Regarding Descartes' Description of the Law of Refraction

  One finds in Descartes' La Dioptrique (1637) a description of the law of refraction with the proportion between the sines of the angles of incidence and those of refraction being the same for all angles of incidence. His discussion is very general and focuses on a ball struck by a tennis racket and bouncing off of the ground for reflection and penetrating it for refraction. For refraction he speculates (see figure on p. 20 in the link above),

 "...In the end, as long as the action of light follows the same laws as the movement of this ball, it must be said that when its rays pass obliquely from one transparent body into another, as the receiption is more or less easier than the first, they turn away in such a manner, that they are all less inclined to the surface of these bodies, from the side where the reception is easier, than that where it's the contrary: and this adjustment is in proportion to that which receives them more easily than the other. But we should take care that this inclination is measured by the quantity of straight lines, such as CB or AH, EB or IG, and the like, compared to each other; not by that of the angles, such as are ABH, or GBI, much less by those similar to DBI, which are called the angles of Refraction. For the ratio or proportion between these angles varies by all the various inclinations of the rays, whereas that which is between the lines AH & IG or the like, remains the same in all the refractions which are caused by the same bodies..."

One can clean this argument up some by assuming a particle of light receives an impulse as it enters a transparent body in the direction of the surface normal altering its trajectory. Let's assume that it is drawn into a denser body increasing its speed in the direction of the normal and so turning it in that direction as is observed.

Before and after the interaction with the surface we find uniform rectilinear motion. The interaction with the surface can be treated as an impulse similar to that of a collision by adding the velocity change to the initial motion.

One finds the proportion between the ratio of the sines is in inverse proportion to the speed as Huygens pointed out. If Δv is positive, the impulse being attractive, the speed increases and the angle of refraction is reduced. If it is negative, as with repulsion, the speed after entering the body will decrease and the angle of refraction increases. One gets a better match with observations if one assumes higher speeds in denser bodies. A complication is that the speed within the body isn't always the same but depends on the angle incidence. Later observations showed that the speed of light decreases in denser bodies.