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. Steve: Ouch! That hurt more than the pulling of the hair did.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. Steve: So, did you at least pull out a gray hair? Thanks for watching! I hope you'll join us again soon for another experiment! Joanna: Since we have a micrometer handy, we can measure the diameter of the hair directly. Since it's small, we can use the small angle approximation, so the sine of theta simply becomes the distance we measured to the minimum, which, in our case, was 8.8 centimeters, divided by the distance to the wall, which, in our case, was about 880 centimeters.ĭoing little math, we find that the diameter of the hair is about 53,000 nanometers, or about 53 microns. Theta is the angle measured off the main beam that lands you on a minimum. Which, for us, is 532 nanometers.Īs far as the sine of theta is concerned. Lambda is the wavelength of the laser light that was used. And, since we used the first one, 'm' is equal to 1. The variable 'm' is a counter that keeps track of which minimum we used. Steve: We can now use this equation to calculate the diameter of the hair. If it isn't, you can use 650 nanometers if you're using a red laser pointer or 532 nanometers if you're using a green one. This should be marked somewhere on the laser itself. The final bit of information that we're going to need is the wavelength of the laser. Do yourself a favor and measure both of these distances in centimeters. We need to know the distance from the center of the pattern to the center of the first dark area and we need to know the distance from the hair to the wall. Joanna: We can also use the pattern to see how wide the hair is by making a few simple measurements. Diffraction and interference are things that waves do, so seeing this pattern tells us that light behaves like a wave. Steve: The pattern is caused by the diffraction and interference of the laser light. You should see a pattern of light that looks like this. Place it a few meters away from the wall and shine the laser through it, making sure that the laser hits the hair. Take a hair, perhaps from a coworker, and tape it in a cardboard frame. Joanna: If you have a laser pointer, and you know how to use it safely, try this.
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