Lenses and Waves

1655-1672 - DE ABERRATIONE 93
its elaboration it consisted of a geometrical derivation of the properties of
spherical aberration. Like Tractatus, it rested on little more than the sine law
and a generous dose of Euclidean geometry.
In the elaboration of the theory of spherical aberration, geometry had the
upper hand. This stands out clearest in the simplifications Huygens
employed. He used a simplified expression in order to determine the amount
of aberration produced by a particular lens. He justified this by comparing
the calculated differences between both expressions. What effects such
differences would have in actual lenses, he did not tell. Nowhere in De
Aberratione does Huygens give an indication that he had considered the
question how the calculated properties of spherical aberration related to its
observed properties. A modern reader would expect otherwise, but Huygens
went about by geometrical deduction exclusively. This geometrical analysis
resulted in a sophisticated theory of spherical aberration in which complex
problems were solved of neutralizing it by configuring spherical lenses
properly.
But Huygens’ goal was not mere theory, he aimed at its practical
application to real lenses and telescopes. This marked him off from his
fellow dioptricians. Had he not applied his theory to design better telescopes
and tested his design, he would not have been confronted with those
disturbing colors. The fact that Huygens was taken by surprise by those
disturbing colors need not surprise us. In his dioptrical study of lenses,
Huygens confined himself to their mathematical properties and excluded the
consideration of colors. Likewise, in his study of halos and parhelia, written
around 1663, he confined himself to tracing the paths of rays of light
through transparent particles in the atmosphere and left out any
consideration of the colors of these phenomena. 180 Colors eluded the laws of
geometry, so he wrote there with even greater conviction than in Tractatus:
“However, to investigate the cause of these colors further; to know why they are
generated in a prism, I want to undertake by no means, I admit on the contrary not to
know the cause at all, and I think that no one will comprehend their nature easily for as
long as some major light will not have enlightened the science of natural things.” 181
That major light had come, it was named Newton, and it had eclipsed
Huygens’ grand project of perfecting telescopes.
Huygens was well acquainted with the disturbing colors produced by
lenses. Dealing with them was, in his view, a matter of trial-and-error
configuring of lenses instead of purposive calculation. When colors came to
disturb the predicted optimal working of his design, he did not do anything
with them. Despite the importance of colors for his project, Huygens did not
elaborate upon his observation that colors might be related to the angle of
180 With connected reproduced in OC17, 364-516. On the dating see OC17, 359.
181 OC17, 373. “Doch de reden van dese couleuren verder te ondersoecken, te weten waerom die in een
prisma gegenereert worden, wil ick geensins ondernemen, emo fateor rationem eorum me prorsus
ignorare, neque facile quemquam ipsas perspecturum arbitror quandiu naturalium rerum scientiae major
aliqua lux non affulserit.”