The experimentally modified Raleigh light scattering technique was utilized to determine the anisotropy of turbidity and, simultaneously, the three elastic constants of "splay" (K-1), "twist" (K-2) and "bend" (K-3) in the n-alkly-cyanobiphenyl (nCB) nematic systems. We found that the anisotropy of turbidity, and hence the elastic constants, are influenced by the sample geometry, i.e. from the surface and bulk effects. We studied the turbidities of uniaxial nematic systems at various sample thicknesses, where by a correct choice of the sample geometry and elimination of the undesired surface and bulk contributions, we then evaluated the corresponding K-1, K-2 and K-3 values. The results are in quantitative agreement with those reported in the literature obtained by the conventional field-induced techniques.