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In the present work we quantify the light intensity reaching the side faces of an externally-coated, rectangular luminescent solar concentrator, and the facets of a cylindrical one. Ray-tracing is used: an analytical model has been constructed and discretized. The main novelties reside in the attribution of a finite thickness and attenuation coefficient to the external layer, and in the comparison between two geometries that have been measured against each other only in the homogeneous limit so far. In previous studies the external material is usually treated as infinitely thin. A physical thickness allows, instead, to calculate the ray-paths, to quantify the absorption losses and to evaluate the efficiency of the concentrator as function of the external layer depth. A set of numerical experiments has been performed, in order to evaluate the efficiency of the concentrator when the thickness and material properties of the outer layer are changed, and to compare the performance of the rectangular to the one of the cylindrical device under various conditions. Qualitatively we find the bilayer device to have greater optical efficiency than a comparable homogenous version. For the cylindrical geometry the factor of improvement over the homogenous device is more strongly dependent on both the thickness and the attenuation of the luminescent layer than for the rectangular geometry.