Lenses and Waves

126 CHAPTER 4
It is beyond dispute that Kepler was crucial to the development of
seventeenth-century optics. With his seminal work, he gave the study of
optics a new start at the beginning of the seventeenth century. What his
influence was exactly is harder to determine. As a result of the advent of
corpuscular conceptions of nature, his explanation of the nature of light was
outdated almost immediately. On the level of theories and mathematical
concepts his influence is clear: his theory of image formation and of vision
were the starting-point of all subsequent studies. However, his contribution
was largely obscured by the uncredited adoption of his ideas by Descartes
most notably. On the level of methodology the matter is less clear. Descartes
called Kepler his “first teacher in Optics”, but what he had been taught he
did not say. 74 He did not, for one thing, adopt Kepler’s candor as regards the
way he discovered things. Seventeenth-century savants found Kepler’s
Renaissance conceptions hard to take and the odor of mysticism that
surrounded him seems to have been responsible for the fact that few
referred to Kepler directly. As regards the way mathematical reasoning could
be applied to understand natural phenomena, he was quickly overshadowed
by Descartes and Galileo. Huygens, in particular, was silent on Kepler as
regards his approach to optics.
4.1.3 THE LAWS OF OPTICS IN CORPUSCULAR THINKING
The new philosophies of the seventeenth century came to see light as an
effect of some material action. As a consequence, the mechanical analogies
used in perspectivist accounts of reflection and refraction were put in a
different light. Discussions of motions and impact regarding the causes of
reflection and refraction were now connected directly with the essence of
light. Yet, accounting for the nature of light was not integrated with
mathematical analysis of the behavior of light rays at one go. This is evident
in Descartes’ account of refraction in La Dioptrique, a peculiar amalgam of
perspectivist and mechanistic reasoning. In La Dioptrique Descartes made
public the sine law, which he had discovered in Paris in the late 1620s during
his collaborative efforts to realize non-spherical lenses (see section 3.1). How
exactly he arrived at the sine law remains a subject for debate, but it is certain
Descartes did not discover it along the lines of his account in La Dioptrique.
Descartes’ account of refraction is difficult to comprehend in twentiethcentury
parlance. A quick detour via the correspondence of Claude Mydorge,
one of his Parisian collaborators, will be enlightening for modern readers. In
a letter to Mersenne from around 1627, Mydorge used a rule to calculate
angles of refraction, given the angles of one pair of incident and refracted
rays (Figure 39). If FE-GE is the given pair, the refraction EN of HE is found
in the following way. Draw a semicircle around E that cuts EF in F. Draw IF
parallel to AB, and from I drop IG parallel to CE, cutting EG in G. Draw a
second semicircle around E through G. Now draw HM, cutting the first
74 AT 2, 86 (to Mersenne, 31 March 1638).