When they travel straight ahead, as in Figure 2(a), they remain in phase, and a central maximum is obtained. (Each ray is perpendicular to the wavefront of a wavelet.) Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. These are like rays that start out in phase and head in all directions. According to Huygens’s principle, every part of the wavefront in the slit emits wavelets. Here we consider light coming from different parts of the same slit. The analysis of single slit diffraction is illustrated in Figure 2. (b) The drawing shows the bright central maximum and dimmer and thinner maxima on either side. The central maximum is six times higher than shown. Monochromatic light passing through a single slit has a central maximum and many smaller and dimmer maxima on either side. In contrast, a diffraction grating produces evenly spaced lines that dim slowly on either side of center. Note that the central maximum is larger than those on either side, and that the intensity decreases rapidly on either side. Figure 1 shows a single slit diffraction pattern. Light passing through a single slit forms a diffraction pattern somewhat different from those formed by double slits or diffraction gratings. Discuss the single slit diffraction pattern.Is no place where the interference is completely destructive. If D, the width of the opening, is less than the wavelength than there It turns out that the points where this destructive interference occurs are all along one line, at an angle (measured from a line perpendicular to the opening) given by: Similarly, the wave from the part of the opening next to the side will interfer destructively with the part of the opening next to the center, and so on - the waves from one half of the opening completely cancel the waves from the other half. This is the condition for destructive interference: the wave from the side of the opening will interfere destructively with the wave from the center of the opening. The waves from each piece of the opening are sent out in phase with each other at some places they will interfere constructively, and at others they will interfere destructively.Ĭonsider a point that is half a wavelength further from the center of the opening than from one side of the opening. If the opening is divided into many small pieces, each piece can be thought of as an emitter of the wave. Interference, both constructive and destructive, is important to understanding why diffraction occurs. The most interesting cases (i.e., the ones with interesting patterns of maxima and minima) are those in which the size of the openings or obstacles is about the same as the wavelength of the wave. Lengths from the two sources to that point differ by an integral numberĭiffraction is the bending of waves that takes place when the wave encounters openings or obstacles. Sources to that point differ by an integral number of wavelengths.ĭestructive interference occurs at a particular point if the path Will occur at a particular point if the path lengths from the two When the sources send out waves in phase, constructive interference For a particular separation and wavelength, the pattern is as shown in the diagram, with constructive interference taking place at certain angles and destructive interference taking place at other angles. The sources are in phase with each other. Consider first the special case of two sources separated by a small distance d, sending out waves of the same frequency. When two (or more) waves of the same frequency interfere, a variety of different results can be obtained. The interference of two waves of the same frequency
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