Our discussion of interference in the previous chapter considered the superposition of two waves. The discussion can be generalized to a situation where there are three or even more waves. Diffraction is essentially the same as interference, except that we have a superposition of a very large number of waves. In some situations the number is infinite. An obstruction placed along the path of a wave (Figure 12), is an example of a situation where diffraction occurs. In simple terms the deviation of light rays from straight path due to some obstacle is known as diffraction. In the case of diffraction the longer wavelengths deviate more compared to the shorter wavelengths, whereas in refraction the shorter wavelengths deviate more compare to the longer ones. In the case of diffraction it is necessary to solve the equation governing the wave in the complicated geometry produced by the obstruction. This is usually very complicated, and beyond analytic treatment in most situations. The Huygens-Fresnel principle is a heuristic approach which allows such problems to be handled with relative ease.
Huygens' principle, proposed around 1680, states that every point on a wavefront acts as the source for secondary spherical wavelets such that the wavefront at a later time is the envelope of these wavelets. Further, the frequency and propagation speed of the wavelets is the same as that of the wave. Applying Huygens' principle to the propagation of a plane wave, we see that a plane wave front evolves into a shifted plane wave at a later time (Figure 12.2). We also show how it can be applied to the propagation of a spherical wavefront. It is also useful for studying the propagation of waves through a refracting medium where the light speed changes with position and is also different in different directions.
Huygens' principle, in its original form cannot be used to explain interference or diffraction. It was modified in the early 19th century by Fresnel to explain diffraction. The modified version is referred to as the Huygens-Fresnel principle. Kirchoff later showed that the Huygens-Fresnel principle is actually consistent with the wave equation that governs the propagation of light.
The Huygens-Fresnel principle states that every unobstructed point on the wavefront acts like a source for a secondary wavelet. The contribution from all these wavelets are to be superposed to find the resultant at any point.
