Christiaan Huygens Explains How Light Waves Advance

This is my third post on the Traité de la lumière [Treatise on Light¹], published in 1690 by Christiaan Huygens (1629-1695). The previous posts were:

• Christiaan Huygens Proposes an Infinite Series of Levels to the Universe

• Christiaan Huygens Presents Ole Rømer's Proof that the Speed of Light is Finite

In this post, I will show how Huygens presents the theory that light is transmitted as a wave through a sea of aether particles. Here is a quick summary:

If, in addition, light takes time for its passage—which we are now going to examine—it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as Sound does, by spherical surfaces and waves : for I call them waves from their resemblance to those which are seen to be formed in water when a stone is thrown into it, and which present a successive spreading as circles, though these arise from another cause, and are only in a flat surface. [p.4]

The wave theory of light proposed by Huygens depends on his previous work on the collision of bodies. This work was published posthumously in 1703 as De motu corporum ex percussione² [The Motion of Colliding Bodies], although most of the propositions therein were ready in 1656.

Huygens supposed that at any given level, the aether is made up of more-or-less spherical particles of similar size, and that they are sufficiently close together that if one moves, it will collide with neighboring particles. His idea is that a light wave passes through a sea of aether particles through the movement of successive particles.

He first begins by examining sources of light, and considers the flame of a candle. At any given moment, every point of the flame is a source of light, hence the source of a light wave, as can be seen in the following diagram.

He explains:

But we must consider still more particularly the origin of these waves, and the manner in which they spread. And, first, it follows from what has been said on the production of Light, that each little region of a luminous body, such as the Sun, a candle, or a burning coal, generates its own waves of which that region is the centre. Thus in the flame of a candle, having distinguished the points A, B, C, concentric circles described about each of these points represent the waves which come from them. And one must imagine the same about every point of the surface and of the part within the flame. [pp.16-17]

From each point, examples here being A, B and C, a circular light wave propagates outwards. From a given point, assuming there continues to be a source of light at that point, successive light waves form concentric circles with that point as center. This holds true for all points in the flame, and these waves overlap each other. And, of course, it should not be forgotten that notwithstanding the use of the word ‘circular’, Huygens considers light waves to be spherical, as was expressed in the first quotation of this post.

Huygens then moves on to the propagation of a light wave from a given point, using the following diagram. If a wave propagates from that point, then every point in which that wave propagates to will in turn propagate its own wave.

He explains:

There is the further consideration in the emanation of these waves, that each particle of matter in which a wave spreads, ought not to communicate its motion only to the next particle which is in the straight line drawn from the luminous point, but that it also imparts some of it necessarily to all the others which touch it and which oppose themselves to its movement. So it arises that around each particle there is made a wave of which that particle is the centre. Thus if DCF is a wave emanating from the luminous point A, which is its centre, the particle B, one of those comprised within the sphere DCF, will have made its particular or partial wave KCL, which will touch the wave DCF at C at the same moment that the principal wave emanating from the point A has arrived at DCF; and it is clear that it will be only the region C of the wave KCL which will touch the wave DCF, to wit, that which is in the straight line drawn through AB. Similarly the other particles of the sphere DCF, such as bb, dd, etc., will each make its own wave. But each of these waves can be infinitely feeble only as compared with the wave DCF, to the composition of which all the others contribute by the part of their surface which is most distant from the centre A. [p.19]

What Huygens is stating is that if a light wave starting in, say, point A, passes through, say, particle B, then the movement of B will itself set off a lesser wave around itself. So, supposing the main wave to have reached the arc DCEF, a smaller wave emanating from B will reach the arc KCL, intersecting the main wave exactly at point C, with a straight line passing through A, B and C.

Huygens continues by focusing on the reach of a light wave over time.

One sees, in addition, that the wave DCF is determined by the distance attained in a certain space of time by the movement which started from the point A; there being no movement beyond this wave, though there will be in the space which it encloses, namely in parts of the particular waves, those parts which do not touch the sphere DCF. [p.20]

At a given moment, only those particles between the source of light and the current reach of the light wave will have moved. Furthermore, the wave moves out in straight lines from the source of light.

And hence one sees the reason why light, at least if its rays are not reflected or broken, spreads only by straight lines, so that it illuminates no object except when the path from its source to that object is open along such lines. For if, for example, there were an opening BG, limited by opaque bodies BH, GI, the wave of light which issues from the point A will always be terminated by the straight lines AC, AE, as has just been shown; the parts of the partial waves which spread outside the space ACE being too feeble to produce light there. [p.21]

Should the light be blocked, say here by opaque bodies BH and GI, then the light will not bend around those bodies. This means that a straight line can be drawn between every point in the current wavefront and the source of light. In fact, no matter how small the opening BG will be made, a straight line can still be drawn back to the source A. So rays of light can be considered to be straight lines.

Now, however small we make the opening BG, there is always the same reason causing the light there to pass between straight lines; since this opening is always large enough to contain a great number of particles of the ethereal matter, which are of an inconceivable smallness; so that it appears that each little portion of the wave necessarily advances following the straight line which comes from the luminous point. Thus then we may take the rays of light as if they were straight lines. [p.21]

Finally, Huygens explains why he posits that the particles should be of similar size.

It appears, moreover, by what has been remarked touching the feebleness of the particular waves, that it is not needful that all the particles of the Ether should be equal amongst themselves, though equality is more apt for the propagation of the movement. For it is true that inequality will cause a particle by pushing against another larger one to strive to recoil with a part of its movement; but it will thereby merely generate backwards towards the luminous point some partial waves incapable of causing light, and not a wave compounded of many as CE was. [p.21]

Huygens’s explanation of the propagation of light waves, based on the supposition of aether particles of similar size, is easy to follow. Now that we understand these basic principles, we can follow his explanations of reflection and refraction.

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1. Christiaan Huygens. Treatise on Light. In which are explained the causes of that which occurs in Reflexion, & in Refraction. And particularly in the strange Refraction of Iceland Crystal. Rendered into English By Silvanus P. Thompson. New York: Dover, 1962. First published by Macmillan and Company, Limited, in 1912.

2. Christiaan Huygens. De motu corporum ex percussione. In Œuvres, Tome seizième, La Haye: Martinus Nijhoff, 1929, pp.8-168.