Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 235
derivation in Principia, Huygens’ model of colliding particles was fairly
economic. Huygens’ focus was on the construction and its applications to
variously deflected rays not on the subtleties of ethereal collisions.
Causes in optics ought to be comprehensible, that is, be mathematical in
the first place. But what about their status? Of course waves were real, they
must be, but were they true? By admitting hypotheses Huygens sacrificed the
full, indisputable certainty Newton wanted to preserve at all costs. According
to him, one could and should conjure up a picture of light propagation, as
long as one showed that the established rules of motion did not leave room
for alternatives. Such a plausible cause could be used subsequently to derive
a possible law of strange refraction. Huygens conjured up a principle to
which all laws of optics could be reduced. The principle was demonstrated
by confirming experimentally conclusions drawn from it. Such a proof was
necessarily indirect and less than fully conclusive. Huygens’ ultimate goal was
not the mechanistic theory per se, but a theory that properly explained the
laws of optics. These conditioned his explanatory theory and were its
ultimate foundation.
Generalizing my findings regarding Huygens’ optics, I have tried to show
how the traditional mathematical science of optics offers useful clues for the
historical understanding for the development of physical optics in the
seventeenth century. Geometrical optics is not the only root, in particular
not in the case of Newton, but I think it is an important one that has been
relatively neglected. To interpret Huygens’ and Newton’s pursuits in optics
as extensions of the mathematical science of optics, reveals some noticeable
similarities that tend to be overshadowed by the vast differences between
them. Let me conclude by setting their eventual publications side by side.
There are many resemblances, as Cohen has amply shown. In particular the
novelty of the subject combined with the imperfectness of both works, has
led him to suggest that Newton may have used Traité de la Lumière as a model
for Opticks. 80 For my argument, the most conspicuous parallel between
Opticks and Traité de la Lumière is the way their mathematical roots are
obscured. Although Opticks preserved the deductive structure of definitions,
axioms, and propositions, the line of inference was clearly experimental. The
deductive structure of Traité de la Lumière is not visualized as such. Moreover,
both publications only established the principles of their new mathematical
sciences of optics. Traité de la Lumière had been intended as the prelude for a
dioptrics in which the mathematical theory would be elaborated by applying
the principles to lenses and their configurations. Newton applied his
principles to a few problems like the rainbow, but did not elaborate his
theory of colors in the way he had done in his lectures. In this way, Traité de
la Lumière and Opticks can be said to spotlight their new ways of doing the
mathematical science of optics.
80 Cohen, “Missing author”, 30-33.