Lenses and Waves

42 CHAPTER 2
their books on telescopic observation contented themselves with a cursory,
qualitative account of the telescope, drawing on Kepler’s lessons. Dioptrice
was the standard theory referred to well until the close of the century, but
mostly as regards the basic theorems on focal lengths and configurations.
Apparently this sufficed the needs of practical dioptrics leaving the
mathematical details superfluous. Had Kepler made things more difficult
than they really were?
This theme may be illustrated with the example of Isaac Beeckman, a
savant who combined an interest in practical affairs with a theoretical
outlook. He was interested in many things, including optics in all its
manifestations, and kept an elaborate diary of his ideas and observations. It
enables us to get an idea what a knowledgeable man would do with the
mathematics of dioptrics. The diary contains numerous notes on visual
observation that show that he read the literature – Aguilón, Kepler –
attentively. In addition, he was familiar with Descartes’ optical ideas and their
development, being in close contact with him on and off since 1618. 114 In the
1620s, Beeckman became interested in telescopes and he acquired some
lenses and instruments and later, in the 1630s, he put much effort in grinding
lenses and building telescopes. 115 Working on them, he encountered the
problem of spherical aberration (and later chromatic aberration) for which
he considered several remedies. The notes concerned are interesting for they
show a basic understanding of the working of lenses – as he would have
acquired from Paralipomena and Dioptrice – but the actual problem, that the
aberration is inherent to the spherical shape of a lens, seems to have eluded
him. Besides the common use of diaphragms to decrease the disturbance,
Beeckman thought up some sagacious ideas like combining lenses on a
spherical surface in order to emulate one large lens or a lens built up in thin
rings like a Fresnel lens. 116 The first idea he tested, just to discover soon that
it did not work and that he had overlooked a basic property of lenses. 117 He
was enough of an experimentalist not to trust ideas blindly. When Descartes
informed him in 1629 of his project of a hyperbolic lens, Beeckman reacted
skeptical. 118
The micrometer and telescopic sights
The principal reason why astronomers did not show much interest in
dioptrics lies, I think, in the fact that the telescope was a qualitative
instrument during the first decades after its introduction. It had revealed
new, spectacular phenomena in the sky, but it had not been deployed in the
114
Schuster, “Descartes opticien” and Van Berkel, “Descartes’ debt”.
115
Beeckman, Journal, II, 209-211; 294-296. For lens grinding see down, page 57.
116
For the second idea see Beeckman, Journal, II, 367-368. For a later consideration see for example: III,
296.
117
Beeckman, Journal, II, 296; 357.
118
Beeckman, Journal, III, 109-110.