Rayleigh’s Scattering and the Blue Sky – Photonick
By CoperNick
Alessandro Santoni
January 22, 2019
In my first article I explained why the sky is dark at night. Now it’s time to understand why it is not dark during the day and why, among all the colors, it is blue. This is a really good question, some aspects of which are still not completely clear.
Firstly, it is important to note that this is not a property of space itself, nor is it exclusively due to the sunlight reaching us. It is instead a phenomenon generated by an interaction: the interaction between light and the Earth’s atmosphere. The moon, which doesn’t have an atmosphere, is in fact always enveloped in darkness, not only at night. Basically, when the Sun’s photons reach the Earth’s atmosphere, some of them interact with the particles within it and are scattered (bounced off), changing their direction of propagation. The result of this interaction is strictly dependent on the size of the particles with which the photons have collided.
The “blue sky effect” is therefore caused by a specific type of interaction between light and tiny gas molecules. This phenomenon is known as Rayleigh’s scattering. The probability of a photon interacting this way is proportional to 1/λ4, where λ is the photon’s wavelength. Therefore during the day, when the Sun is high in the sky, the following scenario occurs:
Fig. 1: Earth’s atmosphere and sunlight scattering [credits]
The blue/purple components of sunlight, having smaller wavelengths than the other visible components, are scattered more strongly, which means that they populate the Earth’s atmosphere and keep bouncing inside it until, after countless interactions, they reach our eyes from every position in the sky, coloring it in its vivid and characteristic blue! The more we look to the horizon, the more the colour blue appears to be lighter, because all the light’s components have more time to scatter, recombine and reach us.
Note an interesting fact: the scattering of light from larger particles in the atmosphere, like dust or water droplets, is independent of λ, which means that in this case all of light’s components interact equally. This results in the white colour of clouds and fogs, which, being composed by particles of steam, scatter all visible components in the same way so that the light that reaches us is a combination of them all therefore appears whitish.
Now it is legitimate to ask: why isn’t the sky purple instead of blue, since purple has a smaller wavelength? That depends on two factors, namely:
- The sensitivity of the human eye to blue light is greater than to purple light.
Fig. 2: Visible spectrum and human eye’s response curve to daylight [credits]
- The purple component is less present in the spectrum of sunlight than the blue one.
For the sake of completeness, it is worth mentioning a more general picture of scattering, called Mie’s scattering, which describes the scattering of electromagnetic radiation on spherical (or cylindrical) objects of any dimension. This formulation reproduces Rayleigh’s scattering in the limit where the length of the “scattering centres” is much smaller than the wavelength of the radiation (i.e the atmospheric particles can be considered pointlike). In addition, both Mie’s and Rayleigh’s scattering are formulated entirely in classical terms, with no reference to the quantum mechanics; if in this article I referenced photons when characterising the interaction of light, it was only to make the explanation clearer.
The mechanism described above is also responsible for the picturesque red skies produced by the setting sun. When the Sun is on the horizon, the light has to travel through a greater section of atmosphere than before. This causes the diffusion not only of the blue and purple components of light, but also, sequentially, of the green and some of the yellow ones. However, the majority of the light that manages to reach us belongs the red wavelength, giving rise to spectacular landscapes!
Fig.3 Picture by Andrea Mauro.
It is worth pointing out that this mechanism is also responsible for sunrises, often as spectacular as sunsets, but not quite as appreciated. As Millor Ferdandes states:
“It is impossible to explain human preferences. Even if built with exactly the same building blocks and both amazing (no one can argue which one is better), the sunset has always had more audience than the sunrise. ”
Maybe if more of us were early risers that would not be the case, who knows!
