Caustics Formation by a Spherical Reflector – Geometric and Wave Field Analysis with Applications in Room Acoustics and Radio Astronomy

Based on the principles of geometrical optics, an analytical description of caustics generated in a spherical mirror is presented. The formation of caustics in a wave field is studied using acoustic and electromagnetic waves as an example. Symmetry of equations describing energy relations in acoustics and electromagnetism is shown. The presence of caustics in natural phenomena is demonstrated, as well as their manifestation in architectural acoustics and astronomy. It is explained why in the sound field in existing halls, rather than the entire caustics, only their cusp is observed, which is perceived as a blurred area with an increased sound level accompanied by unusual values of acoustic room parameters. The influence of caustics on the efficiency of spherical and parabolic antennas used in radio astronomy is discussed.