Rayleigh-Gans equation

The Rayleigh-Gans equation for the angular dependence of the intensity of the scattered light is given for spherical particles of low refractive index by the equation [45] ... 

A graphical solution for all maxima and minima has been determined by Pierce and Maron [93] who, together with Elder [94,95] extended equations (10.21) and (10.22) beyond the Rayleigh-Gans region, (ffj - 1 0) to 1.00 < /M < 1.55, deriving the following formulae ... 

In Equation 14.22 the subscripts RDG and R denote Rayleigh-Debye-Gans and Rayleigh. In Equation 14.23b q is the scattering wave vector to be discussed below. 

The distance, d, is measured from an arbitrary reference point and may include a portion of the distance traveled by the incident beam as well as by the scattered beam. These equations assume that the electric field at the scattering point is not modified on crossing dielectric boundaries. This assumption is referred to as the Rayleigh-Gans approximation . Deviations from this assumption can be treated in simple cases such as in the Mie scattering from spheres. 

Equations 8.27 and 8.28 are not satisfied if al k = 0.3 and n - 1 = 0.3, but these values lead to a value of 0.09 for the left-hand side in Equation 8.34, whieh is satisfied. Thus the Rayleigh-Gans-Debye result can be extended to systems not covered by Rayleigh scattering alone. Further, for n very close to one, much larger values of a, the length scale characterizing the dispersed phase, can be tolerated. 

Rayleigh-Debye-Gans (RDG) approximation, and its accuracy will be addressed below. For a solid sphere, equation (18.19) is readily evaluated. The result reads as follows ... 

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