More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths ( 1 2 λ, 3 2 λ, 5 2 λ, etc. If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively. Waves start out from the slits in phase (crest to crest), but they will end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively. Thus different numbers of wavelengths fit into each path. Each slit is a different distance from a given point on the screen. To understand the basis of such calculations, consider how two waves travel from the slits to the screen. The fact that the wavelength of light of one color, or monochromatic light, can be calculated from its two-slit diffraction pattern in Young’s experiments supports the conclusion that light has wave properties. Note that the sign of an angle is always ≥ 1. Opposite means opposite the given acute angle. The sine of an angle is the opposite side of a right triangle divided by the hypotenuse. The plurals of maximum and minimum are maxima and minima, respectively.Įxplain that monochromatic means one color. Both are pronounced the way you would expect from the spelling. It will be useful not only in describing how light waves propagate, but also in how they interfere. 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 the wave is located at time t. These are drawn later at a time, t, so that they have moved a distance s = v t s = v t. 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 17.4 shows how Huygens’s principle is applied. Huygens’s principle states, “Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself.
He used wavefronts, which are the points on a wave’s surface that share the same, constant phase (such as all the points that make up the crest of a water wave). The Dutch scientist Christiaan Huygens (1629–1695) developed a useful technique for determining in detail how and where waves propagate. Although wavelengths change while traveling from one medium to another, colors do not, since colors are associated with frequency.
It follows that the wavelength of light is smaller in any medium than it is in vacuum. Where λ λ is the wavelength in vacuum and n is the medium’s index of refraction. As it is characteristic of wave behavior, interference is observed for water waves, sound waves, and light waves. Here we see the beam spreading out horizontally into a pattern of bright and dark regions that are caused by systematic constructive and destructive interference. Passing a pure, one-wavelength beam through vertical slits with a width close to the wavelength of the beam reveals the wave character of light. The laser beam emitted by the observatory represents ray behavior, as it travels in a straight line. In Figure 17.2, both the ray and wave characteristics of light can be seen. Interference is the identifying behavior of a wave. However, when it interacts with smaller objects, it displays its wave characteristics prominently. As is true for all waves, light travels in straight lines and acts like a ray when it interacts with objects several times as large as its wavelength.
The range of visible wavelengths is approximately 380 to 750 nm. Where c = 3.00 × 10 8 c = 3.00 × 10 8 m/s is the speed of light in vacuum, f is the frequency of the electromagnetic wave in Hz (or s –1), and λ λ is its wavelength in m.
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