Lenses and Waves

1653 - TRACTATUS 29
chapter of Paralipomena, Kepler explained how images are formed on the
retina. In order to account for spherical aberration, he argued that the pupil
as well a the slightly a-spherical shape of the posterior side of the humors
diminish the severest aberrations. Kepler’s analysis was based on his study of
refraction in the fourth chapter of Paralipomena. In this chapter, he had tried
unsuccessfully to find an exact law of refraction, but his understanding of
refraction at plane surface sufficed for discussing the focusing properties of
spheres at least qualitatively. 62
With this Kepler completed his theory of image formation. It had
originated in the solution of an anomalous astronomical observation and its
ultimate rationale was astronomical observation. With his definition of optics
and its indispensability to cosmology, Kepler fits in a Ramist trend in the
sixteenth century that Dupré refers to with ‘the art of seeing well’ and to
which Risner also belongs. 63 The full title of Paralipomena starts with Ad
Vitellionem paralipomena, quibus astronomiae pars optica traditur, …. In his preface,
Kepler proclaimed eclipses to be the most noble and ancient part of
astronomy: “… these darknesses are the astronomers’ eyes, the defects are a
cornucopia of theory, these blemishes illuminate the minds of mortals with the
most precious pictures.” 64 The eye being the fundamental instrument of
observation, to Kepler a reliable theory of visual perception was
indispensable for astronomers. His perspectivist forebears had not treated
the matter satisfactorily and thus he had provided the necessary additions to
Witelo. Revolutionary additions, to be sure. The eye perceives dots rather
than things and in the analysis of vision “… we should not look to entire
objects, but to individual points of objects, …” 65 Kepler had made it clear
that all rays from an object point partake in the formation of images, whose
sharpness is not evident beforehand. Image formation was no longer a
matter of tracing individual rays from object to image. The task of the
optician now became to determine exactly how a bundle of rays is brought to
focus again after it is emitted by a point of an object.
Lenses
Kepler approached the newly invented telescope in the same manner as the
pinhole and the eye. The working of the telescope should be properly
understood if it were to be used in astronomical observation. For Kepler,
this meant that a mathematical theory was required, a mathematical theory of
the telescope so to say. He had already treated lenses briefly in the final
proposition of chapter five of Paralipomena. At that moment spectacle glasses
were new topic in optical literature. Kepler expressed his amazement that no
62
Kepler’s efforts to find a law of refraction are discussed below, in section 4.1.2.
63
Dupré, Galileo, the telescope, 31.
64
Kepler, Paralipomena, 4 (KGW2, 16). “… hae t e n e b r a e sint Astronomorum o c u l i , hi d e f e c t u s
doctrinae sint a b u n d a n t i a , hi n a e v i mentes mortalium preciosissimis p i c t u r i s illustrent.”
Translation Donahue, Optics, 16.
65
Kepler, Paralipomena, 201 (KGW2, 181). “Itaque non oportet nos ad res totas respicere, sed ad rerum
singular puncta, …” Translation Donahue, Optics, 217.