Rayleigh scattering is the scattering of light by particles in the atmosphere. According to Rayleigh`s law of scattering, the amount of scattering of light is inversely proportional to the fourth power of the wavelength. From the relationship between scattering and wavelength, we understand that shorter wavelengths scatter more. Because blue light has a shorter wavelength than red light, it scatters more. where are is the radius of the particle, λ is the wavelength of light, and x is a dimensionless parameter that characterizes the interaction of the particle with incident radiation such as: Objects with x ≫ 1 act as geometric shapes that scatter light according to their projected area. In the intermediate region x ≃ 1 of Mie scattering, interference effects develop due to phase variations on the surface of the object. Rayleigh scattering applies when the scattering particle is very small (x ≪ 1, with a particle size < 1/10 of the wavelength) and the entire surface radiates again with the same phase. Because particles are positioned randomly, scattered light arrives at a certain point with a random collection of phases. It is incoherent and the resulting intensity is only the sum of the squares of the amplitudes of each particle and therefore proportional to the fourth inverse power of the wavelength and the sixth power of its size.   Wavelength dependence is characteristic of dipole scattering and volume dependence applies to any scattering mechanism. In detail, the intensity of light scattered by one of the small spheres of diameter d and refractive index n from a beam of unpolarized light of wavelength λ and intensity I0 is characterized by Rayleigh scattering by a mathematical formula that requires a particle scattering light to be much smaller than the wavelength of light.
Rayleigh scattering is also an important mechanism for wave scattering in amorphous solids such as glass and is responsible for attenuating acoustic waves and attenuating phonons in glasses and granular materials at low or not too high temperatures. [clarification needed] [ref. needed] The Tyndall effect was named after 19th century physicist John Tyndall. Tyndall scattering, e.g. colloidal particle scattering, is significantly more intense than Rayleigh scattering due to the larger particle size. The above expression can also be written in relation to individual molecules by expressing the dependence on the refractive index in terms of molecular polarizability α, proportional to the dipole moment induced by the electric field of light. In this case, the Rayleigh scattering intensity for a single particle in CGS units is given by The high wavelength dependence of scattering (~λ−4) means that shorter (blue) wavelengths are more dispersed than longer wavelengths (red). The angle at which sunlight is scattered into the atmosphere by the molecules of individual gases varies inversely as the fourth power of the wavelength; Therefore, blue light, which lies at the shortwave end of the visible spectrum, is much more scattered than long-wave red light. This leads to the blue color of the sunny sky, as the viewer only sees stray light in directions other than towards the sun. Rayleigh`s laws also predict the variation in the intensity of scattered light with direction, one result being that there is complete symmetry in the forward scattering and backward scattering models of individual particles. In addition, they predict the polarization of scattered light.
However, this interaction changes the polarization of the incident light to some extent. For this reason, part of the light energy is absorbed by the molecules of the air. This energy is then re-emitted in different directions, which triggers a scattering of light, more precisely, called Rayleigh scattering. The proportion of light scattered by particle scattering over the unit displacement length (e.g. meters) is the number of particles per unit volume N times the cross section. For example, the main constituent of the atmosphere, nitrogen, has a Rayleigh cross section of 5.1×10−31 m2 at a wavelength of 532 nm (green light).  This means that at atmospheric pressure, where there are about 2×1025 molecules per cubic meter, about a fraction of 10−5 of light is scattered for every meter of displacement. It is important that the dispersion/scattering does not take place due to the collision, but to the side effect of the electromagnetic interaction between photons and particles in the medium. Rayleigh scattering is an interesting phenomenon that speaks of elastic scattering of light or electromagnetic radiation by gas molecules smaller than the wavelength of light or radiation, sometimes scattering by solid (dielectric diffusers) and liquid is possible. Scattering by particles of a size comparable to or greater than the wavelength of light is usually handled by Mie theory, discrete dipole approximation and other computational techniques. Rayleigh scattering applies to particles that are small in terms of wavelengths of light and optically “soft” (i.e. with a refractive index close to 1).
The theory of anomalous diffraction applies to optically soft but larger particles. Rayleigh`s law of scattering expresses that the amount of scattering of light is inversely relative to the fourth power of the wavelength. Rayleigh`s λ−4 diffusion can also be demonstrated by porous materials. An example is the strong optical scattering caused by nanoporous materials.  The high contrast of the refractive index between the pores and the solid parts of the sintered alumina results in very strong diffusion, with light completely changing direction every five microns on average. λ−4 scattering is caused by the nanoporous structure (a narrow pore size distribution around ~70 nm) obtained by sintering monodispersive alumina powder. For example, the color of the sky is blue because of the scattering of sunlight by the atmosphere. The high wavelength dependence of scattering (~λ−4) means that shorter wavelengths (blue) are more dispersed than longer wavelengths (red). This causes indirect blue light from all regions of the sky. Rayleigh scattering is a good approximation of how light scattering occurs in different media where scattering particles are small (parameter).