Lenses and Waves

THE 'PROJET' OF 1672 131
the first assumption, he stated an exact relationship between the medium and
the length of a ray. Combined with the second assumption – which was not
new – the sine law could be derived. Mathematically speaking, the proof – as
Newton later phrased it – was not inelegant. It was fairly undisputed in the
seventeenth century and the starting point for much optical investigations. 82
Descartes’ first assumption was more than a purely mathematical
assumption, which brings us to the second level of inference that holds the
physical properties of rays. The physics of rays had been central in
perspectivist optics, but the content of Descartes’ assumptions was
innovative. According to Sabra and Schuster, stating a positive dependence
of the motion of light on the density of the medium, irrespective of the
direction of propagation, made up the decisive break with tradition. 83
Descartes may have drawn inspiration for this from his reading of
Paralipomena (which he did not acknowledge at all in La Dioptrique). In
proposition XX of chapter 1 and the sequel section of chapter 4, Kepler also
associated the propagation of a ray with the medium. Descartes may have
read Kepler’s diagrams physically, so that the length of the rays represent the
action of light as affected by the media. 84 Descartes’ diagram represented the
actions involved when a ray enters a refracting medium and served to justify
his assumptions. He did so by drawing an analogy between a refracted ray
and a tennis ball struck through a frail canvas by the man in the diagram
(Figure 40).
As we have seen, these mechanical analogies had a long history in optics
with a direct line from Alhacen to Kepler and, now, Descartes. The
mechanical analogies had a different meaning for Descartes than for his
perspectivist forebears. To an Alhacen the motions of bodies compared to
light only with respect to its propagation, not its essence. According to
Descartes light was essentially corpuscular. He made clear that they went
further than a mere analogy:
“… when [rays] meet certain other bodies they are liable to be deflected by them, or
weakened, in the same way as the movement of a ball or a rock thrown in the air is
deflected by those bodies it encounters. For it is quite easy to believe that the action or
the inclination to move which I have said must be taken for light, must follow in this
the same laws as does movement.” 85
However, Descartes took care not to transgress the conceptual and
methodological boundaries of perspectiva openly. He presented his account
82
Huygens’ case is discussed below in section 4.2.1., Newton in section 5.2.2. of the next chapter. This
theme is leading in Dijksterhuis, “Once Snel breaks down”. Newton’s view is cited below on page 133,
footnote 98.
83
Sabra, Theories, 97-107; Schuster, Descartes, 333-334.
84
Schuster, “Descartes opticien”, 279-285; Schuster, Descartes, 334-336.
85
Descartes, AT6, 88-89. “mais, lors qu’ils rencontrent quelques autres cors, ils sont sujets a estre
détournés par eux, ou amortis, en mesme façon que l’est le mouvement d’une balle, ou d’une pierre iettée
dans l’air, par ceux qu’elle rencontre. Car il est bien aysé a croire que l’action ou inclination a se mouvoir,
que j’ay dit devoir estre prise pour la lumiere, doit suivre en cecy les mesmes loys que le mouvement.”
(Translation based on Olscamp)