Why the Sky is Blue

So today I finally return to the world of physics and optics posts with a classic question that gets asked by children to their parents and qualifying exam committees to their examinees alike*. Why is the sky blue?

The first part of the answer is fairly easy to find with a judicious Google search: Rayleigh scattering!

In optics, several types of scattering, classified by the size of the particle doing the scattering, whether the collision is elastic (the incoming photon leaves with the same energy it started with) or inelastic (it loses energy in the collision to the thing its colliding with). Rayleigh scattering, named after Lord Rayleigh who did a lot of work in optics near the end of the 19th century, is scattering that is elastic, and the scattering object is smaller than the wavelength of the incoming photons**. The degree to which the incoming light is scattered is inversely proportional to the fourth power of the wavelength. So a longer wavelength photon will be less scattered than a shorter wavelength photon.

Sunlight is broad spectrum thermal light. For this discussion, we only care about the visible portion of the spectrum, which is roughly evenly distributed in incoming intensity. Once the sun's light hits the earth's atmosphere, it will encounter diffuse gas in the upper layers. The wavelength of the light is on the order of 10^-7  m, while the atoms it encounters have nuclei on the order of 10 ^-14 m, 10 million times smaller.

Not to scale

When the light strikes a nucleus, its component wavelengths get scattered according to the rules of Rayleigh scattering.

The red end of the light spectrum gets scattered in a roughly forward direction, while the blue/purple end of the spectrum gets scattered off to the side.  Most explanations end here, but that leaves most people wondering why the sky isn't purple.

The answer to that part of the question has nothing to do with Rayleigh scattering and everything to do with the human eye. As you can see in this link, the peak color sensitivity of the human eye is in the green (550 nm is green, 700 nm is red, 475 is blue). This is one reason why you don't see blue and purple laser pointers--our eyes don't pick them  up all that well. (Red laser pointers are the most popular because they are dirt cheap after cd players became consumer items, and because a poorly made green laser pointer emits UV laser light.) So when our eyes are presented with a little green, and a lot of blue and purple light, what we see is  blue tinged with green. If you don't believe there is green in it, go ask a painter to paint the sky for you and see if they don't include a dash of green. .

And that, my online friends, is why the sky is blue.

~PhysicsGal


*Yes, this was one of the questions in the oral portion of my qualifying exam.

**I will mention this very briefly for purposes of this post, and discuss it in greater length in a later post: light exhibits both particle-like and wave-like properties.  We can speak of photons (particle-like) being scattered elastically, but also of photons having a wavelength and frequency (wave-like).