Lenses and Waves

142 CHAPTER 4
it clear what kind of problem strange refraction constituted
for the wave theory (Figure 46). It shows the strange
refraction of a perpendicular ray along with, what seems to
be, the propagation of waves. 126 After having passed the
refracting surface, the waves proceed obliquely to their
direction of propagation, which contradicts the assumptions
of Pardies' theory. Thus this tiny sketch illustrates what
Huygens called the ‘difficulté’ of strange refraction.
Strange refraction posed a problem for the explanation of
ordinary refraction that Huygens intended to adopt and he
first wanted to solve it. His first attempt is recorded in those
ten notebook pages. The notes are revealing. Despite the fact
that strange refraction was a problem of waves, this tiny
sketch is the only place where waves enter his investigation.
Instead, Huygens approached strange refraction in a rather traditional way.
He tried to find out what mathematical regularities rays refracted in Iceland
crystal might display. This was the same way Bartholinus had approached the
phenomenon, namely by trying to find a law describing the behavior of
strangely refracted rays.
4.2.1 BARTHOLINUS AND HUYGENS ON ICELAND CRYSTAL
Huygens began by recording the
main characteristics of the crystal
(Figure 47). 127 With explicit
reference, he reproduced the
crystallographic data of
Bartholinus. The crystal has the
form of a parallelepiped, of which
the obtuse angles of each
parallelogram like ACB are 101.
Consequently, the angle AXB
between faces GOCA and FOCB is
10340' and those between lines
OC and CI (bisecting angle BCA) is
Figure 46
Waves through
the crystal.
7234'. A ray of light falling on a
Figure 47 Shape and main angles of the crystal.
face of the crystal is double
refracted. One of the refractions conforms to the sine law, whereby the
index of refraction is approximately 5 to 3, a value Bartholinus had
determined empirically. The other refraction does not follow the sine law
and is therefor called extraordinary or strange. Huygens observed some
physical characteristics of the crystal as well, in particular the fact that the
126 I experienced some difficulty seeing this sketch as a two-dimensional section, as most historians have
done. I once thought it was meant to be drawn in perspective, a ray refracted out of the paper towards the
reader. Despite this ambivalence, I think after all that the two-dimensional interpretation is correct.
127 Hug2, 173v and 175r. OC19, 407-408; Bartholinus, Experimenta, 8-11 and 40.