Waves-Matter Interactions: Spherical waves, plane waves and Huygens's Principle.

  Unlike the previous section where we looked at how waves interact with each other to form new waves, in the following pages we will look at what happens when waves encounter different objects and materials. We will find that how waves interact with themselves is still critical to understanding how waves interact with matter. Wave interference forms the basis of wave-matter interactions such as reflection, refraction, and diffraction.

  Before we start discussing wave-matter interactions, it's important to understand in more detail how waves are formed and how they travel. There are two basic types of waves: spherical and plane waves. A spherical wave is generated by a point-like source, with the spherical wavefronts (connected parts of the wave which all share the same displacment, such as crests on a water wave) spreading radially outward from the point source. The wavefronts in plane waves form parallel planes that are all traveling in the same direction, perpendicular to the planes' surfaces. Spherical waves and plane waves are shown in the cartoon below:

In the case above the gray wavefront lines indicate the crests (displacement maxima) os the waves, with the troughs (displacement minima) occuring halfway between the crests. Notice that if one is very far from the point source generating spherical waves and if one looks at only a small area of the wavefront, spherical waves begin to look like plane waves.

  In this section we will mainly deal with plane waves interacting with matter, so we will begin with a simple model for producing plane waves using a series of point sources.

What is the Huygens's Principle? How does Huygens's Principle apply to wave propagation?

The Dutch physicist, Christian Huygens ( 1629 - 1695 ) contributed greatly to study of waves in the 17th century. Being a proponent of the wave theory of light he explained how waves travel by producing vibrating wavelets that result in new "wavefronts" being produced. This theory is called Huygens's Principle and it explains the propagation of waves in any medium. Waves propagate, or regenerate themselves by producing many vibrating wavelets along the surface of a wavefront. This principle can be used to explain the shape of the wavefront produced by vibrating wavelets.

Huygens used the idea of vibrating point wavelets, which produce spherical waves that travel from each point outward. These waves reinforce one-another when they overlap exactly one wavelength later. What determines the shape of a wavefront is the shape of the locus of points that these wavelets possess. He used this idea to explain the reflection and refraction of light waves. In the simulations below notice how the number of vibrating wavelets effects the shape of the wavefront produced.

Experiment with this simulation to develop a more thorough understanding of Huygens's Principle and how it explains the propagation of waves. Start with a single source that is producing spherical waves. What happens when you start adding sources? Compare the wave that is produced by a finite length array of sources with that produced by the diffraction of light by a single aperture.

Use the above simulation to answer the following questions?