CHAPTER II

ON REFLEXION

Having explained the effects of waves of light which spread in a homogeneous matter, we will examine next that which happens to them on encountering other bodies.  We will first make evident how the Reflexion of light is explained by these same waves, and why it preserves equality of angles.

Let there be a surface ab; plane and polished, of some metal, glass, or other body, which at first I will consider as perfectly uniform (reserving to myself to deal at the end of this demonstration with the inequalities from which it cannot be exempt), and let a line AC, inclined to ad, represent a portion of a wave of light, the centre of which is so distant that this portion AC may be considered as a straight line; for I consider all this as in one plane, imagining to myself that the plane in which this figure is, cuts the sphere of the wave through its centre and intersects the plane ab at right angles.  This explanation will suffice once for all.

[Illustration]

The piece C of the wave AC, will in a certain space of time advance as far as the plane ab at B, following the straight line CB, which may be supposed to come from the luminous centre, and which in consequence is perpendicular to AC.  Now in this same space of time the portion A of the same wave, which has been hindered from communicating its movement beyond the plane ab, or at least partly so, ought to have continued its movement in the matter which is above this plane, and this along a distance equal to CB, making its own partial spherical wave, according to what has been said above.  Which wave is here represented by the circumference SNR, the centre of which is A, and its semi-diameter an equal to CB.

If one considers further the other pieces H of the wave AC, it appears that they will not only have reached the surface ab by straight lines HK parallel to CB, but that in addition they will have generated in the transparent air, from the centres K, K, K, particular spherical waves, represented here by circumferences the semi-diameters of which are equal to km, that is to say to the continuations of HK as far as the line BG parallel to AC.  But all these circumferences have as a common tangent the straight line BN, namely the same which is drawn from B as a tangent to the first of the circles, of which A is the centre, and an the semi-diameter equal to bc, as is easy to see.

It is then the line BN (comprised between B and the point N where the perpendicular from the point A falls) which is as it were formed by all these circumferences, and which terminates the movement which is made by the reflexion of the wave AC; and it is also the place where the movement occurs in much greater quantity than anywhere else.  Wherefore, according to that which has been explained, BN is the propagation of