Huygens Principle

Christiaan Huygens (1690): Every point on a primary wavefront serves as a source

of secondary spherical wavelets, such that the primary wavefront at some later time is the envelope of these wavelets. Moreover, the wavelets advance with a speed and frequency equal to those of the primary wave at each point in space.

What does this imply?

Every point on a wavefront acts as a point source

reradiating the energy in all directions.

Fresnel (19th Century) Super position of the secondary waves must take into

account the amplitude and the phase of the wavelets.

This is necessary when considering barriers encountered by the wavefront. Some wavelets will be blocked and the sum of the remainder describes the resulting wavefront.

Obliquity factor

As you can see from the previous diagram using Huygens + Fresnel we should see a backward going

wave. An Obliquity factor is added )cos1()( 21 +=K

where is the normal to the wavefront that suppresses

the backward going waves. The combined theory, including the obliquity factor

added by Fresnel, is called the Huygens Fresnel principle.

All properties of wave propagation can be calculated from the above, including reflections, refraction and diffraction. See Hecht Section 4.2.2 for a derivation of Snells law using Huygens Principle.