Diffraction Grating - Simulation

<h1>Text Preview</h1> <p> Because the wavelengths of visible light are relatively short, it is difficult to make direct observatons of light wave interference phenomena. It is also difficult to produce light from two coherent sources. During the early 19th century, Thomas Young solved these problems by using a single light source to illuminate two narrow, closely spaced slits. Light emerging from the two slits serves as two coherent sources. When he passed light through the slits and projected it onto a screen, Young observed that a series of bright fringes appeared, rather than the two lines that some scientists thought would appear if light consisted of a simple stream of particles. Light waves are diffracted by the slits. and this causes the waves to spread out and interfere with one another, resulting in a pattern consisting of a bright central fringe flanked by a series of symmetrical light and dark fringes. Young's experiment proved the wave nature of light because interference and diffraction are phenomena that only occur with waves. Now, let's quantify some of the things we have been discussing. Let the distance to the screen be L, and the distance of a bright fringe at point A to the central fringe be x sub m. The angle between A and a normal line between the slits is theta. The path length of the light from the two slits differs by an amount given by the product of the slit separation d, and the sine of the angle theta. Remember that for constructive interference, the path difference between two waves must be an integral number of wavelengths. For what condition does a dark fringe, representing destructive interference, appear on the screen? ... A dark fringe occurs when the path difference is an odd number of half wavelengths. The wavelengths of the individual colors of visible light can be estimated from this experiment. If the angle theta is very small, then the wavelength of a monochromatic source can be estimated by measuring the distance from the central maximum to a bright fringe. Given the experimental setup shown, what is the color of the monochromatic light source if the distance to the second order bright fringe is 27 millimeters? ... The calculated wavelength corresponds to the color red. If we perform this experiment with only one slit, we again obtain an interference pattern of light and dark fringes, though in this case the bright central fringe is much wider. Using a derivation similar to that for the double-slit experiment, the condition for the appearance of dark side fringes can be determined to be a function of the product of the slit width w and the sine of the angle theta. The distances from the dark fringes to the central maximum can be estimated from the slit width and the distance to the screen. For a given wavelength, as the slit width decreases, the fringes become wider and the distance between them increases. The width of the central maximum is twice the width of the side fringes. What would the interference pattern be if we performed the experiment using many slits instead of one or two? ... The number of fringe patterns would increase and the bright fringes become sharper. A device to diffract light waves that consists of thousands of slits per centimeter is known as a "diffraction grating." The conditions required a diffraction grating to produce bright fringes are the same as for the double-slit setup. Because of the sharp patterns produced by diffraction gratings, they are used in research spectrometers for producing precise wavelengths of light.</p> <p id="TextCopyright">Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education</p>