Lenses and Waves

THE 'PROJET' OF 1672 111
In the ‘Projet’ the third chapter was only indicated by a title and a single
remark: “Iceland crystal” and “difficulty of the crystal or talc of Iceland. its
description. shape. properties.” 16 Iceland crystal was a rarity from the barren
nordic lands displaying remarkable properties. This had been known for
ages, but a sample had recently been brought to Copenhagen to increase the
collection of curiosities of the Danish king. Danmark’s leading
mathematician, Erasmus Bartholinus, then made a study of the crystal and its
phenomena and reported on its strange refraction properties in 1669 in a
treatise called Experimenta crystalli islandici disdiaclastici (1669). The strange
refraction of Iceland crystal contradicted the sine law. It refracts a
perpendicularly incident ray, which is impossible according to the sine law.
Still, Iceland crystal had no relevance whatsoever to telescopes. So why
would Huygens include it in his ‘Dioptrique’? The reason is that strange
refraction constituted a problem for Pardies’ explanation of refraction. The
‘difficulté’ of Iceland crystal was that the refraction of the perpendicularly
incident ray could not be reconciled with the assumption that rays are
normal to waves. Huygens did not say this explicitly, but the place where he
indicated the ‘difficulté’ makes it clear that Iceland crystal was a problem for
Pardies’ explanation of refraction. Moreover, in his first notes on the
phenomenon of around the same time, Huygens explicitly phrased the
problem this way. 17
We now see why Huygens would want to include strange refraction in a
treatise on the dioptrics of the telescope. If his explanation of refraction
were to be acceptable, it should not be contradicted by this particular kind of
refraction. But why would he care for the tenability of the explanation so
much? Huygens had not bothered to explain refraction before. Part of the
answer lies in the fact that it was customary to do so. Books on geometrical
optics usually contained a preliminary account of the nature of light and the
causes of the laws of optics. The explanation of the sine law was to complete
Huygens’ dioptrics so that it could be published as a proper treatise in
geometrical optics. It would also complete his critique of Descartes’ La
Dioptrique. As his theory of spherical lenses corrected the latter’s failure to
explain the telescope properly, the projected explanation of the sine law
would correct the difficulties in Descartes’ explanation.
Waves would do the job, assuming that the problem of strange refraction
could be settled. But what job exactly would they do? Just before the sketch
of his explanation of refraction Huygens added an epistemological remark.
An utterance of this kind is rare with Huygens, and this one is particularly
illuminating:
“Although it suffices to pose these laws as principles of this doctrine, as they are very
certain by experience, it will not be unbecoming to examine more profoundly the cause
of the refraction in order to try to give also that satisfaction to the curiosity of the mind
16
OC13, 743: “Cristal d’Islande” and 739: “difficultè du cristal ou talc de Islande. sa description. figure.
proprietez.”
17
See below at the beginning of section 4.2.