Propagation of an outside launched, 60 GHz, TEM00 focused microwave beam that couples to the ordinary mode for electron cyclotron heating (ECH) in the Texas Experimental Tokamak (TEXT) is examined via transmission measurements at low power ( approximately 40 mW). For a plasma density profile of n(r)=n(0) exp(-r/22.5)2.9, refraction and absorption at the fundamental resonance are shown to remain in overall fair agreement with the results of simple geometrical optics (WKB) ray tracing and linear absorption optical depth models up to a wave cut-off density of nc=4.5*1013 cm-3. Further details of the propagation that include the consequences of beam self-diffraction are modelled using the beam propagation method. An excess of transmitted power (by a factor of 2-3 on-axis) was observed at the highest central densities, n(0)/nc >0.9, where the propagation is shown to become sensitive to weak short-scale-length variations in the core density profile