Lenses and Waves

THE 'PROJET' OF 1672 119
matter. In this way he followed up on the mechanical analogies employed in
perspectivist causal accounts, but he did not do so without appropriating that
line of reasoning to his own means. “For it may be permissible here for me
to use the words of the optical writers in a sense contrary to their own
opinion, and carry them over into a better one.” 50 Kepler went on to develop
the analysis of a ball spun into water by distinguishing between the dynamics
of the parallel and perpendicular components of its motion, whereby light is
rarified in the former direction and merely transported in the latter direction.
He then proceeded with a short discussion of the underlying physics, to wit
the statics of a balance. In this way Kepler transformed the mechanical
analogies employed by his perspectivist forebears to illuminate the
mathematics of refraction into a physical foundation of the analysis of
refraction. The account in chapter 1 only yielded a qualitative understanding
of refraction, and only partial for that matter, for Kepler did not discuss the
passage of light into a rarer medium.
At the opening of chapter 4, ‘De Refractionum Mensura’, Kepler still
lacked an exact law of refraction. He needed this ‘measure’ in the first place
for his account of the dioptrics of the eye in the next chapter (see above
section 2.1.1.), but in the end principally for his account of atmospheric
refraction later in Paralipomena. After all, it was a treatise in the optical part of
astronomy for which the laws of optics were instrumental. Nevertheless my
discussion will be confined to the optics per se: Kepler’s tour the force to
tackle the mathematics of refraction.
Kepler began with a review of the received opinions regarding the
measure of refraction. In this section, he tied in with the traditional approach
of considering the physical properties of light rays and their components.
After negating several opinions, Kepler laid down the - in his view - generally
established understanding: first, that the density of the refracting medium is
the cause of refraction and, second, the angle of incidence contributes to its
cause. The question therefor was how these two aspects are connected.
Kepler ran through several options as they had been set forth, rejecting each
as insufficient. Next, he contemplated how the two said aspects could
correctly be combined. 51 Kepler proceeded to represent these conditions
geometrically (Figure 36). BC is the refracting surface of a medium BCED and
AB, AG, AF are incident rays. Kepler now extended the medium to DEKL,
thus representing the greater density of its surface. He then constructed a
refracted ray FQ by drawing HN perpendicular to the lower surface and
joining N at the imaginary bottom with F. 52 Comparing the results of this
method with Witelo’s table, Kepler simply concluded that it was refuted by
50
Kepler, Paralipomena, 16 (KGW2, 27). “Liceat enim hîc mihi verba Opticorum contra mentem ipsorum
usurpare, et in meliorem sensum traducere.”
51
Kepler, Paralipomena, 85-87 (KGW2, 85-86)
52
This is equivalent with sini : tanr = constant. Lohne, “Kepler und Harriot”, 197. Compare Buchdahl,
“Methodological aspects”, 283.