Lenses and Waves

140 CHAPTER 4
question raised by the new philosophies of what status the corpuscular
nature of light should have and how it ought to explain the laws of optics.
4.2 The mathematics of strange refraction
Kepler and Descartes had drawn attention to the problem of the relationship
between a theory expounding the true nature of light and the mathematical
behavior of light rays. It remains to be seen how Huygens considered this
issue. What exactly did he mean by explaining refraction with waves? What
were those waves and how would he proceed from there to the sine law?
The statements in the ‘Projet’ suggest that his opinion about causal accounts
was similar to Barrow’s. Explaining refraction was a rather non-committal
affair to satisfy the minds of the particularly curious. Still, he wanted to solve
the problem strange refraction posed for Pardies’ explanation of ordinary
refraction. Apparently, the nature of light was serious enough a matter for
Huygens first to wish to get this inconsistency out of the way. 118 Given the
definition of the problem, the line of his first attack of strange refraction is
rather surprizing.
Huygens’ first attempt at understanding strange refraction is found on
some ten pages in his notebook. 119 In my view, it must have taken place
around the same time he noted down the ‘Projet’, somewhere during the
second half of 1672. 120 On the first pages Huygens jotted down some
sketches characterizing the phenomenon. The first shows five pairs of
incident and refracted rays (Figure 44). One of each pair, indicated by the
letter r is refracted regularly (‘regelmatig’) according to the sine law, the other
one indicated by the letter o is refracted irregularly (‘onregelmatig’). 121 Below,
Huygens wrote what is irregular about it:
“The perpendicularly incident [ray] is refracted It does not make a double reflection.” 122
118 Ziggelaar correctly points out that the problem of strange refraction was a reason Huygens did not
directly elaborate ‘Projet’ (which he sees as a new plan for a treatise on dioptrics), but he does not discuss
his first attempt to solve it beyond a single, and incorrect, characterization. Ziggelaar, “How”, 181-182.
See also page 162.
119 Hug2, 173v-178v. It consists of seven pages numbered by Huygens (175r-178r), preceded by two and a
half pages with some notes and followed by a page containing a further note plus the record of an
experiment performed in 1679 (discussed in section 5.3.1) Parts of their content are reproduced in OC19,
407-415.
120 I disagree with the editors of the Oeuvres Complètes regarding the dating of the papers. I think this first
study took place around the time of Pardies’ letter, much earlier than they presume. On 4 September
1672, hardly a month later, Huygens wrote to his brother Constantijn, saying he was not yet going to
publish “what I have observed of the crystal or talc of Iceland” (OC7, 219. “…ce que j’ay observè du
Chrystal ou Talc d’Islande; …”). I think this remark refers to his discovery of another peculiar
phenomenon displayed by Iceland crystal – polarization – recorded on the final pages of his investigation.
The discovery is in OC19, 412-414. The editors date these between December 1672 and June 1673, but it
is possible that they – or similar notes now lost – were written at the same, earlier date.
121 Hug2, 173v. One half of Hug2, 174r is torn away; the page contains a remark that seems of a later date.
122 Hug2, 173v; OC19, 407. “Perpendiculariter incidens refringitur Non facit duplicem reflexionem.” The
editors combine this with a remark written on Hug2, 175v.