Lenses and Waves

THE 'PROJET' OF 1672 151
“I have imagined that in the crystal there are two different matters, and that there are
likewise two different ones in the air or ether where the motion happens that we call
light. And that the two motions of undulation of these two matters of the ether have
power to move each its analogous matter of the two that compose the crystal, and
reciprocally, that these different matters of the crystal being stirred, these would be able
to impress this motion of light only upon its analogous matter of the ether.” 146
In this case ray AB contains both motions, whereas CE and DF contain only
the motions belonging to strange and ordinary refraction respectively. But
then, Huygens said, it remains to be seen why CE and DF are split up for
other positions of the crystals.
“Which is very difficult, because for this it is required, that these rays CE, DF, although
not composed when hitting the surface LN of the crystal in some direction, are able to
move the two different matters that compose it, and in other directions not.” 147
Besides this puzzling phenomenon, the actual problem of strange refraction
was not really near its solution. Huygens concluded his first study of strange
refraction with a formulation of the true problem with the anomalous
refraction of the perpendicular, accompanied by a sketch of a Pardies-like
explanation (Figure 45 on page 142):
“How can the perpendicular ray become oblique by the refraction, for it happens that
the waves will not be at right angles to the line of their extension or emanation,
contrary to what our hypothesis of light demands.” 148
Huygens had now found a means to construct a strangely refracted ray,
which he apparently preferred over Bartholinus’ law. It was more general but
Huygens still did not have a clue towards an explanation. The core of his
alternative ‘law’ was the refracted perpendicular, which indeed was the core
of the problem of strange refraction. Maybe Huygens thought that
explaining strange refraction might benefit from the mathematical regularity
expressed by his law, or the other way around. As of yet, he had no idea
what might happen to waves so as to explain strange refraction, nor do his
notes suggest that he had considered the matter in any detail. He had
extended ordinary refraction by adding a strange component. What this
component – or any of the components in Descartes’ derivation – might
mean in terms of waves he had not considered. At this point Huygens may
have brought some clarity to the behavior of strangely refracted rays, but the
146 Hug2, 178r; OC19, 413-414. “Pour rendre raison du phenomene de la page precedente, je me suis
imaginè que dans ce crystal il y a deux matieres differentes, et qu’il y en a pareillement deux differentes en
l’air ou ether dont le mouvement fait ce que nous appellons lumiere. Et que les deux mouvements
d’undulation de ces deux matieres de l’ether ont pouvoir d’emouvoir chacun sa matiere analogue des deux
qui composent le crystal, et que reciproquement, ces matieres differentes du crystal estant esbranlees, ne
sçavroient imprimer ce mouvement de lumiere qu’a leur matiere analogue de l’ether.”
147 Hug2, 178r; OC19, 414. “Ce qui est tres difficile, car il faut pour cela, que ces rayons CE, DF quoyque
non composez en frappant en certain sens la surface du crystal LN, puissent esbransler les 2 differentes
matieres qui le composent, et en d’autres sens point.”
148 Hug2, 178v; OC19, 414-415. “Comment le rayon perpendiculaire peut il devenir oblique par la
refraction, car il arrivera que les ondes ne seront pas a angles droits a la ligne de leur extension ou
emanation, contre ce que demande notre hypothese de la lumiere.”