Refraction bends waves toward the medium with slower speed

Evidence

Huygens’s method works as follows: we start with a wavefront representing some wave incident on a “scene” that may include different materials. We want to construct the wave farther along the direction of propagation. Along the initial wavefront, we locate the centers of arcs of constant radius; the “envelope” of the new arcs is the new wavefront, also of constant phase. If the arcs are half a wavelength in radius, the new wavefront will be a crest if the old one was a trough. To understand refraction, we slightly modify Huygens’s original illustration. In figure 2.9, a wave is traveling in the direction of the line segment D-A, with perpendicular wavefronts— for example, A-C and the lines K-L. Suppose τ is the time it takes for the wavefront to travel the distance from C to the leftmost L. This distance is the radius of the Huygens arcs used to propagate wavefronts in the upper medium. (We have drawn a few of these in red.) Along the interface between the two media, the wavefronts will advance between the adjacent points labeled K in a given time τ. Inside the medium indicated by the rectangle, the speed is lower, and we draw correspondingly smaller radius arcs. The arc whose center is the rightmost point labeled K has such a smaller radius and represents the progress of part of the wavefront from that point in one unit of time τ. Huygens has drawn an arc of twice this radius from the adjacent point K to its left, representing a time 2τ since the wavefront entered there, and three times the radius from the point to the left of that. This is the correct procedure, as can be seen by the intermediate wavefronts inside the medium (colored blue) given by the lines labeled K-O. The new wavefronts are not parallel to the old wavefronts outside and above the medium. We have thus constructed the new wavefront inside the medium. Employing the rule that the energy flow is perpendicular to the wavefronts, we see that there is a new direction A-N inside the medium compared to the old direction D-A of propagation above the medium. We have shown that the wave refracts as it enters the medium of slower wave speed. Notice that the ray bends toward the medium with slower wave speed—this is a useful rule to remember about refraction. — Eric J. Heller, Why You Hear What You Hear- An…, 179

Categorization

• DEFINE: Explains Huygens’ principle and why refraction bends toward slower media — a core mechanism for sound behavior.
• XREF: Raybending toward slower speed explains why sound travels farther at night over cool ground and Snell’s law optics.