The condition is calculated for many dielectric cylinders to be randomly distributed for the coherent wave in the medium. The condition is useful for the computer simulation of random distribution of scatterers and for precise calculation of the equivalent dielectric constant of the medium.

A piece of information on the polarization effects on the effective dielectric constant εeff of a medium whose dielectric circular cylinders are randomly distributed is obtained by analyzing εeff for both E-wave and H-wave incidences. Our numerical analysis shows clearly the difference of εeff between E-wave and H-wave incidences and also shows the difference of εeff between our method and the Foldy's approximation.

The effective dielectric constant εeff of discrete random medium composed of many dielectric spheres has been analyzed by EFA (Effective Field Approximation), QCA (Quasicrystalline Approximation) and QCA-CP (Quasicrystalline Approximation and Coherent Potential) in the case where the optical path length is very large in the medium. These methods lead to a reasonable K for non-large dielectric constants of spheres, while their methods yield an unphysical dependence of εeff on large dielectric constants of spheres: that is, the εeff does not become large for increasing the dielectric constant. In this paper, we remove the unphysical dependence and present new results for εeff of our method, comparing with the results for εeff of EFA, QCA and QCA-CP.