# Scattered light

In an optically homogeneous medium (with constant refractive index and absorption), the light progresses in a straight line. Strictly speaking, this is the case only in a vacuum. Any change in the optical properties will deflect the light beam from its path. This physical process, which is referred to as the scattering of light by particles, causes the phenomenon of turbidity.

Fig. 46: Light propagation in a homogeneous medium (A) and in the presence of an obstacle (B)

The phenomenon is not limited to particles visible to the naked eye or in a microscope, however. Even in pure air or pure water, some scatter occurs at the molecules. Though this molecular scatter is very small, it can never be neglected entirely: for example, the sky looks blue because the sunlight is being scattered by the air's molecules.

One process that takes place when light is scattered is diffraction, and another is the excitation of radiation. Diffraction occurs because of the light's wave character: if a wave passes an obstacle in the immediate vicinity, it will be deflected from its path. The deflection angle depends on the relation between the wavelength and the size of the obstacle. The second process occurs because the atoms are excited, i.e. raised to higher energy levels, to radiate off the light that has struck them. This light will be radiated in various directions, depending on the particle characteristics, in accordance with the laws of light refraction, reflection, and dipole radiation. (A mirror's reflection is a special case of this.)

The following Figure illustrates the variables that affect the intensity of the scattered light.

Fig. 47: Light scatter caused by a spheroidal particle

The diagram shows an incident light beam with intensity Iin and wavelength striking a spheroidal particle. The intensity  Isc  of the scattered light is a function of the scatter angle, the particle size, the wavelength, and the optical properties of the particle and the medium.

Symbolically, then,

$I_{\text{sc}} = I_{\text{sc}} \left( \theta, \lambda, d, n \right)$

where Θ represents the scatter angle, d the particle diameter, λ  the wavelength, and n the refractive index in relation to the medium.

The explicit formulation of this equation is the subject of scatter theory. In the case of spheroidal particles, the general solution for any values of the variables is provided by the Mie Theory. It encompasses the Rayleigh Theory (Rayleigh scatter), which addresses the special case of very tiny particles (< 0.05 µm). The equation has a complex mathematical structure that lends itself to solution by computer.

A practical application of scattered light measurement is determination of the turbidity value, which provides information on the concentration of solids in liquid and gaseous media.

Index

### Contact

{{selectedCountry.Name}} {{country.Name}}