Lenses and Waves

1677-1679 –WAVES OF LIGHT 201
If Newton and Huygens had comparable opinions about the nature of
mechanistic principles, the took opposite positions regarding their status and
their relationship to the laws of optics. The way Huygens derived and
presented his law of strange refraction would have been unacceptable for
Newton, who had gone to such great lengths to erase all traces of
speculation from his experimentally established theory of light and colors.
Huygens deliberately used hypotheses to explain the observed properties of
light. True, this implied speculation, but to do so was inevitable when it came
to explanations.
“One will see here demonstrations of the kind as not to produce a certainty as great as
those of geometry, and that even differ much from it, for whereas the geometers prove
their propositions by secure and incontestable principles, here the principles are verified
by the conclusions drawn from them; as the nature of these matters does not allow that
this is done otherwise.” 131
The wave theory belonged to ‘la Physique’, offering a plausible explanation
of the empirical truths on which ‘l’Optique’ was founded. Yet, explanation
was not arbitrary. In order to be plausible an explanation ought to employ
proper ‘raisons de mechanique’. His principle of wave propagation satisfied
this demand. But still, it was probable at best. It derived no proof value from
being plausible. Huygens did not claim a priori truths. Consequently, the
burden of proof for the wave theory did not rest with its merits as a
mechanistic theory. The raison d’être of Huygens’ principle was that ‘all
properties of light, and everything pertaining to its reflexion and its
refraction, can be explained principally by this means’. 132 His ‘principal
foundation’ should not be judged at face value but on its adequacy to derive
the laws of optics.
Pardies’ theory had the same focus on explaining the laws of optics.
Huygens pointed out the advantage of his principle of wave propagation
precisely in this context. It filled a gap in Pardies’ demonstrations of the laws
of reflection and refraction. What this gap was, and why his own
demonstrations were better, Huygens did not explicate. He had found a
better ‘foundation’ for deriving the laws of optics. Huygens was rather
awkward in spelling out the mechanics of wave propagation in full and did
not always – as in the case of strange refraction – elaborate it in full detail.
His focus was on his principle of wave propagation. First of all, he assured
himself that all properties of reflection and refraction could be reduced to it.
His wave theory had developed accordingly. In his notes on caustics and the
explanation of strange refraction, Huygens satisfied himself that he could
construct a propagated wave in the troublesome situation of caustics, and a
refracted ray in the equally troublesome situation of strange refraction.
131 Traité, “Preface”, [2-3]. “On y verra de ces sortes de demonstrations, qui ne produisent pas une
certitude aussi grande que celles de Geometrie, & qui mesme en different beaucoup, puisque au lieu que
les Geometres prouvent leurs Propositions par des Principes certains & incontestables, icy les Principes se
verifient par les conclusions qu’on en tire; la nature de ces choses ne souffrant pas que cela se fasse
autrement.”
132 See the passage quoted above on page 174.