Research initiated as part of a bachelor's thesis in physics at the Universitat Autònoma de Barcelona (UAB) has culminated in a new analytical description of the muon-based calibration of dual-mirror Cherenkov telescopes. The work solves a problem that had remained open for more than 30 years because of the geometric complexity of these optical systems: determining precisely how much Cherenkov light produced by a muon reaches the camera, taking into account the shadows cast by the secondary mirror and the camera itself.