When sound passes through a door, we expect to hear it everywhere in the room and, thus, expect that sound spreads out when passing through such an opening (see Figure 5). What happens when a wave passes through an opening, such as light shining through an open door into a dark room? For light, we expect to see a sharp shadow of the doorway on the floor of the room, and we expect no light to bend around corners into other parts of the room. The ray bends toward the perpendicular, since the wavelets have a lower speed in the second medium. Huygens’s principle applied to a straight wavefront traveling from one medium to another where its speed is less. Snell’s law can be derived from the geometry in Figure 4, but this is left as an exercise for ambitious readers. This explains why a ray changes direction to become closer to the perpendicular when light slows down. Since the speed of light is smaller in the second medium, the waves do not travel as far in a given time, and the new wavefront changes direction as shown. Each wavelet in the figure was emitted when the wavefront crossed the interface between the media. The law of refraction can be explained by applying Huygens’s principle to a wavefront passing from one medium to another (see Figure 4). The direction of propagation is perpendicular to the wavefront, as shown by the downward-pointing arrows. The tangent to these wavelets shows that the new wavefront has been reflected at an angle equal to the incident angle. The wavelets shown were emitted as each point on the wavefront struck the mirror. Huygens’s principle applied to a straight wavefront striking a mirror. The wavelets closer to the left have had time to travel farther, producing a wavefront traveling in the direction shown. As the wavefront strikes the mirror, wavelets are first emitted from the left part of the mirror and then the right. The new wavefront is a line tangent to the wavelets.įigure 3 shows how a mirror reflects an incoming wave at an angle equal to the incident angle, verifying the law of reflection. Each point on the wavefront emits a semicircular wavelet that moves a distance s = vt. Huygens’s principle applied to a straight wavefront. In addition, we will see that Huygens’s principle tells us how and where light rays interfere. We will find it useful not only in describing how light waves propagate, but also in explaining the laws of reflection and refraction. Huygens’s principle works for all types of waves, including water waves, sound waves, and light waves. The new wavefront is a line tangent to the wavelets and is where we would expect the wave to be a time t later. These are drawn at a time t later, so that they have moved a distance s = vt. Each point on the wavefront emits a semicircular wave that moves at the propagation speed v. A wavefront is the long edge that moves, for example, the crest or the trough. The new wavefront is a line tangent to all of the wavelets.įigure 2 shows how Huygens’s principle is applied. Starting from some known position, Huygens’s principle states that:Įvery point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The Dutch scientist Christiaan Huygens (1629–1695) developed a useful technique for determining in detail how and where waves propagate. The direction of propagation is perpendicular to the wavefronts (or wave crests) and is represented by an arrow like a ray. A transverse wave, such as an electromagnetic wave like light, as viewed from above and from the side. The view from above is perhaps the most useful in developing concepts about wave optics. The side view would be a graph of the electric or magnetic field. From above, we view the wavefronts (or wave crests) as we would by looking down on the ocean waves. A light wave can be imagined to propagate like this, although we do not actually see it wiggling through space. Discuss the propagation of transverse waves.įigure 1 shows how a transverse wave looks as viewed from above and from the side.
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