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Rayleigh Scattering:
Rayleigh scattering is the scattering of light, or other electromagnetic radiation, by particles much smaller than the wavelength of the light. It can be extended to scattering from particles up to about a tenth of the wavelength of the light.

It occurs without changing the wavelength of the incident light and hence is considered to be elastic scattering (since the photon energies of the scattered photons is not changed).

Note that, scattering in which the scattered photons have either a higher or lower photon energy is called Raman scattering.

Mie Scattering:
Mie theory is a complete analytical solution of Maxwell's equations for the scattering of electromagnetic radiation by spherical particles. The rigorous result for the scattering cross-section is called the Mie scattering cross-section.

Mie solution is named after its developer German physicist Gustav Mie. However, Danish physicist Ludvig Lorenz and others independently developed the theory of electromagnetic plane wave scattering by a dielectric sphere.

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