The huygens-fresnel principle

The huygens-fresnel principle

In order to proceed with the discussion we have to define two terms. A wave front is the surface of constant phase. In a plane wave these are planes andin a spherical wave these are spheres. A ray travels perpendicular to the fronts.

Huygens postulated that as a wave propagates through a medium each point on the advancing wavefront acts as a new point source of the wave. This iscorrect physics for the water waves but not for light waves. However the Helmholtz equation for diffraction of EM waves gives a solution identical tothat give by Huygens' principle.

Look at the figure which shows a wavefront AB coming to a surface and is reflected creating the front CD. The point A hits the surface first. The pointB hits a time $vt$ later. During that time a spherical wave is emitted from A and travels a distance $vt$ . In fact this happens for every point along the wavefront. The next figureattempts to show how a number of waves line up along the line DC and that this is perpendicular to the line AD.

From this we see that $$\sin {\theta }_i=\frac{vt}{AC}$$ and $$\sin {\theta }_r=\frac{vt}{AC}$$ so ${\theta }_i={\theta }_r$

For refraction a similar thing happens. See figure (geometric optics / Huygens refraction.vsd )