Why is the Sky Blue?
Scattering is the short answer, and primarily due to Rayleigh scattering. So, what is scattering? Our earth has a blue sky because of the way light from the sun interacts with the air. Air contains about 78% Nitrogen and 21% Oxygen with the remaining 1% containing Argon, CO2 and other gases. (Of course there is a lot of water vapor as well, and when it condenses, clouds form.)
Light from the sun contains all the colors of the rainbow: longer wavelengths (red and orange) are lower in energy and shorter wavelengths (blue and violet) are higher in energy.
This is a good place to introduce the photopic curve of the human eye. We’ll use wavelength in nanometers, (nm) which is 10-9 meters. Each person’s retina is sensitive to electromagnetic radiation in a very narrow window.
Without going into the details of the rods and cones, or the differences between the scotopic and photopic responses of the eye, let us consider the image shown above: the black curve represents a typical human sensitivity to light. Red is the longer wavelength, up to about 700nm with decreasing sensitivity into the near infrared; violet is the shorter wavelength that we can detect, down to about 400nm and diminishes into the near ultraviolet. The maximum sensitivity of the eye is located at just about 555nm, which is a greenish-yellow color.
Next, we need to consider the light from the sun. I measured the solar irradiance shown in the figure (blue curve) on a clear sunny day on July 20, 1999 at 2:00 pm in Sunnyvale California using a scanning spectroradiometer by Optronic Laboratories, model OL-752, in 2nm increments. I only measured 250 to 800nm because this fully encompassed the photopic curve, (and because this was the limitation of the equipment). Note that both curves in the figure are normalized for simplicity.
Lord Rayleigh demonstrated (late 1800’s) that scattering of light is elastic: this means that energy is not lost in the absorption of incident light by an atom or molecule in air, and subsequent reemission by that particle. Therefore, the incident (i) and scattered (s) energies are the same, hνi = hνs, where ν is the frequency of light incident and scattered, and h is Planck’s constant.
Consider the next figure, which shows scattering from a single particle. Light, as mentioned above, has a wavelength from about 400 to 700nm. A particle in the air has a diameter of approximately 0.1nm. However, the electric field from light (especially shorter wavelengths such as blue) can excite bound electrons in atoms and molecules in the atmosphere to their excited states. When electrons return to their bound states and reemit light at the same frequency, we call this Rayleigh scattering.
In Rayleigh’s equation, note the strong dependence on wavelength, λ, for the observed light intensity, I. Io is the intensity of incident light, N is the number of particles, α is a polarization parameter, θ is the angle from incident photon to its scattered direction and R is the distance between the observer and particle. In this equation, I is proportional to 1/λ4. This means that blue scattering intensity is approximately 9.4 times more intense than that for red. All colors of light scatter in the atmosphere, but blue light is so much more intensely scattered that the sky appears blue to the eye.
Another reason blue light is so strongly favored can be found in the first figure above. The sun’s light peaks at about 475nm, right in the middle of the blue part of the spectrum!
Finally, note the (1+cos2θ) term. This term scales the scattered intensity as a function of θ: scattering is ½ the intensity at 90 degrees compared with θ=0 or 180 degrees. A single photon can scatter multiple times on its way to the ground with a random direction in each scattering event. This is the reason the sky looks evenly blue in all directions. There is one exception however: very close to the sun, the sky almost appears white. I will leave this as a good research topic for further studies into scattering.