lake can be blue is that when white light passes through several meters of water or more, the water molecules partially absorb the red end of the spectrum, and the light eventually reflected to a viewer is left primarily blue. Bohren and Fraser pointed out that the atmosphere has too little water to make this kind of absorption significant in the bluing of the sky.

The sky's color has also been attributed to the layer of ozone molecules that extends from about 10 to about 40 kilometers in altitude, with a peak density at about 25 kilometers. The molecules have absorption bands at the red end of the spectrum. Perhaps the red components of sunlight are weakened as the light passes through the ozone layer, so that the light finally reaching the ground is dominated by blue. Bohren and Fraser argued that although there is certainly depletion of the red by ozone, it plays a minor role in determining the blue of the sky. When you look up at the daytime sky, you intercept light that has passed through too little ozone for the absorption to matter. At twilight, when the rays travel a slanted (and hence longer) path through the ozone layer to reach you, the ozone absorption is more important, but even then the main reason for the sky's blueness is the Rayleigh mechanism.

In daytime the blue of the sky dulls toward the horizon, and in a band of about five degrees from the horizon the sky is often white. Since the air molecules along a line of sight to the horizon must, like any others, scatter light by the Rayleigh mechanism, what can have happened to the blue? Bohren and Fraser explained that the lack of color is due to the long path through the atmosphere taken by light reaching you when you look toward the horizon rather than looking up. The added distance means the light scatters many more times before it reaches you.

Some light scatters from molecules that are not very distant [see illustration directly below]. From them you receive light that is dominated by the blue. Much more distant molecules also scatter blue-dominated light in your direction, but your distance from those molecules means that the light undergoes repeated scattering before it reaches you. In each scattering event the light scattered toward you is light scattered in the forward direction, so that its blue component is weakened; after many scattering events that light ends up being dominated by the red half of the spectrum. The result is that you receive mostly the blue half of the spectrum from nearer molecules and mostly the red half from more distant molecules. The combination is white, and that is the color of the sky in the direction of the horizon.

The same effects explain the colors of dark mountains seen on a clear day. If the mountains are not too distant, their image is bluish, because blue-dominated light is scattered by the air molecules between you and the mountains. Somewhat more distant mountains may be even bluer, but those that are very far off are white-just as the horizon is.

According to Bohren and Fraser, the light from a setting sun would actually be orange (between red and yellow) instead of red if it scattered only from air molecules along its way to you.

They pointed out that the reason the color is instead usually a rich red is that the light normally scatters not only from molecules but also from very small particles and aerosols in the atmosphere.

When you look in a direction close h to the sun at any time of day, you intercept some of its bright light scattered forward by those same small particles and aerosols, and so that region of the sky is brighter than it would be if the particles were absent. When the sun is high, its surround is bright white. When it is low, on the other hand, the light reaching the particles has already been reddened by Rayleigh scattering and the surround is bright red. The greater the density of the particles, the brighter the surround and the sharper the circumference of the setting sun.

I have been assuming that the particles and aerosols alluded to so far are smaller than about .1 micron, and that as a result they scatter light by the Rayleigh mechanism just as molecules do. Particles that are somewhat larger than .1 micron scatter light by a much more complex mechanism, which is called Mie scattering after Gustav Mie, the German physicist who developed a theoretical model for such scattering at the beginning of this century. Mie scattering by a sizable particle is actually a form of diffraction, with most of the light being sent forward in a narrow cone. Red light is spread over a wider cone than blue light, and so the continuing beam becomes bluer. (In h simple diffraction the light waves that strike a particle spread out and also travel around the particle and into its "shadow region." In Mie scattering the behavior of the light is harder to interpret, and I shall not consider its details.)

During twilight on a clear evening the zenith (the sky directly overhead) becomes bluer than it is during the day. The extra blueness seems strange, considering that the horizon near the sun may be quite red. Several explanations for the bluing have been given, the likeliest of which involves the ozone layer. When light from the sun takes a slanted path through the layer at sunset, the ozone's absorption of the red end of the spectrum leaves the beam dominated by the blue end in spite of the Rayleigh scattering the beam encounters along the way. The beam becomes even more dominated by blue light if it also slants through a layer of particles large enough to introduce Mie scattering. After the light has been blued by either mechanism or both of them, some of it then scatters to you from the zenith by the Rayleigh mechanism, and you see a purer blue coming from there than you do in the daytime.

Just after sunset the shadow of the earth begins to rise from the eastern horizon. The border of the shadow is usually red or rosy purple. The color is due to light that has been reddened by Rayleigh scattering during its long passage through the lower reaches of the atmosphere. Near where you see the top "edge" of the shadow some of the light undergoes Rayleigh scattering and returns toward you. When you intercept the light, you perceive red at the top edge.

Below the edge the upper part of the shadow may be a faint blue. The blue tint is probably due to sunlight that travels through higher, less dense parts of the atmosphere, where the blue component of the beam is not weakened as much as it is in a beam that passes lower in the atmosphere, which encounters more air molecules. The light may actually be appreciably blued if it passes along a slanted path through the ozone layer or through a particle layer that forces Mie scattering. Near the earth's shadow some of the light undergoes Rayleigh scattering and travels into the shadow, where it again undergoes Rayleigh scattering before it heads toward you. Since this scheme involves multiple scatters, the blue light you finally intercept from the shadow region is dim. It is perceptible because you see it against the dark shadow of the earth.

About 10 minutes after the sun has set a purple patch occasionally develops above it somewhere between 30 and 75 degrees from the zenith. The patch, which is often called the "purple light," seems to depend on the presence of a layer of particles at an altitude of from 16 to 20 kilometers, in the lower part of the ozone layer. The particles might be dust from a desert or fine ash from volcanic eruptions or large forest fires.

In 1967 Aden B. Meinel and Marjorie Pettit Meinel of the University of Arizona pointed out that such a layer might be formed not by particles but by another product of volcanic eruptions. If an eruption emits a large amount of sulfur dioxide, when the gas mixes up to the base of the ozone layer, it interacts with the ozone to produce sulfates. When the sulfates precipitate onto condensation nuclei, a Mie-scattering aerosol is formed.

In their beautiful book Sunsets, Twilights, and Evening Skies the Meinels have suggested that the purple patch is the product of very red light and very blue light that is scattered from different regions of the sky. The red component comes from sunlight that has skirted the earth, passing through so much atmosphere that Rayleigh scattering has made the light red. Some of this light scatters to you from the particle layer-presumably by Mie scattering if the particles are large enough and by Rayleigh scattering if they are smaller; in any case you receive extra red light because of the presence of the particles.

The blue component comes from sunlight that passes through higher parts of the atmosphere and so does not redden as much. (I might add that since the light passes through the ozone layer along a slanted path, it may be dominated by the blue end of the spectrum because of absorption.) Some of the light undergoes Rayleigh scattering, and blue light is sent toward you. Both the red and the blue components travel along your line of sight when you view the patch, and the combination creates the impression of purple light.

The reason other parts of the sky are not purple is that you receive different mixtures of colors, rather than simply red and blue, when you look toward them; they may have a variety of hues that depend on your angle of view. The colors are particularly brilliant when the particle layer is dense and extensive, as it often is after a major volcanic eruption. The 1883 explosion of Krakatau near Java produced brilliantly colored sunsets for about five years, and sunsets were colored by the 1963 explosion of Agung on Bali for about three years.

A second (but much rarer) purple light, which appears in about the same part of the sky as the first one but between an hour and a half and two hours after sunset, is still not well understood. Some twilight watchers think it is caused by the same particle layer as the first purple light. If the layer is extensive, some of the light that scatters from the part of the layer well below the horizon may scatter again from the part of the layer that is in view. Provided the light is bright enough, you would then see a faint purple patch.

An alternate explanation involves a second layer of particles at an altitude of from 80 to 90 kilometers, in a region of low temperature at the junction of the mesosphere and the ionosphere above it. These particles may be of terrestrial origin but are more likely from space; the earth intercepts a vast amount of comet and asteroid debris that may occasionally produce an extensive particle layer in the low-temperature region. Sunlight scattered by the layer is certainly too faint to be perceived during the day or even at early twilight, but it might be seen when most of the atmosphere in view is in the shadow of the earth and the layer is still illuminated by the sun. The increasing amount of light pollution from urban environments may well make observations of this second purple patch even rarer in the future.

Bibliography

POLARIZATION AND SCATTERING CHARACTERISTICS IN THE ATMOSPHERES OF EARTH, VENUS, AND JUPITER. David L. Coffeen in Journal of the Optical Society of America, Vol. 69, No. 8, pages 1051-1064; August, 1979.

RAYLEIGH SCATTERING. Andrew T. Young in Physics Today, Vol. 35, No. 1, pages 42-48; January, 1982.

SUNSETS, TWILIGHTS, AND EVENING SKIES. Aden Meinel and Marjorie Meinel, Cambridge University Press, 1983.

COLORS OF THE SKY. Craig F. Bohren and Alistair B. Eraser in The Physics Teacher, Vol.23, No. 5, pages 267-272; May, 1985.

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