Lenses and Waves

228 CHAPTER 6
Traité de la Lumière. For Huygens it went without saying to apply mathematics
to matter in ‘Physique’ just like it was done ‘Optique’, in spite of the very
different nature of this was matter.
Besides the difference in tone in the way Huygens and Newton made
public their achievements, there is, of course, a big difference in the
character of their pursuits. Each created a form of physical optics by
mathematizing new domains of light, but of an essentially different nature.
Newton mathematized a new range of optical phenomena (which Huygens
did not); Huygens extended mathematics into the new kind of realm of the
unobservable, hypothetical nature of light (what Newton could do equally
well but only did so privately). In each case, traditional geometrical optics
was a major starting point, yet embedded in different natural philosophical
contexts and problem definition. Huygens primarily responded to the issues
raised by mechanistic philosophy, continuing along the lines of mathematical
optics that run from Alhacen over Kepler to Descartes. The roots of
Newton’s optics were more diverse. As much, if not more, as his optics was
guided by his proficiency in and commitment to mathematical science, it was
informed by his quest for the true nature of matter. In addition to
mathematical optics, it built on the teachings of experimental philosophy and
questions of matter theory articulated by Aristotle, Descartes and Gassendi,
and Boyle.
Despite these differences, the development of their pursuits show
conspicuous similarities. Huygens and Newton came to their novel ways of
doing optics only after they had moved beyond the confines of traditional
geometrical optics. At an early stage, each worked much closer to the tenets
of traditional geometrical optics than there final theories suggest. In section
4.2, I have shown that, in first attack on strange refraction in 1672, Huygens
approached the phenomenon in a traditional way aimed at establishing the
properties of rays interacting with Iceland crystal. Only at a later stage did he
focus his attention on the mechanics of waves involved. Newton likewise
formulated a law of dispersion in his Optical Lectures that defined additional
properties of rays to mathematically account for the amount of dispersion.
In these lectures he also allowed himself an epistemological freedom of
solely providing a rational foundation that can only be understood in the
context of geometrical optics. 67 In addition, both employed a similar strategy
in their early efforts to fathom the mathematical regularities of the two
phenomena of strange refraction and color dispersion that challenged the
universality of the newly discovered law of refraction. Both extended on
Descartes’ analysis of ordinary refraction adding some extra component to
the (now irregularly) refracted ray. These examples, which I have elaborated
in detail elsewhere, serve to show that mathematization also involves
transferring to new domains ideas and strategies from established fields of
67 See Shapiro, Fits, 24-26.