15.2 Huygens' Principle

15.2 Huygens' Principle

This principle, stated originally by the Dutch Scientist Christiaan Huygens, is a geometrical method for finding, from the known shape of a wavefront at some instant, the shape of the wavefront at some later time. Huygens assumed that every point of a wavefront may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave.

The new wavefront at a later time is then found by constructing a surface tangent to the secondary wavelets or, as it is called, the envelope of the wavelets.

Fig. 15.2 illustrates Huygens's principle. The original wave front AB is traveling outward from a source, as indicated by the arrows. We want to find the shape of the wave front after a time interval $t$. We assume that $v$, the speed of propagation of the wave, is the same at all points. Then in time $t$ the wavefront travels a distance $vt$. We construct several circles (traces of spherical wavelets) with radius $vt$, centered at points along AB. The trace of the envelope of these wavelets, which is the new wavefront, is the curve CD.

All the results that we obtain from Huygens's Principle can also be obtained from Maxwell's equations, but Huygens's simple model is easier to use.

(Fig. 15.2: Formation of new Wavefront from a previous wavefront)