Editing Total internal reflection (section)

=== Discovery ===

The surprisingly comprehensive and largely correct explanations of the [[rainbow]] by [[Theodoric of Freiberg]] (written between 1304 and 1310)<ref>Boyer, 1959, p.{{nbsp}}110.</ref> and [[Kamāl al-Dīn al-Fārisī]] (completed by 1309),<ref>Kamāl al-Dīn al-Fārisī, [[:File:Autograph by Kamāl al-Dīn al-Fārisī 3.jpg|''Tanqih al-Manazir'']] (autograph manuscript, 708&nbsp;[[Hijri year|AH]] / 1309&nbsp;[[Common Era|CE]]), Adilnor Collection.</ref> although sometimes mentioned in connection with total internal reflection (TIR), are of dubious relevance because the internal reflection of sunlight in a spherical raindrop is ''not'' total.<ref group=Note>For an external ray incident on a spherical raindrop, the refracted ray is in the plane of the incident ray and the center of the drop, and the angle of refraction is less than the critical angle for water-air incidence; but this angle of refraction, by the spherical symmetry, is also the angle of incidence for the internal reflection, which is therefore less than total. Moreover, if that reflection were total, all subsequent internal reflections would have the same angle of incidence (due to the symmetry) and would also be total, so that the light would never escape to produce a visible bow.</ref> But, according to [[Carl Benjamin Boyer]], Theodoric's treatise on the rainbow also classified optical phenomena under five causes, the last of which was "a total reflection at the boundary of two transparent media".<ref>Boyer, 1959, pp.{{nbsp}}113, 114, 335.&nbsp; Boyer cites J.{{nbsp}}Würschmidt's edition of Theodoric's ''De iride et radialibus impressionibus'', in ''Beiträge zur Geschichte der Philosophie des Mittelalters'', vol.{{nbsp}}12, nos.{{nbsp}}5–6 (1914), at p.{{nbsp}}47.</ref> Theodoric's work was forgotten until it was rediscovered by [[Giovanni Battista Venturi]] in 1814.<ref>Boyer, 1959, pp.{{nbsp}}307, 335.</ref>

[[File:Johannes Kepler by Hans von Aachen.jpg|thumb|Johannes Kepler (1571–1630)]]

Theodoric having fallen into obscurity, the discovery of TIR was generally attributed to [[Johannes Kepler]], who published his findings in his ''[[Dioptrice]]'' in 1611. Although Kepler failed to find the true law of refraction, he showed by experiment that for air-to-glass incidence, the incident and refracted rays rotated in the same sense about the point of incidence, and that as the angle of incidence varied through ±90°, the angle of refraction (as we now call it) varied through ±42°. He was also aware that the incident and refracted rays were interchangeable. But these observations did not cover the case of a ray incident from glass to air at an angle beyond 42°, and Kepler promptly concluded that such a ray could only be ''reflected''.{{r|mach-2003}}

[[René Descartes]] rediscovered the law of refraction and published it in his ''[[Dioptrique]]'' of 1637. In the same work he mentioned the senses of rotation of the incident and refracted rays and the condition of TIR. But he neglected to discuss the limiting case, and consequently failed to give an expression for the critical angle, although he could easily have done so.{{r|sabra-1981}}