Acc. to literature these nano particles show Mie scattering, but how do we confirm it either really thses nano particles show Mie scattering or Rayleigh scattering?

Howdy Sankara,

Mie scattering

The term Mie theory is used on occasion; however, it is misleading because it does not refer to an independent physical theory or law. The phrase "the Mie solution (to Maxwell's equations)" is therefore preferable. Currently, the term "Mie solution" is also used in broader contexts, for example when discussing solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or generally when dealing with scattering problems solved using the exact Maxwell equations in cases where one can write separate equations for the radial and angular dependence of solutions.

Mie solutions are implemented in a number of codes written in different computer languages such as Fortran, Matlab, Mathematica. These solutions are in terms of infinite series and include calculation of scattering phase function, extinction, scattering, and absorption efficiencies, and other parameters such as asymmetry parameter or radiation torque. Current usage of the "Mie solution" indicate series approximation to solution of Maxwell's equations. There are several known objects which allow such a solution: spheres, concentric spheres, infinite cylinders, cluster of spheres and cluster of cylinders, there are also known series solutions for scattering on ellipsoidal particles. For list of these specialized codes examine these articles

Codes for electromagnetic scattering by spheres — solutions for single sphere, coated spheres, multilayer sphere, cluster of spheres

Codes for electromagnetic scattering by cylinders — solutions for single cylinder, multilayer cylinders, cluster of cylinders.

A generalization that allows for a treatment of more general shaped particles is the T-matrix method, which also relies on the series approximation to solutions of Maxwell's equations.

Raleigh scattering

Rayleigh scattering describes the elastic scattering of light by spheres which are much smaller than the wavelength of light. The intensity, I, of the scattered radiation is given by

I = I0 (frac{ 1+cos^2 (theta) }{2R^2})(frac{2pi}{lambda})^4(frac{ n^2-1}

{n^2+2})^2(frac{d}{2})^6

where I0 is the light intensity before the interaction with the particle, R is the distance between the particle and the observer, theta is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.

It can be seen from the above equation that Rayleigh scattering is strongly dependent upon the size of the particle and the wavelengths. The intensity of the Rayleigh scattered radiation increases rapidly as the ratio of particle size to wavelength increases. Furthermore, the intensity of Rayleigh scattered radiation is identical in the forward and reverse directions.

The Rayleigh scattering model breaks down when the particle size becomes larger than around 10% of the wavelength of the incident radiation. In the case of particles with dimensions greater than this, Mie's scattering model can be used to find the intensity of the scattered radiation. The intensity of Mie scattered radiation is given by the summation of an infinite series of terms rather than by a simple mathematical expression. It can be shown, however, that Mie scattering differs from Rayleigh scattering in several respects; it is roughly independent of wavelength and it is larger in the forward direction than in the reverse direction. The greater the particle size, the more of the light is scattered in the forward direction.

The blue colour of the sky results from Rayleigh scattering, as the size of the gas particles in the atmosphere is much smaller than the wavelength of visible light. Rayleigh scattering is much greater for blue light than for other colours due to its shorter wavelength. As sunlight passes through the atmosphere, its blue component is Rayleigh scattered strongly by atmospheric gases but the longer wavelength (e.g. red/yellow) components are not. The sunlight arriving directly from the sun therefore appears to be slightly yellow while the light scattered through rest of the sky appears blue. During sunrises and sunsets, the Rayleigh scattering effect is much more noticeable due to the larger volume of air through which sunlight passes.

In contrast, the water droplets which make up clouds are of a comparable size to the wavelengths in visible light, and the scattering is described by Mie's model rather than that of Rayleigh. Here, all wavelengths of visible light are scattered approximately identically and the clouds therefore appear to be white or grey.

Hope this helps a bit,

Frank