The wavefront

Imagine a source that generates a disturbance propagating through space: we can define the wavefront as the locus of the points in space that, at a given instant, are reached by the wave disturbance generated by the source at a precise earlier instant. Obviously, considering different instants we obtain different wavefronts. By suitably choosing the instants at which to "photograph" the wavefronts (for example all equally spaced, one period apart) we can obtain a particularly effective description of the wave: the distance between two wavefronts, measured perpendicular to the wavefronts themselves, gives the wavelength.

plane wavefront: the rays are all parallel to each other	curved wavefront: the properties of the medium change from point to point	circular wavefront: the source of the waves is a point at the centre.

Note also that, if the speed of the wave is the same in all directions, the wavefront coincides with the locus of the points equidistant from the source and reached by the wave. In this situation the shape of the wavefront fully reflects any symmetry of the source that generated the wave.

For example

Why talk about a wave ray

You will have noticed that the previous illustrations also contain "arrows" that unambiguously indicate the direction in which the wavefront advances. Apart from their graphical meaning, they could also be interpreted as "rays" emitted by the source: after all, if an observer is hit by a very rapid sequence of wavefronts (for example acoustic or light ones), how can they know that what is acting on them is not instead a swarm of particles whose trajectories are given by those rays?

The two descriptions do not exclude each other unless the system of wavefronts is made to interact with experimental apparatus or, simply, with objects that unambiguously reveal its wave behaviour. In certain physical situations some wave phenomena (above all those concerning light) can be correctly interpreted without resorting to the heavy mathematical formalism of waves and their visualisation in terms of wavefronts. Light seems rather to behave like a set of "rays" perpendicular to the wavefronts.

Think for example of

• the straight-line propagation of a ray of light
• the reflection of a "ray" of light
• the formation of shadows
• a "ray" of light passing through the "slit" of our roller shutter

For all these phenomena (even the great Newton thought so!) it seems natural to imagine light as made of tiny, very fast "corpuscles".

To tell the truth, Newton would have been in serious difficulty describing other light phenomena discovered later.

Think for example of:

• the phenomenon of refraction, that is, the change in direction of light rays when light passes from one medium to another (e.g. air-glass): Newton explained it with corpuscles, but his theory predicted that light would be faster in denser media than in air, the opposite of what Foucault measured in 1850 (in water)
• the phenomenon of destructive interference between light rays that seem to cancel each other (light+light=darkness)
• the phenomenon of diffraction, that is, the fact that in certain experimental situations light rays seem able to go around obstacles

Geometrical optics

When, at the beginning of the nineteenth century (1801-1803), the decisive Young's experiment seemed to show unambiguously that light was a wave, the description of light in terms of "light rays" was kept (because it is simpler) in all those situations in which it appeared consistent with the experimental results. Even today the theory that explains how mirrors and lenses work is taught essentially in terms of the "light rays" hypothesis. The part of optics (that is, of the study of light phenomena) in which light is described by means of "rays" is called geometrical optics.

In which situations does light show its wave nature?

Answering this question obviously means defining the scope of geometrical optics. It has been seen that whenever light is "forced" to interact with physical systems (slits, obstacles, etc.) whose dimensions are comparable to (or smaller than) the wavelength of the light itself, it gives rise to those phenomena (interference, diffraction, etc.) that are the "trademark" of wave behaviour. If we consider that light is an electromagnetic wave with a wavelength ranging from 400 (violet light) to 700 (red light) nanometres, it becomes immediately clear why in ordinary situations light hardly shows its wave nature (even Newton had been deceived!).

What has been said about the appearance of the wave nature of light obviously applies to every type of wave. Many phenomena were immediately labelled as wave phenomena because the wave that describes them has wavelengths comparable to the dimensions of the objects it interacts with (think of sea waves, or of sound)

Links and further reading

• For a concrete visualisation of how the wave nature shows itself, we suggest visiting the app on the page virtual waves laboratory. Many guided experiments are proposed in detail on the page 2D Waves app paths
• For the application and the limits of the theory of wave rays in explaining the phenomenon of the rainbow, see the page waves and rainbows
• By a sort of irony of history, the corpuscular theory of light (albeit with a more refined interpretation of the corpuscles) was revived in 1905 by Albert Einstein to explain the experimental results of the photoelectric effect.
• To fully grasp the importance of the description in terms of wavefronts, visit the section Huygens' principle
• For a review of sources of sound waves see the page power of a sound source