Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 233
project. They express his unique combining of mathematical science and
experimental philosophy. In mathematical science, including Galileo’s ‘nuova
scienza’, experiment was used as a tool of verification of hypotheses and
theories. From the experimental philosophers, Newton adopted the heuristic
use of the experiment, to discover and explore new phenomena and
properties. Yet Newton looked upon his experiments with the eye of a
mathematician. He saw rays and he looked for laws and did so by measuring
and analyzing mathematically the outcomes of his experiments. In so doing
he extended geometrical optics to new properties of rays: colors.
In the Optical Lectures, Newton still confidently proposed properties of
light by reason, but he soon qualified his statements. In particular after the
disputes over the ‘New Theory’, he distinguished the certainty of
mathematical demonstration from the conditional certainty of experimental
conclusions. 77 Explaining his view on the certainty of mathematical science to
Hooke in 1672, he wrote “… the absolute certainty of a Science cannot
exceed the certainty of its Principles”. And in optics these principles were
physical. 78 In his view different refrangibility was an experimentally proven
property of rays and the true cause of the appearance of colors, and he was
trying to convince Hooke of it. Newton maintained the conceptual primacy
of the light ray in optics, thus ensuring the connection of his theory of colors
with the mathematical science of optics. He did not take the physical
significance for granted, like traditional geometrical optics, but carefully
defined its mathematical and physical meaning respectively, and carefully
determined its properties experimentally. The theory of fits of Book 2 of
Opticks, in which he attributed periodicity to rays and that should account for
the colors in thin films, can be seen as the culmination of this project of
establishing a mathematical science of colors.
As such, the project had foundered, however. Newton had not been able
to establish the theory of unequal refrangibility as a mathematical science of
colors. The first step in finding the laws of colored rays was to establish a
one-to-one correspondence between the color of a ray and its index of
refraction. The next, crucial step for the science of colors to become
mathematical was to determine the regularity of the various indices by means
of a law of dispersion. Having dropped the ‘Cartesian’ dispersion law of the
Optical Lectures, in Opticks he resorted to a law whose validity, both by reason
and experiment, was unclear. This is only a symptom of the fact that Newton
never succeeded in elaborating the mathematical science of colors projected
in the lectures. 79 The first book of Opticks is the direct descendant of the
Optical Lectures, but Newton had transformed his theory of unequal
refrangibility from a mathematical deduction into an experimental
exposition. In this he consolidated the presentation of the ‘New theory’.
77
Shapiro, Fits, 12-14.
78
Newton, Corrspondence 1, 187-8. Cited and discussed in Shapiro, Fits, 36-38.
79
See the quote above on page 227