Lenses and Waves

Chapter 6
1690 - Traité de la Lumière
Retrospection upon the coming about of the wave theory
in the context of Huygens’ oeuvre
and the mathematical sciences in the seventeenth century
Huygens’ new science of optics developed in a markedly contingent way. If
he had not conceived of a plan for the elusive publication of his dioptrics; if
he had not fallen in with the custom of providing some explanation for
refraction; if he had not recognized the problem strange refraction posed for
his Pardies-like explanation of refraction; if he had not decided to include it
in his treatise; if he had not pressed ahead after his investigations of strange
refraction of 1672; and if Rømer had not compelled him to devise the special
experiment of 1679. If all this had been otherwise, then his celebrated wave
theory had not come about. In that case, some time, some kind of
‘Dioptrique’ may have been published. As a treatise in geometrical optics it
would hardly have marked itself off from – say – Barrow’s lectures, except
for its practical outlook. But Traité de la Lumière was something different.
What had begun as a fairly conventional, natural philosophical introduction
to a treatise on dioptrics had become a new way of treating light
mathematically that went beyond traditional geometrical optics. We are now
ready to look back and ask how the wave theory related to the seventeenthcentury
development of optics and of mathematical science in general and,
second, what light it sheds on Huygens’ oeuvre.
Traité de la Lumière was not presented by its author as a revolutionary new
way of doing optics. Hypotheses were simply inevitable in these matters,
Huygens said as a matter of fact, and he did not draw attention in any way to
the special character of his principle of wave propagation and his account of
strange refraction. Did he realize he was breaking new ground? We cannot
read his mind, of course, but there is reason to think that he did not value his
findings in the same vein as we do, as some kind of methodological
innovation, that is. He never abandoned the original plan of 1672, in which
his theory of light would be a preparatory part to his dioptrics. Only at the
very last moment did he abandon his plan to publish a ‘dioptrica’ and created
a ‘traité de la lumière’. He published his wave theory in 1690 as Traité de la
Lumière, a title he had chosen at the very last moment. He did so after many
hesitations over the best way to present his wave theory, which suggests that
Huygens himself was also not sure about its exact status.
The publication of the wave theory took no less than twelve years. The
years after its presentation at the Académie witnessed Huygens’ step by step