For a mixture of two materials with permittivities  and  with corresponding volume fractions  and , D.A.G. Bruggeman proposed a formula of the following form:
Here the positive sign before the square root must be altered to a negative sign in some cases in order to get the correct imaginary part of effective complex permittivity which is related with electromagnetic wave attenuation. The formula is symmetric with respect to swapping the d and m roles. This formula is based on the equality
where  is the jump of electric displacement flux all over the integration surface,  is the component of microscopic electric field normal to the integration surface,  is the local relative complex permittivity which takes the value  inside the picked metal particle, the value  inside the picked dielectric particle and the value  outside the picked particle,  is the normal component of the macroscopic electric field. Formula (4) comes out of Maxwells equality . Thus only one picked particle is considered in Bruggemans approach. The interaction with all the other particles is taken into account only in a mean field approximation described by . Formula (3) gives a reasonable resonant curve for plasmon excitations in metal nanoparticles if their size is 10 nm or smaller. However, it is unable to describe the size dependence for the resonant frequency of plasmon excitations that are observed in experiments