For my research I am interested in the transmission characteristics between a transmitter (Tx) and a receiver (Rx) situated in a circular room. In particular, it is important for me to know the number of paths a ray can take such that it reflects exactly once off the walls of the room.
Since reflections occur such that the incident ray has the same angle relative to the normal as the reflected ray, I tried to use vectors to attack the problem but the math became very unwieldy.
Empirically, I have found that depending on the situation of the transmitter and receiver, there could be 2, 3, or 4 paths—no more, no less. There is an exceptional case where the transmitter and receiver are co-located at the centre, in which case there are infinitely many paths.
Can my experimental result be validated (or denied) analytically?