Theoretical Investigations on the Light Scattering of Colloidal Spheres. III. Analytical Expressions for Turbidity Approximating the Performance of the Mie Equations Prior to the First Maximum

Analytical expressions are developed for the specific turbidity in dispersed systems of light scattering spheres. They yield particle diameters approximating over an appreciable range of α and m values and within better than 5% those obtained from the Mie-equations. The m range encompassed satisfactorily by the equations exceeds appreciably the range of validity of the Rayleigh-Gans and Debye equations. The limiting lower and upper values of α and m to which the equations are applicable, are defined quantitatively.