# Reflection and Refraction with Huygens Wavelets

Near the beginning of the eighteenth century, Dutch physicist Christiaan Huygens proposed that each point in a wave of light can be thought of as an individual source of illumination that produces its own spherical wavelets, which all add together to form an advancing wavefront. This interactive Java tutorial is designed to illustrate the reflection and refraction of light according to the multiple wavelet concept, now known as the Huygens' principle.

The tutorial initializes with an incident wavefront of light propagating through a medium (Medium 1) at angle of 45 degrees towards second a medium (Medium 2) that possesses a different refractive index than the first. When the wavefront encounters the interface between the two media, a portion of the light is reflected and another part is refracted. The periodic rows of miniature semicircular red waves represent the Huygens wavelets that together compose the incident and reflected wavefronts, while the solid red line indicates the direction of propagation for the incident and reflected wavefronts. As illustrated in the tutorial, the Huygens wavelets combine to form a wavefront that is perpendicular to the direction of propagation. Wavelets that penetrate the media boundary to become refracted are portrayed in blue, as is the line passing through the center of the refracted beam that denotes their direction of propagation. The speed of the tutorial as well as certain characteristics of the light beam and surrounding mediums can be adjusted by operating the various sliders. Translating the Incident Angle slider produces a change in the angle of incoming light. Similarly, the refractive indices of the two media may be altered by moving one or both of the Refractive Index sliders.

During Huygens' lifetime, and for a long period thereafter, scientists argued about the nature of light, some believing that it was composed of particles and others that it consisted of waves. Both standpoints have since been discovered to be partially correct but, at the time, scientists generally supported only one of the seemingly opposing views based upon how well it could explain the behavior of light. Although almost a hundred years would pass before his became the dominant viewpoint, Huygens' principle could adequately explain many optical phenomena, but was most adept in its representation of refraction.

As can be observed in the tutorial, according to the Huygens model of light, a small portion of each angled wavefront impacts the second medium before the rest of the front reaches the interface. This portion of the wavefront begins to move through the second medium while the rest of the wave is still traveling in the first medium. The speed at which the wavelets travel through is dependent on the refractive indices of the media. If the second medium has a higher refractive index than the first, then the light slows down, and vice versa. Since in either case the wavefront is then traveling at two different speeds, it bends into the second medium, thus changing the angle of propagation.

Reflection, according to Huygens, could also be explained through the concept of wavelets. As demonstrated in the tutorial, when wavelets are reflected from the interface between the two media, they do not change speed since there is no change in refractive index. Instead, when the wavelets impact the surface of the second medium, they are reflected according to their arrival angles, but with each wave turned back to front, producing a reversed image.

#### Contributing Authors

Shannon H. Neaves, Robert T. Sutter, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.