Bouncing light beams and the Hamiltonian analogy

Abstract

In this work we use the unusual behaviour of a light beam in a diffusion cell as an experimental introduction for university students of physics and engineering to the optical - mechanical analogy. We have found that the lecture demonstration is a key element in the development of the presentation and subsequent use of the analogy. Riassunto. In questo lavoro si utilizza l'inusuale comportamento di un fascio luminoso in una cella di diffusione come introduzione sperimentale, per studenti di fisica e di ingegneria, all'analogia tra il comportamento di una particella materiale ed un fascio luminoso (Analogia di Hamilton). La dimostrazione didattica rappresenta un elemento chiave nello sviluppo della presentazione e del successivo utilizzo dell'analogia.

Medieval Arab Contributions to Optics

“…Ibn al‐Haytham went against accepted wisdom by arguing that light has a finite speed. The beginning of the analogy between geometrical optics and mechanics — usually attributed to Descartes — can be traced to Ibn al‐Haytham (Ambrosini, Ponticiello, Spagnolo, Borghi, & Gori, ). Equipped with these basic facts, Ibn al‐Haytham tackled several natural phenomena, such as dispersion of light into constituent colors; rainbows; shadows; eclipses; atmospheric refraction; twilight; and the moon illusion (moon appears bigger on the horizon than when it is higher in the sky).…”

Wavelength-Dependent Modifications in Helmholtz Optics

“…Here the relevant examples are Fermat's principle in optics and Maupertuis' principle in mechanics. The beginning of the analogy between geometrical optics and mechanics is usually attributed to Descartes (1637), but actually it can traced back to Ibn Al-Haitham Alhazen (965-1037) (Ambrosini et al, 1997). The analogy between the trajectory of material particles in potential fields and the path of light rays in media with continuously variable refractive index was formalized by Hamilton in 1833.…”

Coordinate Geometric Generalization of the Spherometer

“…A comprehensive account of the Medieval Arab contributions to optics can be found in [15]- [35]. The beginning of the analogy between geometrical optics and mechanics, usually attributed to Descartes, can be traced to Abu Ali al-Hasan ibn al-Haytham (965-1039, known as Alhacen/Alhazen, the Latin transliteration of his first name al-Hasan, see [36]- [42] for details).…”