Lenses and Waves

128 CHAPTER 4
Refraction in La Dioptrique
Descartes began La Dioptrique with an explication of the way rays of light
enter the eye and are deflected on their way to it. He did not intend to
explain the true nature of light, he said, as the essay ought to be intelligible to
the common reader. He took the liberty, he said, to employ a threesome of
comparisons between the behavior of light and everyday phenomena:
“…; imitating in this the Astronomers, who, although their assumptions are almost all
false or uncertain, nevertheless, because these assumptions refer to different
observations they have made, do not fail to draw many true and well-assured
conclusions from them.” 76
First, light acts like the white stick that enables a blind man to sense objects;
it is an action instantaneously propagated through a medium without matter
being transported. Second, this action is like the tendency of a portion of
wine in a barrel of half-pressed grapes to move to a hole in the bottom. It
works along straight lines that can cross each other without hindrance. In
other words, light is not a motion but a tendency to motion:
“And in the same way, considering that it is not so much the movement as the action
of luminous bodies that must be taken for their light, you must judge that the rays of
this light are nothing else but the lines along which this action tends.” 77
Although essentially light is a tendency to movement rather than actual
motion, with respect to the deflections from its straight path rays of light
follow the laws of motion, Descartes maintained. So, in the third
comparison, the way light interacts with mediums of different nature is
compared to the deflections of a moving ball encountering hard or liquid
bodies. Thus the three comparisons of the first discourse of La Dioptrique
established a qualitative basis for the mathematical account of refraction in
the next.
The second discourse ‘Of refraction’ opens with an account of reflection
providing the conceptual basis for Descartes’ explanation of the ‘way in
which refractions ought to be measured’. 78 It introduces a crucial distinction
with regard to the powers governing the motion of an object: one that works
to continue the ball’s motion and one that determines the particular direction
in which the ball moves. 79 Instead of the more accurate ‘absolute quantity of
force of motion’ and ‘directional quantity of force of motion’, for sake of
convenience I will speak of ‘quantity’ and ‘direction’ both of which may
76 Descartes, AT6, 83. “imitant en cecy les Astronomes, qui, bien que leurs suppositions soyent presque
toutes fausses ou incertaines, toutefois, a cause qu’elles se rapportent a diverses observations qu’ils ont
faites, ne laissent pas d’en tirer plusieurs consequences tres vrayes & tres assurées.” (Translation based on
Olscamp)
77 Descartes, AT6, 88. “& ainsy, pensant que ce n’est pas tant le mouvement, comme l’action des cors
lumineus qu’il faut prendre pour leur lumiere, vous devés iuger que les rayons de cete lumiere ne sont
autre chose, que les lignes suivant lesquelles tend cete action.” (Translation based on Olscamp)
78 “… en quelle sorte se doivent mesurer les refractions”, AT6, 101-102.
79 “Seulement faut il remarquer, que la puissance, telle qu’elle soit, qui fait continuer le mouvement de cete
balle, est differente de celle que la determine a se mouvoir plustost vers un costé que vers un autre, …”
AT6, 94.