Lenses and Waves

1677-1679 –WAVES OF LIGHT 171
of the ellipse in the crystal. Yet, the most important difference between both
laws is their nature. Whereas the proposal of 1672 was fully phrased in terms
of rays and their components, the new law utilizes waves, unobservable and
hypothetical entities expressing the mechanistic nature of light. The refracted
ray is constructed by means of the tangent to the ellipse, by means of waves
and their properties. The unrefracted oblique ray and the refracted
perpendicular have become secondary to the speeds with which light
propagates through the crystal. The core of the new law was the strange
mode of wave propagation in Iceland crystal. With this Huygens had fully
departed from both his own line of thinking of 1672 and from Bartholinus’.
He had returned to his ideas regarding the nature of light to understand the
peculiar phenomena displayed by Iceland crystal.
The EUPHKA of 6 August 1677 signaled the solution to what Huygens
saw as the problem of strange refraction. As with his proposal of 1672 – and
also with Bartholinus’ law – no empirical confirmation is given. Huygens
had, by the way, improved his empirical data. He introduced an accurate
method of determining crystallographic angles that required only one
measurement. 37 Yet, he had not improved or added optical data, nor did he
explicitly verify his new law empirically. Huygens seems to have been fully
convinced that the ‘cause’ he had found was valid. What was the ‘cause of
strange refraction’ Huygens had found? The EUPHKA did not hail the
discovery of spheroidal waves. Instead, it hailed the invention of the way a
strangely refracted ray could be constructed by means of the ellipse.
Although Huygens said what the ellipse was – which in retrospect was
sufficient – he was relatively silent on the question how the construction
should be interpreted in terms of waves. Drawing on a distinction made by
Shapiro, we can say that Huygens was more concerned with the question how
an spheroidal wave could explain strange refraction than with the question
whether it could. 38 He did not explain the idea that light produces a spheroid
wave in the crystal. Only implicitly did he assume that the speed of
propagation or the action of the crystal differs in each direction. As with his
principle of wave propagation, the physical concepts underlying the
mathematical construction were at the back of his head, but he did not take
the trouble to elaborate them.
The proof of the pudding was in the eating: before spelling out the idea
of his principle of wave propagation, Huygens first saw to it that it could be
successfully applied. He found out that, with his new idea, he could
understand both caustics and strange refraction in terms of waves. He
focused on the new mathematical structure of wave propagation, and even
this he did not elaborate in detail. In his notes, he did not explain if and how
the construction conformed to his ideas on the propagation of light waves.
He only brooded a little on the composition of the crystal. Scattered around
37
Discussed in Buchwald, “Experimental investigations”, 313-314..
38
Shapiro, “Kinematic optics”, 238-239.