Our analysis of the superposition of waves from distinct sources, such as two loudspeakers or the two slits in a double-slit experiment, has tacitly assumed that the sources are point sources, with no measurable extent. To understand diffraction, we need to think about the propagation of an extended wave front. This is a problem first considered by the Dutch scientist Christiaan Huygens, a contemporary of Newton.

Huygens lived before a mathematical theory of waves had been developed, so he developed a geometrical model of wave propagation. His idea, which we now call Huygens’ principle, has two steps:

1. Each point on a wave front is the source of a spherical wavelet that spreads out at the wave speed.

2. At a later time, the shape of the wave front is the line tangent to all the wavelets.

FIGURE 33.12 illustrates Huygens’ principle for a plane wave and a spherical wave. The line tangent to the wavelets of a plane wave is a plane that has propagated to the right. The line tangent to the wavelets of a spherical wave is a larger sphere.

FIGURE 33.12 Huygens’ principle applied to the propagation of plane waves and spherical waves.

FIGURE 33.12 Full Alternative Text

Huygens’ principle is a visual device, not a theory of waves. Nonetheless, the full mathematical theory of waves, as it developed in the 19th century, justifies Huygens’ basic idea, although it is beyond the scope of this textbook to prove it.