Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the 33 m, about three times smaller than the width of the doorway). Sound has wavelengths on the order of the size of the door and bends around corners (for frequency of 1000 Hz, λ = c / f = ( 330 m / s ) / ( 1000 s − 1 ) = 0. What is the difference between the behavior of sound waves and light waves in this case? The answer is that light has very short wavelengths and acts like a ray. 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 27.8). 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. Snell’s law can be derived from the geometry in Figure 27.7, but this is left as an exercise for ambitious readers.įigure 27.7 Huygens’s principle applied to a straight wavefront traveling from one medium to another where its speed is less. 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 27.7). 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. In addition, we will see that Huygens’s principle tells us how and where light rays interfere.įigure 27.6 Huygens’s principle applied to a straight wavefront striking a mirror. 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 t later. These are drawn at a time t t later, so that they have moved a distance s = vt s = vt. Each point on the wavefront emits a semicircular wave that moves at the propagation speed v 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 27.5 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. Figure 27.4 A transverse wave, such as an electromagnetic wave like light, as viewed from above and from the side.
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