In this work we propose means to determine the dispersion of light in a semiconductor total internal reflection (TIR) planar waveguide featuring dielectric response of excitons from a quantum well (QW). The given theoretical apparatus is then used to reproduce the data experimentally acquired when probing the AlGaAs-based waveguide (with a GaAs QW in its waveguiding layer) with a continuous laser through a coupling grating and then gathering the light transmitted through the waveguiding layer.