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 the wave AC at the moment when the piece C of it has
arrived at B. For there is no other line which like BN is a common
tangent to all the aforesaid circles, except BG below the plane AB;
which line BG would be the propagation of the wave if the movement
could have spread in a medium homogeneous with that which is above the
plane. And if one wishes to see how the wave AC has come successively
to BN, one has only to draw in the same figure the straight lines KO
parallel to BN, and the straight lines KL parallel to AC. Thus one
will see that the straight wave AC has become broken up into all the
OKL parts successively, and that it has become straight again at NB.
Now it is apparent here that the angle of reflexion is made equal to
the angle of incidence. For the triangles ACB, BNA being rectangular
and having the side AB common, and the side CB equal to NA, it follows
that the angles opposite to these sides will be equal, and therefore
also the angles CBA, NAB. But as CB, perpendicular to CA, marks the
direction of the incident ray, so AN, perpendicular to the wave BN,
marks the direction of the reflected ray; hence these rays are equally
inclined to the plane AB.
But in considering the preceding demonstration, one might aver that it
is indeed true that BN is the common tangent of the circular waves in
the plane of this figure, but that these waves, being in truth
spherical, have still an infinitude of similar tangents, namely all
the straight lines which are drawn from the point B in the surface
generated by the straight line BN about the axis BA. It remains,
therefore, to demonstrate that there is no difficulty herein: and by
the same argument one will see why the incident ray and the reflected
ray are always in one and the same plane perpendicular to the
reflecting plane. I say then that the wave AC, being regarded only as
a line, produces no light. For a visible ray of light, however narrow
it may be, has always some width, and consequently it is necessary, in
representing the wave whose progression constitutes the ray, to put
instead of a line AC some plane figure such as the circle HC in the
following figure, by supposing, as we have done, the luminous point to
be infinitely distant. Now it is easy to see, following the preceding
demonstration, that each small piece of this wave HC having arrived at
the plane AB, and there generating each one its particular wave, these
will all have, when C arrives at B, a common plane which will touch
them, namely a circle BN similar to CH; and this will be intersected
at its middle and at right angles by the same plane which likewise
intersects the circle CH and the ellipse AB.
[Illustration]
One sees also that the said spheres of the partial waves cannot have
any common tangent plane other than the circle BN; so that it will be
this plane where there will be more reflected movement than anywhere
else, and which will therefore carry on the light in continuance from
the wave CH.
I have also stated in the preceding demonstration that the movement of
the piece A of the incident wave is not able to communicate itself
beyond the plane AB, or at least not wholly. Whence it is to be
remarked that though the movement of the ethereal matter might
communicate itself partly to that of the reflecting body, this could
in nothing alter the velocity of progression of the waves, on which
the angle of reflexion depends. For a slight percussion ought to
generate waves as rapid as strong percussion in the same matter. This
comes about from the property of bodies which act as springs, of which
we have spoken above; namely that whether compressed little or much
they recoil in equal times. Equally so in every reflexion of the
light, against whatever body it may be, the angles of reflexion and
incidence ought to be equal notwithstanding that the body might be of
such a nature that it takes away a portion of the movement made by the
incident light. And experiment shows that in fact there is no polished
body the reflexion of which does not follow this rule.
But the thing to be above all remarked in our demonstration is that it
does not require that the reflecting surface should be considered as a
uniform plane, as has been supposed by all those who have tried to
explain the effects of reflexion; but only an evenness such as may be
attained by the particles of the matter of the reflecting body being
set near to one another; which particles are larger than those of the
ethereal matter, as will appear by what we shall say in treating of
the transparency and opacity of bodies. For the surface consisting
thus of particles put together, and the ethereal particles being
above, and smaller, it is evident that one could not demonstrate the
equality of the angles of incidence and reflexion by similitude to
that which happens to a ball thrown against a wall, of which writers
have always made use. In our way, on the other hand, the thing is
explained without difficulty. For the smallness of the particles of
quicksilver, for example, being such that one must conceive millions
of them, in the smallest visible surface proposed, arranged like a
heap of grains of sand which has been flattened as much as it is
capable of being, this surface then becomes for our purpose as even
as a polished glass is: and, although it always remains rough with
respect to the particles of the Ether it is evident that the centres
of all the particular spheres of reflexion, of which we have spoken,
are almost in one uniform plane, and that thus the common tangent can
fit to them as perfectly as is requisite for the production of light.
And this alone is requisite, in our method of demonstration, to cause
equality of the said angles without the remainder of the movement
reflected from all parts being able to produce any contrary effect.