By combining the concept of "two-exterior spaces"with the common T-matrix formulation

the modified T-matrix formulation of a scatterer is derived. As an example of application

the problem of multiple scattering of EM waves by a half-space of randomly distributed dielectric spheres is analyzed by using the modified T-matrix formulas of a sphere. A transcendental equation for determining the effective wavenumber of the random medium is obtained under Foldy’s approximation. The numerical results in the low-frequency limit show that the modified Tmatrix approach with Foldy’s approximation is only applicable for the sparse distribution of the scatterers. As the distribution of the scatterers is dense

the quasicrystalline approximation together with the pair distribution function of the scatterers has to be used.