Rayleigh scattering

Rayleigh scattering
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Name	Rayleigh scattering
Caption	The blue color of the sky is caused by Rayleigh scattering of sunlight by atmospheric molecules.
Fields	Physics, Optics, Atmospheric science
Namedafter	John William Strutt, 3rd Baron Rayleigh

Rayleigh scattering. It is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. This fundamental process, named for John William Strutt, 3rd Baron Rayleigh, is responsible for the blue color of the daytime sky and the reddening of the sun at sunrise and sunset. The scattering intensity is inversely proportional to the fourth power of the wavelength, making shorter blue wavelengths scatter far more efficiently than longer red wavelengths in the Earth's atmosphere.

Physical explanation

The phenomenon occurs when the electric field of an incoming electromagnetic wave induces a dipole moment in a particle, such as a nitrogen or oxygen molecule. This oscillating dipole then re-radiates energy as a secondary wave, scattering the light in all directions. For the scattering to be considered Rayleigh scattering, the particle size must be significantly smaller than the wavelength of light, typically less than one-tenth the wavelength. This condition is perfectly met for visible light interacting with atmospheric gases. The scattered light retains the same wavelength as the incident light, making the process elastic, though a tiny fraction involves Raman scattering. The angular distribution of the scattered intensity is symmetric, being proportional to (1 + cos²θ), where θ is the scattering angle.

Mathematical description

The mathematical framework was first derived by John William Strutt, 3rd Baron Rayleigh in 1871. The key result is that the intensity *I* of light scattered by a single small particle is proportional to *I* ∝ *I₀* / λ⁴, where *I₀* is the incident intensity and λ is the wavelength. This strong wavelength dependence is the origin of the blue sky. The complete expression for the scattering cross-section σ for a dielectric spherical particle of radius *a* and refractive index *n* is given by σ = (2π⁵/3) * (a⁶/λ⁴) * ((n² - 1)/(n² + 2))². This formula is a cornerstone in the Mie theory, which provides a more general solution for scattering by spheres of any size. The total scattering from a gas is derived by considering the number density of scatterers, as applied in studies of the Earth's atmosphere.

Applications and examples

The most ubiquitous example is the blue color of the sky, a direct consequence of the preferential scattering of blue sunlight. Conversely, at sunrise and sunset, light passes through a longer atmospheric path, scattering away blue light and leaving the dominant red hues. This principle is used in remote sensing to correct for atmospheric effects in satellite imagery from platforms like NASA's Landsat program. In astronomy, Rayleigh scattering explains the reddening of light from distant stars due to the interstellar medium. It is also critical in lidar technology for atmospheric profiling and in designing optical fibers for telecommunications to minimize signal loss. The phenomenon even explains the blue color of some bird feathers and the iris of some human eyes, where structural coloration is not involved.

History and discovery

Although the blue sky had been observed for millennia, its correct scientific explanation emerged in the 19th century. Early work by John Tyndall suggested scattering by dust particles, but John William Strutt, 3rd Baron Rayleigh provided the correct theoretical treatment in 1871, attributing it to the molecules of the air itself. His seminal paper, published in the Philosophical Magazine, established the inverse fourth-power law. Later, the theory was experimentally verified and extended. The phenomenon was named in his honor, and his work laid the groundwork for later developments in scattering theory, including contributions by Gustav Mie and Albert Einstein, who explained critical opalescence using similar principles.

Related scattering phenomena

Rayleigh scattering is a specific case within a broader family of light scattering processes. Mie scattering describes scattering by particles comparable to the wavelength, such as aerosols, and is not as wavelength-sensitive, often causing white haze. Tyndall effect is scattering by colloidal particles and is prominent in phenomena like the blue tint of smoke. Brillouin scattering and Raman scattering are inelastic processes involving a change in photon energy due to interaction with acoustic phonons and molecular vibrations, respectively. Compton scattering involves the inelastic scattering of high-energy X-ray photons by charged particles like electrons, a key concept in quantum mechanics established by Arthur Compton. Thomson scattering is the classical elastic scattering of electromagnetic radiation by free charged particles. Category:Scattering Category:Atmospheric optics Category:Light