Lenses and Waves

1653 - TRACTATUS 35
fancied – he regarded himself as the only authority in these matters. 85 Shortly
after he wrote ‘De telescopio’ he died, and the text remained unknown until
1940.
De Radiis Visus et Lucis of De Dominis is well-known for its discussion of
the rainbow, but it also contains an account of lenses and the telescope. Like
Della Porta, De Dominis maintained perspectivist theory. His theory did not
go beyond a brief, qualitative theory of the refraction of visual rays by lenses.
In this way it avoided the problems revealed by Della Porta’s theory. It does
not seem to have counted as a serious alternative to Dioptrice. Unlike Kepler,
De Dominis was rarely referred to in matters dioptrical. In the widely read
Rosa Ursina (1630), Scheiner adopted Kepler’s theory of image formation. He
elaborately treated the construction and use of telescopes. Scheiner discussed
the properties of lenses and their configurations, but he did not incorporate
the quantitative part of Dioptrice – his account remained qualitative. Another
authoritative book on geometrical optics at the time, Opticorum Libri Sex
(1611) by the Antwerp mathematician Aguilón, did not discuss refraction or
lenses at all.
Dioptrice had been a reaction to Galileo’s neglect to explain the telescope
dioptrically in Sidereus Nuncius. Although quite an able mathematician, Galileo
never developed a theory of dioptrics. He applied himself to the
improvement of the instrument by making better lenses and optimizing the
quality of telescopic images. His friend Sagredo did take an interest in the
dioptrics of lenses, but was not encouraged to pursue his study. Galileo
wanted him to concentrate on matters of glass-making and lens-grinding. 86
On Dioptrice Galileo kept silent altogether. 87 Apparently, this self-styled
mathematical philosopher was not interested in the mathematical properties
of the instrument that had brought him fame. He did, however, have a clear
understanding of the working of lenses and telescopes. Dupré has recently
argued that Galileo relied on a tradition of practical knowledge, of mirrors in
particular, that had developed in the sixteenth century next to the
mathematical strand on which my account focuses. 88
2.2.2 THE USE OF THE SINE LAW
The exact law of refraction Kepler had to make do without, was soon found.
More than that, it had been within his reach. The English astronomer
Thomas Harriot had discovered it in 1601. After the publication of
Paralipomena, he and Kepler had corresponded on optical matters. However,
the correspondence broke off before Harriot had revealed his discovery. 89
Long before that, but unknown until the late twentieth century, the tenth-
85
Ronchi, “Refractione au Telescopio”, 56 and 34. “They know nothing of perspective.” and “... and it
pleases me that the idea of the telescope in a tube has been mine; ...”
86
Pedersen, “Sagredo’s optical researches”, 144-148.
87
KGW4, “Nachbericht”, 476.
88
Dupré, Galileo, the Telescope, chapters 4 to 6 in particular.
89
Harriot is discussed in section 4.1.2.