The Huygens–Fresnel principle

Most phenomena that may occur during the propagation waves, such as reflexion, refraction or diffraction, can be explained in terms of the Huygens–Fresnel principle. This principle states that each point of an advancing wave front is the centre of a new disturbance and the source of a new train of waves and the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium that the wave has already passed.

Using the Huygens–Fresnel principle to explain diffraction

Arne Nordmann (CC BY-SA)

Let us apply the Huygens–Fresnel principle to explain diffraction. Before the obstacle, the wave fronts (that is, the collections of points in a wave that are in the same phase at a given time, such as crests or troughs) are lines (assuming, for simplicity, that we have two-dimensional waves, such as ripples on the surface of water), since each point in the preceding wave front has emitted identical circular waves in sync and the superposition of these will result in a straight wave front (see the figure). This is only true in the strict sense if the wave front extends to infinity in both directions.

After the obstacle, this condition is no longer met. Only a small part of the wave front passing through the slit will continue to emit secondary waves (indicated as yellow dots in the figure) — the rest are blocked by the obstacle. The circular waves emitted by the secondary sources at the fringes will no longer be flattened by superposition with the waves emitted by their neighbours as they no longer have any neighbours. As a result, the wave emerging from the slit will bend at the fringes.

Using the Huygens–Fresnel principle to explain refraction

Arne Nordmann (CC BY-SA)

Using a similar logic, one can also account for refraction on the grounds of the Huygens–Fresnel principle. In the case shown in the figure, a wave enters a new medium where its speed of propagation is less than in the old medium. As we explained above, the wave fronts will be straight as theoretically an infinite number of circular waves in sync will superpose.

The left edge of the wave front will reach the boundary first. From then on, the secondary waves emanating from there (the leftmost yellow dot in the figure) will remain circular waves, but their wavelength will be reduced — the frequency stays the same and the speed of propagation is less. This means that the circular wave fronts of the secondary waves will be more closely packed. If we draw up the resultant wave fronts (for instance, using a compass), they will continue to be straight lines, but their direction of propagation will change.