Do Leonardo da Vinci’s drawings, room acoustics and radio astronomy have anything in common?

Abstract

After introducing Leonardo da Vinci’s (LdV) predecessors in the field of light propagation research, his drawings on the topic of reflecting light by a spherical mirror are analysed. The discovery of LdV is presented, according to which, at an infinitely distant source of rays, a small fragment of the canopy is enough to generate a focus, while the rest of the mirror forms a caustic for which LdV did not indicate an application. An analytical description of the energy concentration in the focus and on the caustic is given, together with its reference to the geometric representation of the acoustic field in rooms. Based on the general principles of wave motion, symmetry is shown in the description of energy relations in acoustics and electromagnetism. It is explained why in the sound field in existing halls, instead of a whole caustic only its cusp is observed, which is perceived as a point-like sound focus. The size of the mirror aperture, shown graphically by LdV, is determined. How the development of receiving techniques increased the mirror aperture compared to the LdV estimate is also shown. The implementation of these improvements is presented via the example of the Arecibo and FAST radio telescopes.