The rainbow is the natural version of the prism experiment. Every droplet of water suspended in a rain shower acts as a tiny spherical prism. Sunlight undergoes three steps: it enters the droplet (first refraction, with dispersion); it is reflected internally off the opposite wall (the condition is not total reflection, but partial reflection); it leaves the droplet (second refraction, with further dispersion).
The exit angle depends on the wavelength: for red, for violet. The observer thus sees red on the outside of the arc and violet on the inside.
In each droplet the light refracts on entering, reflects off the inner wall, and refracts again on leaving: dispersion at each refraction separates the colours.
Secondary rainbow
Sometimes a second, wider and fainter arc appears above the primary one, with the colours reversed (violet outside, red inside). It is produced by two internal reflections in the droplet: the sequence refraction–reflection–reflection–refraction. Each partial reflection loses intensity, so the secondary arc is weaker.
Goethe against Newton
Goethe spent thirty years of his life trying to dismantle Newton’s Opticks (1810: Zur Farbenlehre). He argued that white is a primary perceptual quality, not a physical superposition of colours. He was wrong on the physical level, but he sensed something profound: the perception of colour does not coincide with the physics of radiation, and is a story about neuro-cerebral systems. The physics and the psychology of vision are, in the end, two different chapters, and Newton was right only in the first.
Collegamenti
Argomenti: Ottica Concetti: Dispersione cromatica · Rifrazione e legge di Snell
Esercizi collegati: Esercizio svolto — Indice di rifrazione cromatico · Problema — Angolo critico di una fibra ottica · Problema — Lo strano cielo del pesce