Reflection and Refraction

²¹ A specimen of this can be found in Reflection and Refraction.

It is in the mouths of all that the angle of incidence and the angle of reflection are equal, and experiments—both phoronomic (kinematic) and optical—favor this.

The very concise and beautiful appearance of the theorem charms one, which has imposed upon even the greatest men, persuading them that the proposition could be demonstrated universally from the abstract nature of motion.

I too believed this until I applied severe inquiry – I noticed that all that work was a game.

I examined the demonstrations of Digby, Descartes, and Hobbes.

I found that the sweetness of the opinion had more value to them than the rigor of the demonstration.

My theory is sufficiently confirmed by the senses.

• Therefore, it should be referred to observations rather than to theorems.

The reason for this constancy, if not from the abstract theory of motion, must at least be rendered from the Hypothesis of Concrete Motion, or the Economy of Present Things.

It was in the interest of the world that the matter be so established: for without this law of reflection, sight and hearing could not exist.

This equality of angles arises from the fact that, although it appears so, the motion of those impinging is not straight.

They continue into a circle or an ellipse in the other part. Consequently, it happens that the Angle of Reflection and Incidence are equal, because each is an angle of contact of one and the same arc on both sides. See the abstract theory of motion, th. 8.9.

If the impact is perpendicular to the sense, the two arcs of impact and repercussion are joined so acutely to each other that the line appears to the sense to be the same.

This cannot be refuted by any experiments, because most motions that appear straight are in reality curved, but so insensibly that all phenomena occur just as if they were truly straight.

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…But there is yet another more frequent reason, and one more congruent with the economy of things, for explaining the equality of the angle of incidence and reflection universally.

To be sure, that which is commonly assumed absolutely of all bodies—that one impinging upon another is struck back or refracted—is only true of Elastic bodies, or those that restore themselves after compression or dilation.

But all sensible bodies are Elastic due to the circulation of the aether.

Therefore, all sensible bodies reflect or refract.

No body considered by itself, unless it were animated by the perpetual ventilation of the aether, would reflect or refract, at least according to these laws commonly reported.

If a body in motion strikes one at rest, it will penetrate it entirely without any refraction, even if the impinging body were the size of a grain of sand and the receiving body were a thousand leagues in thickness.

If both the receiver and the impinging body move, and the blow is directed into the center of motion, and in that same line, the stronger will overcome the slower, or if they are equal, rest will follow.

If the impact is eccentric, a new motion around its own center will be added to the prior motion.

If they concur in different lines, or make an angle with equally swift motion, both will move along the line bisecting the angle, or, if it is not bisectable, they will rest; all of which pertains to demonstrating according to the abstract theory of motion.

But the face of sensible bodies is plainly another thing.

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For all hard things are so by a certain internal motion returning into themselves.

All things are discontinuous, whence other things being equal, mass effects more; all things are Elastic, or compressed, and soon being left to themselves, they are restored to their prior state by the gyration of the aether.

A person who confuses these laws of apparent motion with the rules of the true [abstract] motion is similar to one who makes no difference between mechanical and geometrical demonstrations.

How do the laws of reflection and refraction follow from the Elasticity (Elatere) of sensible things?

As far as reflection is concerned: if a hard body, or one restoring itself, strikes another hard body which it cannot penetrate, it will nevertheless compress it according to the line in which it falls, continued into the receiving body itself.

The receiving body, however, will immediately react along that line in which it best can: in a perpendicular impact, it can do so no other way than that in which the impact was made.

Consequently, the impinging body will return by the way it came.

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But in an oblique impact, it will react from that region in which the thing is still whole, or in which compression has not yet been made, into which therefore the other compressed parts attempt to recover themselves—that is, the line opposite to the line of impact makes a divarication.

Therefore, with the same angle to the surface, but into the other region.

This reaction is so much stronger as the impact was swifter, all other things being equal (for the speed of the restoring part is as great as that of the compressing part).

Likewise, it is stronger as the impinging and receiving bodies are harder (because the vibration is so much more violent, like bows suddenly released).

If both are hard, not only is the impinging body repelled by the receiver, but also from itself; just as we, by repelling the earth with our feet, make a leap.

Therefore, with the concurrence of both being so strong, and with a vibration reciprocated several times like that of strings, the air between both—being intercepted no less than the internal air of any body—is compressed and then scattered again, producing a sound so strong and varied.

With all things being restored as much as possible to their prior state by the gyration of the aether, it is no wonder that such a vehement reflection follows.

I hope that such a physical reason for reflection has now finally been rendered.

The matter deserves a delineation, but it is foreign to this [brief] sketch, though it will not be lacking in its own time[cite: 1, 2].

Refraction is a certain mixed penetration of reflection.

Whence it is partly transmission and partly deflection.

It approaches or departs from obliquity only as much as the resistance or density of the medium allows.

This is because among sensible bodies, almost only the aether truly moves by itself, and it is the “first mover” (primum dektikon), while other things move through it[cite: 1, 2].

Hence it happens that no impediment can be objectified to motion without it being propagated, for all pores are pervasive to the aether, and it is always animated by weary new supplements.

Hence it also happens that even if, through the abstract theory of motion, every reaction detracts from speed, nevertheless, on the contrary, in sensible bodies, speed is preserved (unless insofar as it usually becomes more insensible by dispersing into many parts).

It detracts from the region or determination, which is the Law of Refraction.

An inflated bladder struck against the floor leaps up so high by a certain elasticity (Elatere) of the compressed air, which attempts to restore itself.

What, then, forbids us from believing that other hard things, when struck against hard things—since they are everywhere full of thick, enclosed air, and full of air compressed by impact—effect a repercussion by a very swift and strong reciprocation, like sounding strings?

(This even lasts for some time, which is why the duration of sounds and vibrations in struck bells is quite long)[cite: 1, 2].

This can be transferred to other phenomena of motions and concurrences, and applied to things with much light.