Lenses and Waves

1677-1679 –WAVES OF LIGHT 179
Figure 70 Construction of the refraction of an arbitrary ray in Traité de la Lumière.
crystal. IK is the common tangent of these wavelets and therefore IK is the
propagated wave and IC the refracted ray. 55
In this construction the line N replaces the unrefracted oblique ray in the
construction of August 1677. It represents the proportion of the speeds of
propagation in the air and in the crystal. As Buchwald explains, it provided
an absolute parameter for the construction. 56 Originally, this proportion
followed from the unrefracted oblique ray. In 1679 he found out, as we will
see in section 5.3.1, that this ray was not parallel to the edge of the crystal.
Although this did not change his construction, he could not use it as a
parameter anymore. Instead he used the line N, introduced as an
observational value:
“To find the length of the line N, proportional to CP, CS, CG, it is through the
observations of the irregular refraction that occurs in this section of the crystal, that it
must be determined; and I find in this way that the ratio of N to GC is a little less than 8
to 5.” 57
With the ellipse construction thus quantitatively determined, Huygens
derived several properties of the strange refraction. He showed which ray
passed without refraction; considered rays outside the principal section, and
discussed the apparent position of images. Finally, Huygens could conclude:
55 Traité, 65.
56 Buchwald, Rise, 315-316. However, Buchwald only discusses the final text of Traité de la Lumière and
therefor does not take into account the historical background of this choice of parameters. On page 317
he raises the possibility that Huygens did not determine the value of N directly - as the next quote
suggests - but deduced it from the angle of the unrefracted oblique ray and subsequently reversed the
calculation to confirm is theory. In the manuscripts he could have caught Huygens more of less in
flagrante delicto.
57 Traité, 66. “Pour trouver la longueur de la ligne N, à proportion des CP, CS, CG, c’est par les observations
de la refraction irreguliere qui se fait dans cette section du cristal, qu’elle se doit determiner; & je trouve
par là que la raison de N à GC est tant soit peu moindre que de 8 à 5.”