Light absorption spectra by interface layer with strong excitonic response in asymmetric dielectric environment are calculated for various angles of incidence of the external light. Appreciable frequency shift of the absorption resonances in the total reflection regime is found. It is shown that higher polarition modes may reveal themselves in absorption spectra of high-ordered excitonic layers with strong exciton-photon interaction. In this case, doublet and triplet structures of absorption spectra emerge for s-and p-polarized light, respectively.The properties of radiative (resonant) polaritons in a two-dimensional excitonic system have been studied theoretically in a number of papers (see, e.g., [1] and references therein). There were found to be three optically active exciton-polariton modes, called T, L and Z modes. These modes are distinguished by their electric field polarization. The T mode has s (or TE) polarization whereas L and Z modes have p (or TM) polarization. Radiative exciton-polaritons were experimentally observed in GaAs/AlGaAs quantum-well (QW) structures [2], CuCl films [3], and in slabs of organic-inorganic PbI-based layered perovskite-type semiconductors [4]. Appreciable renormalization of the polariton frequency under strong coupling between excitons and radiation field was predicted [1,5] and observed experimentally [3].In an earlier study [1] we analyzed theoretically the dispersion and radiative properties of polaritons in a layer with strong excitonic response in symmetric dielectric environment in the non-perturbative electromagnetic (EM) approach. Although the exciton-photon coupling was treated in [1] non-perturbatively, the response of excitonic layer was approximated by making use of the effective boundary conditions (EBCs). The EBCs satisfactorily describe excitonic layers in the long-wavelength approximation (LWA), when an excitonic layer is much thinner than the wavelength of photons in the excitonic-layer material. However, the LWA may be invalid even for geometrically thin layers in the frequency range close to the excitonic pole, in which the dielectric function dramatically increases if the damping of excitons is small enough and/or exciton oscillator strength is large. In this case, the retardation of EM field across the excitonic layer may become important and, hence, higher polariton modes may reveal themselves [3,5].Reflectivity spectra of excitonic layers in GaAs QW structures have been studied for oblique incidence of the external light [6]. Reflectivity spectra in the transmission regime exhibit peaks corresponding to radiative (resonant) exciton-polariton excitation, while in the attenuated total reflection (ATR) regime the spectra of the surface exciton-polaritons are revealed. However, the total reflection (TR) regime, when excitonic layer is located directly at the interface between the prism and substrate media, has not been addressed in earlier papers.