Blue Sky

The blue color of the sky is caused by the scattering of sunlight off the molecules of the atmosphere. This scattering, called Rayleigh scattering, is more effective at short wavelengths (the blue end of the visible spectrum). Therefore the light scattered down to the earth at a large angle with respect to the direction of the sun's light is predominantly in the blue end of the spectrum.

Note that the blue of the sky is more saturated when you look further from the sun. The almost white scattering near the sun can be attributed to Mie scattering, which is not very wavelength dependent.

Rayleigh Scattering

Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. It is Rayleigh scattering off the molecules of the air which gives us the blue sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be:

Rayleigh scattering can be considered to be elastic scattering since the photon energies of the scattered photons is not changed. Scattering in which the scattered photons have either a higher or lower photon energy is called Raman scattering. Usually this kind of scattering involves exciting some vibrational mode of the molecules, giving a lower scattered photon energy, or scattering off an excited vibrational state of a molecule which adds its vibrational energy to the incident photon.

Mie Scattering

The scattering from molecules and very tiny particles (< 1 /10 wavelength) is predominantly Rayleigh scattering. For particle sizes larger than a wavelength, Mie scattering predominates. This scattering produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for larger particles.

Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives us the the white light from mist and fog.

Greenler in his "Rainbows, Haloes and Glories" has some excellent color plates demonstrating Mie scattering and its dramatic absence in the particle-free air of the polar regions.

Rayleigh and Mie Scattering

Sky Saturation and Brightness

As a qualitative examination of sky brightness and the saturation of the blue sky color, measurements of the color of the sky photograph were made from a computer monitor using Adobe Illustrator's color tools. None of the data should be taken as quantitatively reliable since the original photo had been transformed several times, and the measurements were taken from a non-calibrated computer monitor. Nevertheless, it might be useful as an example of the progressions of sky color.

A series of points on the sky image were chosen starting from the left, indicated by the white dots superimposed on the image above. It is clear to the eye that the progression leads to a brighter sky and to a blue color which is less saturated, or more pastel. Measurements of the color and brightness were made at each point based on amounts of red, green and blue present. In the graph at upper left, the blue brightness was normalized to 1 and the red and green expressed as a fraction of the blue. One result was that the green was significantly brighter than the red. This is consistent with Rayleigh scattering which emphasizes the shorter wavelengths. Another result was that the red and green increased as a fraction of the blue, indicating that the color was becoming less saturated. This can be interpreted as blue mixed with an increasing fraction of white light, which is consistent with the light being a combination of Rayleigh and Mie scattering. As you approach the sun's direction, the Mie scattering accounts for a larger fraction of the total light, and the Mie scattered light is essentially white. The graph of overall brightness above is just the sum of all three colors, with a maximum of 1 being white on the monitor. The increasing brightness along the path of the data is again consistent with a combination of Rayleigh and Mie scattering. The Mie scattering has a strong forward lobe and increases as you approach the sun's direction.