Growing up, we all have those big life questions that catch our interest. Those with a penchant for nature, for instance, may ask such questions as: where do the Moon’s phases come from, what are rainbows, why is the sky blue? The answers to these questions, as may be given to a scientifically-inclined young mind, are reflection of sunlight, refraction of light through atmospheric moisture, and Rayleigh scattering, respectively. This last answer, however, while a popular one, often goes without further elaboration.
Rayleigh scattering, named for John William Strutt, 3rd Baron Rayleigh, is how light is scattered through air. Blue light bounces around more than red light, making the sky appear blue. However, this definition, while the most popular, overlaps several different types of scattering, rendering this explanation incomplete.
There are many forms of optical scattering — too many to properly explain. Indeed, even peer-reviewed publications have confused what constitutes Rayleigh scattering, but the true definition, as used in optics and scattering theory, is relatively narrow. Put formally, Rayleigh scattering is the elastic scattering of light off of fine particles with an intensity proportional to the inverse of the wavelength of the photon raised to the fourth power.
To clarify the above description, let us take it element by element. “Elastic scattering” refers to elastic interactions between the incident (approaching) photons and the molecules of the surrounding medium. In physics, “elastic” means that kinetic energy is conserved, meaning that the photon does not lose any energy in the collision. Were the collisions in question not elastic, it would not be Rayleigh scattering, but Raman scattering, named for Indian physicist Chandrasekhara Venkata Raman.
Next, “fine particles” is not a true scientific term, but a qualitative relationship. For Rayleigh scattering to apply, the particles of the surrounding medium — in this case air — must be much smaller in diameter than the wavelength of the incident photon, which they indeed are. If the particles were comparable in size to the wavelength of the incident light, the process would be Mie scattering, named for German physicist Gustav Mie. Were the particles to additionally be non-spheroidal and in suspension, the effect would be Tyndall scattering, named for Irish physicist John Tyndall.
Last, the wavelength of a photon is inversely proportional to its energy; that is, the higher the energy of the photon, the shorter its wavelength, and the more it oscillates. Under Rayleigh scattering, higher-energy light scatters more than lower-energy light. Because the sun produces white light — which is a mixture of the entire spectrum of visible light — higher-energy blue light scatters more than lower-energy red light, making the sky appear bluish; the sky, however, does not appear purple because the sun produces relatively little violet light. The resulting color is a washed-out, classic sky blue.
That is, of course, looking at the midday sky. During twilight, parts of the sky will appear red. This is because the light from the sun, due to it being on the horizon, must travel through much more of the atmosphere to reach the eye. Here, Rayleigh scattering works against blue light, as, by the time it reaches the eye, it has been scattered to almost nothing, leaving the less-scattered red light to fill the gap.
This still fails to capture the breadth of Rayleigh scattering. Mathematician Rayleigh, in addition to qualifying this phenomenon, quantified it, providing basic models of light scattering in air, today called Rayleigh’s approximation. This model has many practical applications, from clearing haze in photographs to facilitating various forms of gas spectroscopy.
Further still, Rayleigh scattering is responsible for the latitudinal (north-south) polarization of sunlight. This polarized light orients the internal compass of several species, most notably migratory birds. However, due to increased background noise caused by urban light pollution interfering with light polarization, such species have much greater difficulty navigating. Were there to be literal background noise (for example, resonance in the air), the effect would become Brillouin scattering, named for French physicist Léon Brillouin.
Asking why the sky is blue opens the door to so many natural phenomena that even professional scientists sometimes get them confused. Nevertheless, even if simply due to scattering, the beauty of the sky persists. So, the next time a child asks you why the sky is blue, it may be best to just tell them “light scattering.”
Sources:
Applied Optics (1981). DOI: 10.1364/AO.20.000533
IEEE Access (2020). DOI: 10.1109/ACCESS.2020.2988144
Georgia Journal of Science (2021). ISSN: 0147-9369
Proceedings of the Royal Society of London (1869). DOI: 10.1098/rspl.1868.0033
Image courtesy of Wikimedia Commons
