Lenses and Waves

168 CHAPTER 5
The solution of the ‘difficulté’ of Iceland Crystal
In August 1677, what we see as Huygens’ principle was nothing but an
implicit application in the analysis of caustics and a tiny sketch reflecting this
idea. Huygens had not yet elaborated his principle nor explained how it
ought to be applied. This did not refrain him from passing on to the puzzle
that still remained: what happens to waves when they enter Iceland crystal?
In his analysis of caustics, Huygens had confirmed Pardies’ premise that
waves are normal to rays. Yet, it had become secondary to his understanding
of wave propagation. But strange refraction still contradicted it.
As we cannot tell with certainty to what extent Huygens was tackling
problems in Pardies’ theory with his study of caustics, it is not clear in what
way the problem of strange refraction was on his mind. In his notebook the
study of caustics is preceded by a single leaf filled with sketches relating to
strange refraction. 32 All relevant matters are reviewed, Bartholinus’ law and
the supposed pores of the crystal, Pardies’ explanation and the propagation
of a ray through successive layers of crystal. No progress, in comparison with
the 1672 investigation, is apparent. Dating the page is hazardous. On the
basis of its place in the notebook it can be prior to December 1674, but it
might as well have been a vacant page Huygens scribbled on later during his
stay in The Hague.
The next allusion to strange refraction follows almost immediately upon
the analysis of caustics and the sketch of his principle. After two pages with
calculations, a diagram of a telescope and another sketch (apparently) of
wavelets, a page follows with intriguing content. 33 From left to right we see
three sketches: a horizontal ellipse with two rays parallel to its axis refracted
to its focus; an ellipse plus axis, yet drawn obliquely; rays refracted with some
wavelets indicated. The last sketch is remarkable, as the refracted ray seems
to be drawn obliquely to its accompanying wave. The problem of strange
refraction had returned, and the following pages make it clear that Huygens
had found the solution: an oblique ellipse. On the mirror page the ellipse
returns, now with some small wavelets and – this was the solution – a
horizontal tangent. 34 The line connecting the point of tangency and the
center of the ellipse makes an angle with the tangent. In other words: ray and
wave intersect obliquely. The speed of propagation of light in Iceland crystal
is not equal in all directions, light spreads spheroidally instead of spherically.
Consequently, the wave is not normal to its direction of propagation.
We are able to understand these sketches in this way, as we have the
hindsight knowledge of Huygens’ elaborating in Traité de la Lumière. In his
notebook he did not explain what precisely the oblique ellipse was and how
it explained strange refraction. On the next three pages, he only offered
32 Hug9, 7r. None of it is reproduced in the Oeuvres Complètes.
33 Hug9, 44v. Not reproduced in the Oeuvres Complètes.
34 Hug9, 45r. Not reproduced in the Oeuvres Complètes.