What is Rayleigh scattering?

Question

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Answer 1

The Classical Physics explanation:

In plain(er) English, you can think of molecules as small conductive spheres. An electric field generates a dipole moment in a conductor (a separation of charge, more negative on one end, and more positive on the other). A changing dipole moment generates radiation (an EM wave).

The changing electric field of an EM wave (light) induces a changing dipole moment in the conductors (air molecules in the case of the blue sky phenomenon.) Some of the energy of the EM wave is absorbed and re-emitted as dipole radiation.

Shorter wavelengths are more susceptible because the more rapidly changing E-field associated with it generates a stronger dipole moment. You can also think of a very long wavelength essentially having no electric field gradient (and so a smaller dipole moment) across the spatial extent of the conductor.

There is also a quantum mechanical derivation for Rayleigh scattering that gives the same mathematical result as the classical derivation (thank goodness!) but I do not understand it qualitative and barely understand the mathematical derivation.

Answer 2

Rayleigh scattering is a process in which electromagnetic radiation (including light) is scattered by a small spherical volume of variant refractive index, such as a particle, bubble, droplet, or even a density fluctuation. This effect was first modeled successfully by Lord Rayleigh, from whom it gets its name. In order for Rayleigh's model to apply, the sphere must be much smaller in diameter than the wavelength (λ) of the scattered wave; typically the upper limit is taken to be about 1/10 the wavelength. In this size regime, the exact shape of the scattering center is usually not very significant and can often be treated as a sphere of equivalent volume. The inherent scattering that radiation undergoes passing through a pure gas is due to microscopic density fluctuations as the gas molecules move around, which are normally small enough in scale for Rayleigh's model to apply. This scattering mechanism is the primary cause of the blue color of the Earth's sky on a clear day, as the shorter blue wavelengths of sunlight passing overhead are more strongly scattered than the longer red wavelengths according to Rayleigh's famous 1/λ 4 relation. Along with absorption, such scattering is a major cause of the attenuation of radiation by the atmosphere. The degree of scattering varies as a function of the ratio of the particle diameter to the wavelength of the radiation, along with many other factors including polarization, angle, and coherence.

Answer 3

Rayleigh scattering (named after Lord Rayleigh) is the scattering of light, or other electromagnetic radiation, by particles much smaller than the wavelength of the light. It occurs when light travels in transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering of sunlight by the atmosphere is the main reason light from the sky is blue.

The amount of Rayleigh scattering that occurs to a beam of light is dependent upon the size of the particles and the wavelength of the light; in particular, the scattering coefficient, and hence the intensity of the scattered light, varies inversely with the fourth power of the wavelength, a relation known as the Rayleigh law. Scattering from spherical particles larger than about a tenth of the illuminating wavelength is explained by the Mie theory.

The intensity I of light scattered by a single small particle from a beam of unpolarized light of wavelength λ and intensity I0 is given by:

I = I_0 \frac{ (1+\cos^2 \theta) }{2 R^2} \left( \frac{ 2 \pi }{ \lambda } \right)^4 \left( \frac{ n^2-1}{ n^2+2 } \right)^2 \left( \frac{d}{2} \right)^6

where R is the distance to the particle, θ is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.

The angular distribution of Rayleigh scattering, governed by the (1+cos2 θ) term, is symmetric in the plane normal to the incident direction of the light, and so the forward scatter equals the backwards scatter. Integrating over the sphere surrounding the particle gives the Rayleigh scattering cross section σs:

\sigma_s = \frac{ 2 \pi^5}{3} \frac{d^6}{\lambda^4} \left( \frac{ n^2-1}{ n^2+2 } \right)^2

The Rayleigh scattering coefficient for a group of scattering particles is the number of particles per unit volume N times the cross-section. As with all wave effects, in incoherent scattering the scattered powers add arithmetically, while in coherent scattering, such as if the particles are very near each-other, the fields add arithmetically and the sum must be squared to obtain the total scattered power.

The strong wavelength dependence of the scattering (~λ-4) means that blue light is scattered much more than red light. In the atmosphere, this results in blue photons being scattered across the sky to a greater extent than photons of a longer wavelength, and so one sees blue light coming from all regions of the sky whereas the rest is still mainly coming directly from the Sun. It should be noted that, despite the use of the term photon, Rayleigh scattering was developed prior to the invention of quantum mechanics and is not based fundamentally in modern theory about the interaction of light with matter. Nevertheless, Rayleigh scattering is a fair approximation to the manner in which light scattering occurs within various media.

During sunrise and sunset the Sun's light must pass through a much greater thickness of the atmosphere to reach an observer on the ground. This extra distance causes multiple scatterings of blue light, but relatively little scattering of red light; this is seen as a pronounced red-hued sky in the direction towards the sun.

If the size of particles are larger than the wavelength of light, light is not separated and all wavelengths are scattered as by a cloud which appears white, as do salt and sugar. For scattering by particles similar to or larger than a wavelength, see the articles on optics and scattering.

http://en.wikipedia.org/wiki/Rayleigh_scattering