Lenses and Waves

1655-1672 - DE ABERRATIONE 95
Newton considered his discovery of different refrangibility an addition to
geometrical optics. A necessary addition because it explained “… how much
the perfection of dioptrics is impeded by this property and how that
obstacle, insofar as its nature allows, may be avoided.” 185 These lines could
have been addressed to Huygens personally, had Newton known of De
Aberratione. Newton was aware that he was breaking new ground. In the
letter he sent to Oldenburg he wrote:
“A naturalist would scearce expect to see ye science of [colours] become mathematicall,
& yet I dare affirm that there is as much certainty in it as in any other part of
Opticks.” 186
These lines were, however, omitted when his ‘New theory’ appeared in
Philosophical Transactions. With his theory Newton went beyond the recognized
boundaries of geometrical optics by extending it to the study of colored rays.
Huygens, on the other hand, stayed within the established domain of
optical phenomena to be studied mathematically. He elaborated his dioptrical
theories in the manner customary in geometrical optics. As a mathematical
theory, the content of Dioptrica did not deviate in any principal way from the
doctrines found in Aguilón or Barrow. In Paralipomena physical
considerations – albeit within the traditional domain of mathematical optics
– were much more integrated in mathematics, but Huygens did not follow
this line of Kepler at this moment. 187 As a topic of mixed mathematics,
geometrical optics was principally a matter of geometrical deduction. The
difference with ‘pure’ geometry was that lines and circles represented
physical objects like rays, reflecting and refracting surfaces. Geometrical
inference was preconditioned by a specific set of postulates: the laws of
optics describing the behavior of unimpeded, reflected and refracted rays.
Or, as Huygens would state it in Traité de la Lumière, optics is a science
“where geometry is applied to matter.” 188
Huygens ‘géomètre’
Thus Huygens treated spherical aberration as a geometrical problem which
ought to be solved by mathematical analysis. Despite the vital importance of
colors for his project, he did not go beyond the traditional boundaries of
mixed mathematics in order to tackle the problem. He confined his
investigation to effects known to be reducible to the laws of geometry.
Geometrical optics did not provide the means to deal with colors, so he left
them to the craftsman. In this sense Huygens’ Dioptrica fits in with his
mathematical science in general. In his studies of circular motion and
consonance he also focused on exploring their mathematical properties on
the basis of established (mathematical) principles.
185
Newton, Optical papers 1, 49 & 283.
186
Newton, Correspondence 1, 96.
187
See section 4.1.2.
188
Traité, 1. “… toutes les sciences où la Geometrie est appliquée à la matiere, …”