Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 231
medium. The conceptualization of refraction as a surface phenomenon was
to culminate in proposition 14 of Principia, where it is articulated as an event
occurring at the boundary layer between two media. It subsequently to be
reformulated entirely in terms of rays and their properties in the proof in
Opticks.
In medium conceptions, refraction could be explained in a much more
straightforward way. The explanation reduced to accounting for the fact that
a change of velocity results in a change in the direction of propagation. In his
explanation of refraction, Descartes inserted this notion into a perspectivist
analysis of refraction. The result was a rather ambiguous account, as he
blended his medium conception of light with a surface conception of
refraction. He was the first to state the propagation of light in terms of
properties of the refracting medium. In the first assumption of his
derivation, he mathematized this insight. Yet, in his second assumption he
maintained the conception of refraction as a surface phenomenon by
attributing the constancy of action to the surface of the refracting medium.
In terms of the corpuscular nature of light, Descartes’ derivation thus
raised more problems than it solved, which his successors did not refrain
from pointing out. The mathematics of Descartes’ derivation, however,
made an indelible impression on seventeenth-century savants. By stating the
interaction between light and media in terms of rays and their actions, the
derivation gained a significance that went beyond refraction per se. It provided
a promising clue to seize all phenomena in which refraction was involved. Extending
Descartes’ diagrams is a strategy that recurred many times in course of the
seventeenth century. Bartholinus took this lead to fathom the behavior of
strangely refracted rays, and Huygens initially did so, too.
Newton in particular would always remain impressed with the cogency of
Descartes’ elegant proof. 74 In Opticks, he preserved it while putting it on a
firmer (emission) foundation than La Dioptrique had done. In his search for a
law of dispersion Newton’s first proposal was an extension of Descartes’
derivation. Naturally, so one would say, as this would preserve the harmony
with monochromatic refraction and preserve the analysis of the
phenomenon in terms of rays. Likewise, when Newton turned his mind to
strange refraction in Opticks, he proposed – without justification – a
construction that added the irregular component of the refracted
perpendicular to the ordinary refraction of each ray. 75 Indeed, the same
construction Huygens had proposed in 1672. So, even after he had dismissed
his ‘Cartesian’ dispersion law (see above 5.2.2), Newton remained confident
that a Cartesian analysis had broader significance for phenomena of
refraction.
74 Shapiro, “Light, pressure”, 239-241.
75 Newton, Opticks, 356-357.