In this paper, we describe a ray-tracing method for spherical lenses and reestablish an equation for calculating the radiation pattern using a spherical lens based on previous literature by modifying the physical optics (PO) integral equation. Using this formula, we calculated the radiation pattern according to the size and point source distance of a single-medium spherical lens and a Luneburg lens. While both lenses showed that the beam width became narrower as the lens size increased, the side-lobe level decreased when the source was located on the surface of the lens in the case of the Luneburg lens and when the source was appropriately distanced from the lens surface in the case of the single-medium spherical lens. In addition, through the analysis of the focal length and the beam forming the focus when parallel rays are incident on a single-medium spherical lens, we show that a single-medium spherical lens with a refractive index of 1.4 to 1.5 can replace a complex Luneburg lens by placing the source at a distance of 0.4 λ to 0.5 λ from the lens surface.