The quantum nature of light and Snell-Descartes law

The nature of light has always intrigued humanity. Among the texts of ancient Greeks that have survived to our days, there are frequent mentions of light and its nature. The first known book on optics is attributed to Euclid in the 3rd century BCE. The phenomenon of refraction, although known for millennia, resisted a mathematical explanation until the modern age. W. Snellius (Snell) was the first to present the correct equation that related the angles of incidence, refraction, and the speeds of light in each medium during refraction, but he did not publish his results. The publication was made by René Descartes. This result is now known as Snell-Descartes’ law or the law of refraction. Descartes treated light as a particle in his deduction. Huygens, in the 17th century, also deduced this law but treated light as a wave. These results differed in terms of the speed of light in more refractive media. The measurement of speed became possible only in the 18th century and corroborated Huygens’ result, indicating the wave nature of light. Interestingly, in 1905, Einstein explained the photoelectric effect by treating light as a particle (quantum of light). But if light also exhibits corpuscular behavior, shouldn’t it be possible to derive Snell-Descartes’ law by treating it this way? In this work, we will demonstrate that it is possible to derive this law from the corpuscular hypothesis of light. Besides its strong didactic appeal, the work engages in an interesting discussion of the current understanding of science regarding the nature of light.

Keywords:
Optics; Snell-Descartes’ Law; Physics; Nature of Light