Thank goodness everyone asks why is the sky blue and no one asks the much harder question of why is the sky bright.
The Short Answer.
The molecules which make up 99% of the earth's atmosphere do not absorb any wavelengths of visible light. Molecules in the air are not like indigo molecules which absorb red light and give blue cloth its color. Molecules in the air are not pigments. However, molecules in the air do scatter blue light more strongly than red light. This means that white sunlight has its blue components scattered to the side while its red components keep traveling straight. White sunlight bathes the atmosphere of the earth. The sky is blue because molecules in the air scatter blue to your eyes more than they scatter red.
But why do molecules in the atmosphere scatter blue light more than red? The oxygen, nitrogen, and water molecules plus the argon atoms that make up most of the air do absorb ultraviolet light, in the region of the spectrum known as UV-C. (It is a good thing they do too, these dangerous germicidal UV wavelengths from the sun are stopped by the atmosphere before they can damage you and become homicidal.) The molecules in the air absorb the ultraviolet because their electron clouds have a resonance frequency in the ultraviolet. This means that if you hit the electron clouds, for example by colliding one atom into a molecule, the electron cloud in the molecule will shake back and forth about the nuclei at a resonant frequency in the ultraviolet.
Hit an atom with electromagnetic radiation and the electron cloud is shaken back and forth at the same frequency as that of the radiation. Shake the atom at resonance and the electron cloud motion builds up until the electromagnetic radiation is absorbed and the electron cloud makes a transition to a higher energy level. Some time after absorption by an atom &emdash;perhaps a hundredth of a microsecond later &emdash; light will be reemitted and the atom goes back to its lowest energy ground state. Often the reemitted light has the same energy and frequency as the absorbed light, however, it may also be reemitted as several lower energy photons. The reemitted light has no phase relationship with the incoming light at all!
When an incident wave of electromagnetic radiation, light, shakes the electron cloud at a frequency far away from resonance, the electron cloud oscillates and reemits light. The reemitted light is not actually absorbed and reemitted, it is slightly delayed, by 10^-15 second or so, so that it has a small phase shift with respect to the incident light. Each time the light passes by an atom, part of it is scattered and comes out with the same frequency or color and a slight phase delay. Since it is delayed by every atom, the net result is a slowing of the apparent speed of light. This is characterized as the index of refraction of a material. The closer the electromagnetic wave is in frequency to the resonant frequency of an atom or molecule, the greater is the amount of light that is scattered by each atom, and also the greater the phase delay.
Blue light is closer in frequency to ultraviolet light than red light , so blue light is scattered more than red light. Quantitatively, the amount of light scattered is proportional to the fourth power of the frequency. So blue light that is twice the frequency of red light is scattered 16 times more strongly. Notice that red light is scattered a little, however it is overwhelmed by the blue scattering.
Why is the sunset red?
When white sunlight passes through a lot of atmosphere the blue is scattered out of the beam leaving the red in the beam. This is why the sky is blue and the setting sun is red.
The scattering occurs at all wavelengths. Violet light is scattered more strongly than blue, but there is less violet than blue in sunlight so the sky is not violet. Indeed there is more yellow and green in sunlight than blue but the combination of the amount of each color present in sunlight times the fraction of power of that wavelength that is scattered makes the sky appear blue.
Exploration: Single scattering and the polarization of skylight.
Most sunlight scatters only one time from an air molecule on its way from the sun to your eye. Light that scatters once at a ninety degree angle will be polarized. Light that is scattered multiple times is not polarized. Look at the blue sky through polarizing sunglasses
Exploration: White opal glass, blue by scattering
In a bead shop you can buy glass beads made from white opal glass. You may also be able to find larger pieces of white opal glass maybe even paperweights (Paperweights of white opal glass were first shown to me by Physics Professor Ken Bresher of Boston University.). In bright light the white opal glass looks blue, however if you shine light through it, the white opal glass looks yellow or even orange. The glass scatters blue light more strongly than red light. The glass itself is clear, just as the air is clear. It does not absorb visible light as a pigment would. However, when the opal glass is made, tiny regions in the glass, smaller than a wavelength of blue light, become crystallized. These tiny regions of crystalline glass scatter light. Glass also has a resonance in the ultraviolet and so blue light scatters more than red light. (Silica aerogel scatters light the same way as white opal glass.)
Why are clouds white?
Clouds are made from water molecules gathered together into liquid drops which are usually larger in diameter than a wavelength of light. Individual water molecules in a gas state have a resonance in the ultraviolet and so scatters blue more than red. However, gather water molecules together into droplets of liquid which are larger than a wavelength of light and the scattered light becomes white.
When light strikes a sharp barrier between, for example air and liquid water, a portion of the light is reflected from the surface. In the case of small water drops the light is reflected in all directions and we say it is scattered rather than reflected. The amount of light scattered is proportional to the number of atoms within a cubic wavelength. (It is as if each photon had a width and a height of one wavelength and that the reflected light interacted with the molecules within a wavelength &emdash; actually 1/2 a wavelength &emdash; of the surface.) Thus red light with twice the wavelength of blue light will scatter from 23 or 8 times as many molecules as blue light. Thus each molecule scatters 16 times more blue light than red because the blue light is closer to resonance, and yet red light photons are scattered by 8 times as many molecules as blue ones because of their longer wavelength. The effects nearly cancel and the light scattered from water drops looks white.
At each surface of a water drop only 4% of the light scatters, however there are many droplets and so many surfaces and so the light suffers multiple scatterings. Clouds are thus opaque and white.
Why is deep water blue?
In addition to their resonance in the ultraviolet, water molecules also have a vibrational resonance in the infrared. This is why water molecules contribute to the greenhouse effect, absorbing infrared from sunlight. If you picture a water molecule as a shadow of Mickey mouse with the hydrogens as the ears, the vibration brings the hydrogen "ears" together and apart. When water molecules bind together to form liquid water, hydrogen bonds form between them. These hydrogen bonds stiffen the the oscillations of the hydrogens and raise the frequency so that it is closer to the red end of the visible spectrum. In fact, both liquid water and ice absorb some red light. This means that light transmitted through liquid water or ice becomes blue.
If there are living organisms in the water that use chlorophyll for photosynthesis this can give a green tint to the water.
If there is sediment in the water this can add some white or yellow scattering and make the deep blue into a pastel blue or milky white or brown.
Why is the sky bright?
Consider a beam of light passing through clean liquid water. Very little is scattered to the side. This is because in one wavelength of light there are thousands of water molecules. Each water molecule scatters light in all directions each with a phase corresponding to the part of the light wave that is hitting it at the moment. The sum of all of these phases is zero! So no light is scattered, (If you sum up all the phases of a sine wave over a complete sine wave you get zero.) However water molecules are always in motion, undergoing a random walk and changing the number of molecules in each half-wavelength of the water. The number of molecules in one half wavelength is different from the next, so the sine waves do not exactly cancel and some light is scattered even by perfectly clean water. The same is true for air. Thus the sky is bright.
The light scatters due to fluctuations in the index of refraction over distances about a wavelength of light in size. The same is true for the white opal glass. Since the scattering by each molecule is stronger in the blue, the overall color of the scattered light is blue.
The number of scattering crystals in each wavelength of light size region is small and varies from one region to the next. This gives rise to the scattering.
Molecules in the atmosphere, I say this rather than "air molecules" because air molecules is a slightly misleading phrase.
Dry air is made up of:
78% Nitrogen molecules, N2
21% Oxygen molecules, O2
1% Argon atoms
In addition the air can also contain a small percentage of water molecules, under 3%.
These percentages are by number of molecules.
So in discussing what the air is made of I should say molecules and atoms, but his phrase although correct begins to get in the way after a few repetitions. So I've chosen to discuss the molecules in the atmosphere, although everything I say also applies to the atoms of argon too.
Air is made of 99% molecules and 1 % atoms.
Amount of light scattered, What I mean here is the power scattered, where power is measured in watts or joules per second.
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Scientific Explorations with Paul Doherty
4 Apr 99