The procedures of proof in optics, just as in all other sciences in which geometry is applied to matter, are based on truths derived from experience; e.g., the fact that light rays are propagated in straight lines, that the angle of reflection is equal to the angle of incidence, and that refraction obeys the sine rule, so well-known today and no less certain than the others.
The majority of those who have written on the different parts of optics have been content to take these truths for granted. Some of the more enquiring strove to discover their origins and causes, seeing that they considered them as inherently wonderful effects of nature. Since, however, the opinions offered, although ingenious, are not such that more intelligent people would need no further explanations of a more satisfying nature, I wish here to present my thoughts on the subject so that, to the best of my ability, I might contribute to a solution of that part of science which, not without reason, is considered to be one of the most difficult. I acknowledge my great indebtedness to those who were the first to start dispelling the strange gloom surrounding these things, and who aroused the hope that they might yet be explained rationally. But, on the other hand, I am not a little surprised to find that very often they considered as most certain and proven, conclusions that were only too flimsy; for to my certain knowledge no one has as yet offered a satisfactory explanation of even the first and most important phenomenon of light, viz., why it is propagated precisely in straight lines, and how light rays arriving from infinitely varied directions cross without impeding one another.
In this book I shall therefore attempt, according to the principles held in contemporary philosophy, to give clearer and more probable reasons for the properties, first of the rectilinear propagation of light, and second of the reflection of light when it encounters other bodies. Then I shall explain those phenomena of the rays, which in traversing different kinds of transparent bodies undergo so-called refraction; and in this I shall also treat of the effects of refraction in the air arising out of differences in the density of the atmosphere.
I shall continue by investigating the strange refraction of light of a particular crystal brought from Iceland. Finally I shall treat of the different forms of transparent and reflecting bodies, by means of which the rays are either made to converge on one point, or else are deviated in most different ways. In this it will be seen with what ease our new theory will lead to the discovery not only of ellipses, hyperbolae and other curves, which Descartes had ingeniously suggested for this effect, but also of those figures which form one surface of a glass, when the other surface is known to be spherical, plane, or of any other shape. ...
Since, now, according to this philosophy, it is held as certain that the sense of vision is only stimulated by the impression of a certain motion of a material acting on the nerves at the back of our eyes, this is a further reason for believing that light consists of a motion of the matter between us and the luminous body. If, furthermore, we pay attention to, and weigh up, the extraordinary speed with which light spreads in all directions, and also the fact that coming, as it does, from quite different, indeed from opposite, directions, the rays interpenetrate without impeding one another, then we may well understand that whenever we see a luminous object, this cannot be due to the transmission of matter which reaches us from the object, as for instance a projectile or an arrow flies through the air, for this is too great a contradiction of the two properties of light, and the second in particular. Thus it must spread in a different way, and precisely our knowledge of the propagation of sound in air can lead us to an understanding of this way.
We know, that by means of air, which is an invisible and impalpable body, sound spreads through the whole of space surrounding its source by a motion which advances gradually from one air particle to the next, and since the propagation of this motion takes place with equal speed in all directions, spherical surfaces must be formed that spread out further and further, finally to reach our ears. Now it is beyond doubt that light also reaches us from luminous bodies by means of some motion which is imparted to the intermediate matter, for we have already seen that this could not have happened by means of the translation of a body that might have reached us from there. If now, as we shall soon investigate, light needs time for its path, it follows that this motion imparted to matter must be gradual, and that, like sound, it must spread in spherical surfaces or waves; I call them waves because of their similarity to those which we see being formed in the water when a stone is thrown into it, and because they enable us to observe a like gradual spreading-out in circles, although they are due to a different cause and only form in a plane surface. ...
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