Lenses and Waves

108 CHAPTER 4
on dioptrics. Under the heading ‘Projet du Contenu de la Dioptrique’, he
first listed the topics he would discuss and then made an outline of the
chapters. 4 The treatise would contain a large part of the dioptrical theory he
had developed since 1653. It would be a comprehensive account of the
refraction of light rays in lenses and their configurations. With this, he finally
prepared to give in to the persistent demands of his correspondents to
publish his dioptrics. He would not be able to present an impressive
innovation, like the cycloïdal pendulum of Horologium Oscillatorium. But also
without the design of a flawless telescope, Huygens had something to offer.
The theory of Tractatus was still worth publishing, despite the fact that
Barrow had gotten ahead of him by publishing the derivation of the focal
distances of spherical lenses from the sine law. A theory elaborating the
dioptrical properties of telescopes was still not available. Huygens had
enough material left to fill up a treatise on dioptrics.
The ‘Projet’ – as I will refer to it – is a key text in the development of
Huygens’ optics. On the one hand, it straightened out the remains of his
previous studies of dioptrics. On the other hand, it pointed a new direction
for his optics that would eventually lead to the Traité de la Lumière. This
direction was sign-posted by two new topics the ‘Projet’ introduced to
Huygens’ optics. First, the treatise would contain a chapter on the nature of
light. Huygens planned to give an explanation of the sine law of refraction in
terms of waves of light. Secondly, he would discuss an optical phenomenon
recently discovered: the strange refraction of Iceland crystal. The topic bears
no relevance whatsoever to the questions about telescopes that had occupied
him in his previous dioptrical studies. The reason for treating strange
refraction was that it posed a problem for the kind of explanation of the sine
law he had in mind. All this is remarkable, for in his dioptrics Huygens had
never before bothered about the nature of light or the cause of refraction.
What is more, in his recent dispute with Newton, he appeared to have a
blind spot for these very subjects.
In this chapter, we follow Huygens’ switch from the mathematical
analysis of the behavior of refracted rays to the consideration of its causes
and the explanation of optical laws. The issue of causes became relevant for
Huygens through the phenomenon of strange refraction. The first attack of
the problem was inconclusive and, moreover, left the issue of the cause of
refraction untouched. Together, this attack and the ‘Projet’ are illuminating,
not only for the development of Huygens’ optics and his conception of
mathematical science, but also for seventeenth-century optics in general.
Optics was in the middle of a transition from medieval ‘perspectiva’ to new
way of dealing mathematically with phenomena of light. This chapter focuses
on the issue of causes and explanations in optics. Over the shoulder of
Huygens we look back to the way Alhacen, Kepler, Descartes dealt with the
4
OC13, 738-745. I date the sketch in 1672, instead of 1673 as the editors of Oeuvres Complètes have it. See
page 92 above and page 140 below.