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Aristotle, Leonardo da Vinci, Newton, Bouguer, de Saussure, Clausius, and Tyndall, have all been attracted to the problem of the blue sky. In a landmark paper in 1871, “On the light from the sky, its polarization and color”, a 29 year old John William Strut (Lord Rayleigh) attempts to show by simple dimensional analysis that particles smaller than the wavelength of light would scatter the light according to the inverse fourth power of the wavelength. It is now known as Rayleigh scattering and it explains why the sky is blue?
The light is electromagnetic radiation. Sunlight ranges from high frequencies (Gamma rays, UV light) to low frequencies (such as the IR and microwaves). Humans see sunlight as the white light, comprising of the colors of the rainbow (VIBGYOR) - the visible part of the radiation. The human eye can perceive only a narrow part of the radiation ranging from wavelengths: 400 nm (shorter wavelength, blue light) to 700 nm (longer wavelength, red light).
The sunlight reaches the earth from a distance of ~149.6 million km. At such a large distance, massive object like our earth is small. Thus, all the light from the sun reaching the earth is in parallel beams; instead of forming an angle over the curvature of the earth’s surface. Before the light reaches our eye, it meets the atmosphere of the earth. Depending on where the observer is on the earth, light has to pass through either 1 atmosphere thickness or multiple levels of atmosphere thickness. This sunlight interacts with the molecules (oxygen, nitrogen, argon, etc.) present in the atmosphere.
When a beam of light radiation interacts with a particle, say a molecule or an atom, the electric field of the radiation affects the charged particles in the air molecules (electrons), causing them to oscillate with the wave. The oscillating electrons, in turn, radiate the energy back into the atmosphere as scattered radiation, spreading over different directions.
The ‘Phenomenon of Scattering of Light of this Nature is the Origin of the Blue of the Sky’.
Scattering occurs when the particle size is comparable to the wavelength of the incident light.
The shorter wavelength (high frequency) blue light of the sunlight causes more oscillations compared to the red light. More oscillations produce more scattering, leading to the blue light scattered more than the other colors of the visible light. Thus the oscillations produced are proportional to the frequency of the light. The more oscillations increase the intensity of the scattered light. The relation thus obtained is that the intensity of the scattered light is proportional to the fourth power of frequency (ʋ4 or 1/λ4). This was the formula derived by Lord Rayleigh to explain the blue of the sky. This renders the scattering of the blue light almost 10 times as efficiently as the red light.
The obvious question then follows, why is not the sky violet, but blue? The scattering of the violet light is too much compared to the blue light; it is scattered away strongly before it reaches the observer, while the red light is not scattered as much as the blue. Similarly, the sky appears red and orange near the horizon, when the travel path length of sunlight is long.
During sunrise and sunset, the color of the sky is not blue because the light travels larger thickness of the atmosphere before reaching the observer and the blue light being scattered more is lost in the process and only the light less scattered is enriched (the red, yellow light) and reaches the eye. This leads to scattering of the entire amount of blue light leaving only the red end of the visual spectrum. The operating range of scattering of light based on the frequency, intensity, distance traveled, and scattering particles, decides the color of the sky.
Authors Bohren, C. F., & Fraser, A. B. explain that in addition to the nature of the scatterers, what you perceive as the color of the sky depends on “the solar spectrum, the wavelength dependence of the scattering and the response of the eye”.
Sources and Further Reading
- Radiation Damping. Light Scattering, Feynman Lectures
- Why is the sky blue? Anthony D. Del Genio of the NASA Goddard Institute for Space Studies and Columbia University
- Colors of the Sky, Bohren, C. F., & Fraser, A. B.
- Hon. J.W. Strutt (1871) XV. On the light from the sky, its polarization and colour , The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41:271, 107-120
This article was updated on 12th February, 2019.