We report internal and attenuated total reflection of light at the interface between glass and a quaterthiophene crystal in the spectral region of the electronic transitions. The bands corresponding to the absorption of the a(u) and b(u) Frenkel exciton states are detected for different polarization of the incident light. In particular, the wave-normal vector being almost perpendicular to the b(u) transition dipole moment allows its transverse component to be accessed, whose excitation in conventional external reflection or transmission spectroscopies is forbidden.