What is diffraction?

When a wave meets an obstacle in its path, or is forced to pass through a small slit, under certain physical conditions that we shall investigate it behaves in a peculiar way: it (and with it the energy it carries) can also reach points that would be unreachable if propagation took place along straight wave rays. It is as if the wave "broke" (hence the name of the phenomenon, from the Latin "diffractus", past participle of de-frangere, first coined by F.M. Grimaldi in 1665) and then recombined, spreading out, beyond the obstacle or the slit. Like interference and polarisation, diffraction is a "trademark" of wave behaviour, and therefore unmistakably reveals the wave nature of whatever produces it (light, sound, water waves, etc.). Diffraction therefore cannot be explained within geometrical optics, but requires a "wave" treatment. At a more qualitative level, Huygens' principle alone can explain the phenomenon, while a more quantitative treatment requires the theory of interference.

Diffraction by an obstacle

What happens if a wave meets an obstacle whose transverse dimensions (that is, perpendicular to the direction of propagation of the wave) become comparable to (or smaller than) the wavelength of the incident wave? To try it out, we invite you to visit our 2D Waves virtual laboratory. Below we suggest a series of guided experiments, but you are free to try out new configurations and new experiments. The app is very intuitive; to understand correctly what you observe, just keep in mind that the coloured areas represent the amplitude of the oscillation. The brighter the colour, the larger the amplitude of the oscillations (green for crests, red for troughs).

• Diffraction by a half-plane
• Diffraction by an obstacle

The experiments leave little doubt: when the size of the obstacle is smaller than the wavelength of the incident wave, the wave carries on almost undisturbed, as if it had not "seen" the object! One might well say: "How can a rock hold back the sea?" Huygens' principle explains the situation perfectly, while the Newtonian corpuscular explanation, which uses straight wave rays (and would always predict the formation of shadow regions beyond the obstacle), is in serious difficulty.

The following table lists the typical wavelengths of some waves and the characteristic sizes of some obstacles.

For example

The diffraction condition is of course relative: waves that are diffracted by certain obstacles do not do so if their wavelength is much smaller than the size of the obstacle!!

Try using the table to answer the first two questions in the section Check your understanding.

Finally, it is worth stressing that when the diffraction conditions are not met (that is, when the size of the obstacle is much larger than the wavelength of the incident wave) we get a well-known phenomenon: the wave cannot get around the obstacle, so a "shadow region" not reached by the energy carried by the wave forms beyond the obstacle. For example, sound waves easily get around a person, but the person casts a shadow when struck by visible light (whose wavelength is much smaller than the typical size of a person). This is why Newton wrongly considered light to be made of corpuscles: in ordinary conditions the conditions for the diffraction of light are certainly not met! Sound waves are stopped by a large wall (a few tens of metres), which the longest radio waves, however, easily get around, such as those of medium-wave and long-wave broadcasting (wavelengths of hundreds of metres or more).

Diffraction by an aperture in a screen

A second type of diffraction, complementary so to speak to the previous one, occurs when the obstacle is huge (compared with the wavelength) but contains a small slit that lets the wave through. To visualise the situation, visit the 2D Waves virtual laboratory and try the experiment described on the page A wave passing through a single slit.

This "sensible experience" seems designed on purpose to highlight the secondary spherical waves predicted by Huygens' principle, and to embarrass the corpuscular interpretation, which would predict, beyond the slit, a wave as wide as the slit itself. The narrower the slit compared with the wavelength, the more the wave spreads out after passing through it: the opening angle of the beam is of the order of the ratio ${\displaystyle \lambda /a}$ between the wavelength and the width a of the slit. If the slit is much wider than the wavelength the spreading is negligible and the wave carries on as a beam of straight rays. Huygens was probably led to formulate his principle partly by observing plane waves on a body of water forced to pass through a small slit (smaller than the wavelength of the waves). Extending his principle to light certainly required more "courage": after all, if we watch light passing through the holes of our window shutter, we see a sharp bright area that reproduces exactly the size and shape of the hole in the shutter. Why does light not seem to be diffracted in this case? We certainly have no intention of telling you: if you have understood the explanations above, the answer will seem obvious!!

Check your understanding

Further reading and links

To find out more about the diffraction of sound waves, visit the dedicated section

• Related questions and answers:
  • Can sound be focused with a "zone plate", as is done with light?