Applicability of the Arago-Biot mixing formula to the effective refractive index of particle suspensions

• We theoretically demonstrate that the Arago-Biot mixing formula can be used to calculate the effective refractive index of a dilute suspension of tenuous particles and finite size. • We provide 2D maps of mathematical errors of the Arago-Biot mixing formula. • We study the error in determining the refractive index of particles in suspension using the Arago-Biot mixing formula and present the results of our analysis graphically. • The method does not require knowledge of the particles' shape or size distribution. • Uncertainties required on experimental measurements are discussed. We study the applicability of the Arago-Biot mixing formula to calculate the effective refractive index of particle suspensions using the anomalous diffraction approximation, when the size of the particles is comparable to the wavelength of radiation. Interest in this mixing formula stems from the fact that it does not require knowledge of the particles' size or shape. Thus, it can be useful for determining the refractive index of particles in suspension of size comparable to the wavelength of radiation, regardless of their shape or size distribution. We present an analysis and graphs in the refractive-index-contrast versus size-parameter 2D space of the error of the Arago-Biot mixing formula and the error of using this mixing formula to infer the refractive index of particles in suspension. We consider non-absorbing and absorbing particles. The results obtained demonstrate the viability of inferring the refractive index of particles in suspension with accuracy in the second decimal place by reducing the refracting index contrast with the matrix medium for particles comparable to the wavelength of light. 2D maps of the relative errore of the anomalous diffraction approximation for spherical particles immersed in water as a function of the size parameter and real refractive index contrast for particles with an imaginary part of their refractive index of: (a) 0, (b) 0.001, (c) 0.01 and (d) 0.025.