Lenses and Waves

THE 'PROJET' OF 1672 139
Lectiones XVIII treated optics as the mathematical science aimed at the
analysis of the behavior of light rays. Priority was with the laws of optics,
being laws of rays that were justified empirically and generally accepted. In
this sense the lectures stood with both feet in traditional geometrical optics.
Yet, Barrow was too conscious of epistemic issues regarding mathematics
and of the new developments in natural philosophy to treat optics in the
outright traditional manner of other contemporary works. A good example is
the Opera mathematica, a mathematics textbook from 1669 by the Flemish
Jesuit Andreas Tacquet, a correspondent of Huygens. In its catoptrical
chapters, Tacquet makes room for a noncommittal survey of explanations of
reflection: some give natural economy as the ‘ratio’ of reflection, others
maintain that the perpendicular component of a ray’s motion is inverted, and
so on. 116 Even Descartes is reviewed, stripped of all corpuscular trimmings to
be sure. Tacquet did not show preference for any of the alternatives, he only
explained the various ways in which the law of reflection could be deduced.
The business of a mathematical student of light was to establish those
properties of rays interacting with varying mediums so that the laws
describing its behavior could be derived logically.
For Barrow mixed mathematics - where natural things are considered in
their quantitative aspects - was a genuine part of mathematics. In his lectures
on mathematics, Barrow effectively discarded the distinction between
sensible and intelligible matter, so that a science like optics could approach
the certainty of geometry. The certainty of inferences only depended on the
certainty of the presuppositions - axioms, postulates, principles. 117 Barrow
presented his explanations as a non-committal elucidation of empirically
founded laws, similar to the mechanical analogies of perspectivist theory.
The new mode of thought regarding the nature of things had changed the
understanding of the nature of light and the causes of reflection and
refraction. Yet, compared to these, corpuscular accounts of the causes of
reflection and refraction obtained a different meaning, as it implied a
potential claim about the true nature of light. This, combined with his
epistemic awareness, may explain Barrow’s reluctance to make strong claims
about his explanations.
In his comments, Barrow considerably qualified the status of his theory
of light and his causal accounts. His focus was on the laws and he did not
elaborate his account of the mechanistic nature of light in any detail or
explore its consequences. He was rather vague about the necessity and role
of such an account. The laws of optics should ‘not be repugnant to reason’
and be given ‘some support of reason’. He invoked a law of motion, but did
not intend to prove the laws like Descartes, by deriving them from his theory
of light. He offered a physical rationale for the laws, without making clear
the exact purpose of his explanations. As a consequence, he parried the
116
Tacquet, Opera mathematica (Antwerp, 1669), Catoptricae libri tres, 217-218
117
Shapiro, Fits, 31-36.