The Wave Theory of Light

The following cannot explain the phenomena of diffraction:

• the corpuscular theory
• the principle of interference when applied only to direct rays and to rays reflected or inflected at the very edge of the opaque screen

The proper theory is in the terms of waves. This is based on:

• the principle of Huygens and
• the principle of interference

Both of these are inferences from the fundamental hypothesis that light consists in vibrations of the aether similar to sound-waves.

• This lets us easily account for the inflection of rays of light at sensible distances from the diffracting body.

The rise of a liquid in a capillary tube occurs between 2 surfaces separated by a finite distance. This is even if the attraction which these surfaces exert on the liquid extends only to an infinitely small distance.

This is because the liquid’s molecules are attracted by the surface of the tube. They also in turn attract other liquid molecules situated within their sphere of action, and so on, step by step.

But in the emission-theory, an analogous explanation is not admissible.

This is because the fundamental hypothesis is that the luminous particles never exert any sensible effect on the path of neighboring particles.

No interdependence of motion is here admissible, for such an assumption would be the assumption of a fluid medium.

But when a portion of the wave-front is intercepted or retarded in its path by interposing an opaque or transparent screen, this transverse equilibrium is destroyed.

Various points of the wave may now send out rays along new directions.

It would be difficult to follow, by analytical mechanics, all the changes which a wave-front undergoes when a part of it is intercepted by a screen.

We do not propose to derive the laws of diffraction in this way.

We do not propose to inquire what happens in the immediate neighborhood of the opaque body, where:

• the laws are very complicated
• the edge of the screen must have a perceptible effect on the position and the intensity of the fringes.

We propose rather to compute the relative intensities at different points of the wave-front only after it has gone many wavelengths beyond the screen.

Thus, the positions at which we study the waves are always separated from the screen by a distance which is very considerable compared with the length of a light-wave.

34. Mathematicians have ordinarily considered only a single disturbance vibrating in an elastic fluid.

Single vibrations are never met with in nature. So we shall not focus on single vibrations.

Disturbances occur in groups, as is seen:

• in the pendulum and
• in sounding bodies.

Vibrations of luminous particles occur in the same way – one after another and series after series.

This hypothesis follows from analogy and as an inference from the nature of the forces which hold the particles of a body in equilibrium.

A single luminous particle may perform a large series of oscillations all of which are nearly equal.

• This is because its density is much greater than that of the fluid in which it vibrates.

This is has already been inferred from the uniformity of the motions of the planets through this same fluid which fills planetary space.

The optic nerve yields the sensation of sight only after having received a considerable number of successive stimuli.

However extended the systems of wave-fronts are, they have limits.

Thus, 2 systems of equal wave-length and of equal intensity, differing in path by half a wave, interfere destructively only at those points in the aether where they meet.

• The 2 extreme half wave-lengths escape interference.

Nevertheless, the various systems of waves undergo the same change throughout their entire extent.

The error introduced by this assumption is inappreciable. We assume, of interference, that these series of light-waves represent general vibrations of the ether, and are undefined as to their limits.