Lenses and Waves

94 CHAPTER 3
incidence of a ray of light. He did not adjust his theory of spherical
aberration, nor the way he intended to counter its effects in telescopes.
Apparently, he saw no possibility to extend dioptrics to the properties of
colors. Colors kept eluding his mathematical understanding. In other words,
he did not take the step to leave the established domain of mathematical
optics. This should not be strongly counted against him, for no-one in the
seventeenth century did so. Except for Newton, who had an extraordinary
scholarly disposition that combined a mathematical outlook with an interest
in material things fostered by experimental philosophy and the new natural
philosophies in general.
Newton did see geometry in colors, but he looked at them from an
entirely different perspective. His studies of prismatic colors had begun
around 1665 with an experiment described by Boyle – with a thread that was
half blue and half red and appeared broken when seen through a prism. 182
Unlike Boyle, he interpreted this in terms of the refraction of rays of light.
He realized that the rays coming from both parts of the thread are refracted
at different angles. In other words, Newton interpreted the phenomenon in
the geometrical terms of rays and angles. On this basis he began his
prismatic experiments, deliberately studying the differences of the angles
with which rays of various colors are refracted. Unlike Descartes, Boyle and
Hooke before him, he tried to make the spectrum as large as possible, by
projecting it as far as possible. 183 He passed the beam of light at minimum
deviation, so that the effect of the width of the beam was minimized. By
turning the prism into a precision instrument, Newton discovered that it was
the principles of geometrical optics that were violated by the spectrum. The
solution of the anomaly consisted of linking ‘color’ with ‘refractive index’
and thus with the sine law of refraction. Different refrangibility reduced
colors to the laws of geometry.
It was not only the mere recognition of geometry that led to different
refrangibility. In order to establish the laws to which colors were subject,
Newton employed experiment in a new way. Combining mathematical
thinking with a heuristic use of experiment, he developed the new
methodological means of quantitative experiment. By measuring the
phenomena produced in his prisms he was able to discover geometrical
properties where previously there had been none.
“But since I observe that geometers have hitherto erred with respect to a certain
property of light concerning its refractions, while they implicitly assume in their
demonstrations a certain not well established physical hypothesis, I judge it will not be
unappreciated if I subject the principles of this science to a rather strict examination,
adding what I have conceived concerning them and confirmed by numerous
experiments to what my reverend predecessor last delivered in this place.” 184
182
Newton, Certain philosophical questions, 467.
183
Westfall, Never at rest, 163-164.
184
Newton, Optical papers 1, 47 & 281.