Lenses and Waves

30 CHAPTER 2
mathematical account of such an important and widespread device existed.
We can understand his surprise, for spectacles had already been invented
around 1300. 66 A brief account by Francesco Maurolyco, that dated back to
around 1521, was not to be published before 1611, in Diaphaneon seu
transparentium libellus. Kepler would not have found much in it to his liking,
for it was a qualitative theory based on a somewhat confusing variant of the
perspectivist theory of vision and refraction. 67 Kepler knew that Della Porta
had written a study of refraction, but he had not been able to lay hands on
De refractione (1593). He dismissed what Della Porta had written in Magia
naturalis, namely that spectacles correct vision because they magnify images.
Kepler elaborated his own account of lenses, dedicating it in Paralipomena to
his patron Ludwig von Dietrichstein, whom he said had kept him busy for
three years with the question of the secret of spectacles. 68 Kepler explained
the beneficial effects of spectacles as follows. Myopic and presbyotic vision
occurs when rays are not brought to focus on the retina but in front of it or
beyond. He gave a short, qualitative discussion of the effect of lenses on a
bundle of parallel rays coming from a distant point. Convex and concave
lenses – for myopics and presbyotics respectively – move the focus of rays to
the retina. Some magnification may occur, but this is not the reason why
spectacle lenses correct vision.
With the introduction of the telescope in astronomy, the qualitative
account of single lenses in Paralipomena did not suffice any more. In Dioptrice,
Kepler extended his theory of image formation to a quantitative analysis of
the properties of lenses and their configurations. 69 As a matter of fact, he was
the one to coin the term ‘dioptrics’. 70 Compared to Huygens’ Tractatus,
Kepler’s dioptrical theory was of more limited scope. His goal was to explain
the formation of images by a telescope. He therefore restricted his theory to
a few types of lenses and mainly confined himself to object points at infinite
distance when incident rays are parallel. The basic concept was the focus of a
lens, the point where parallel rays intersect after refraction. Kepler could not
determine the focal distance with the exactness we have seen with Huygens.
He could not, for example, determine the exact route of a ray through the
refractions at both surfaces of a lens. The main obstacle in the way of a more
extensive treatment was the fact that Kepler did not know the exact law of
refraction. In Dioptrice, he used an approximation that was valid only for
angles of incidence below 30º, and that, even so, applied solely to glass.
According to this rule the angle of deviation is one third of the angle of
66
Rosen, “The invention of eyeglasses”, 13-46.
67
Lindberg, “Optics in 16th century Italy”136-141. Maurolyco had preceded Kepler in his analysis of the
pinhole image: Lindberg, “Optics in 16th century Italy”, 132-135; Lindberg, “Laying the foundations”.
68
Kepler, Paralipomena, 200-202 (KGW2, 181-183).
69
Malet, “Kepler and the telescope” offers a detailed discussion of Dioptrice, without however presenting it
as a part of the ‘optical part of astronomy’.
70
Kepler, Dioptrice, dedication (KGW4, 331).