Radiation of charged particles moving in presence of dielectric targets is of significant interests for various applications in accelerator and beam physics. Typically, the size of the target is much larger than the wavelengths under consideration. This fact gives us an obvious small parameter and allows developing approximate methods for analysis. We develop two methods: the “ray-optical method” and the “aperture method”. We applied the aperture method to different dielectric objects such as a cone, a prism, and a concentrator of Cherenkov radiation. This paper is mainly devoted to the case of dielectric ball with vacuum channel. Using the aperture method, we obtain analytical results, demonstrate typical graphics for the radiation field, and give comparison with COMSOL Multiphysics simulations.