This paper provides details of a spectroscopic investigation of a thermal 87Rb atomic vapour. The experiment was conducted with an external magnetic field of 1.5 T in the Voigt geometry. Very good quantitative agreement between experimental data and theory is found for all four Stokes parameters—with RMS errors of ∼1.5% in all cases. From the fits to our experimental data a value for the magnetic field strength is extracted, along with the angle between the magnetic field and the polarisation of the light. The effects of the cell window birefringence on the optical rotation signals are characterised. This allows us to carry out precise measurements at a high field strength and arbitrary geometries, allowing further development of possible areas of application for atomic magnetometers.