This article investigates the validity of the physical optics/geometrical optics (PO/GO) approximation in modeling low-permittivity integrated lens antennas when there is significant illumination of the shadow region as a function of the feed and lens geometry. The comparative analysis reveals that for certain extended hemispherical lenses, feed illumination of the lens surface beyond the critical angle leads to significant discrepancies in radiation pattern and antenna gain between PO/GO predictions and full-wave simulations. These discrepancies are traced to the constructive far-field contribution of the shadow region currents relative to those originating from the top lens region below the critical angle. The measurements of fabricated extended hemispherical lenses confirm these findings, showing up to 2-dB gain enhancement over PO/GO predictions and showcasing the limitations of traditional high-frequency modeling techniques in capturing this phenomenon. The significant gain enhancement, along with the clean measured radiation patterns, highlights the potential of using lens antenna designs with feeds that provide strong shadow region illumination. These findings provide new insights into the development of high-performance integrated lens antennas for advanced communication and sensing applications.