HUYGENS' PRINCIPLE

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Introduction	Doppler effect with light Light and colour 2-D and 3-D wavefronts Wave nature of matter	Data Glossary
Learning Outcomes
After studying this section, you will be understand Huygens' Principle.

Introduction:

The Dutch physicist, astronomer and mathematician Christiaan Huygens was a leading proponent of the wave theory of light. He developed a principle, actually a geometrical construction (), that became very useful in calculating the propagation of a wavefront. In this way, reflection, refraction, interference and diffraction could be treated geometrically.

While Huygens' Principle is applicable to all wave motion, it is of special importance in geometrical optics.

Imagine a wave spreading out in a circle, proceeding from a primary point source. (A small stone dropped into a pond is a good example), depicted in the above diagram on the left. A circle drawn around the source can be drawn, and any point on the circumference of that circle can then be considered as a new, secondary source, now shown above, middle (only some circles are shown). The envelope of all these circles, or wavelets, constitute a new, secondary wavefront. Again, new circles may be drawn, and a new wavefront constructed as before (above, right).

Point sources will produce circular wavefronts. As new wavefronts are generated, segments will approximate to straight lines, all the more if the circular wavefront has a large diameter. Straight wavefronts may be produced by straight vibrations, as one might find in a ripple tank. The following should be noted:

One must assume that the amplitude of the wavelets is zero in the backward direction, to correspond to the physical reality that no wavefront generates another wavefront in a direction opposite to the direction of travel of the wave. Thus, the wavelets should be drawn as semicircles. The position of a secondary wavefront at a time Δt is vΔt where v is the velocity of the wave. The radius of the wavelets are therefore vΔt. Line drawn perpendicular to the wavefront represent "light rays", and indicate the direction of travel of the wave.