![]() ![]() One ray travels a distance λ λ different from the ray from the bottom and arrives in phase, interfering constructively. The difference in path length for rays from either side of the slit is seen to be a sin θ θ.Īt the larger angle shown in part (c), the path lengths differ by 3 λ / 2 3 λ / 2 for rays from the top and bottom of the slit. By symmetry, another minimum occurs at the same angle to the right of the incident direction (toward the bottom of the figure) of the light.įigure 4.4 Light passing through a single slit is diffracted in all directions and may interfere constructively or destructively, depending on the angle. In other words, a pair-wise cancellation of all rays results in a dark minimum in intensity at this angle. In fact, each ray from the slit interferes destructively with another ray. ![]() A ray from slightly above the center and one from slightly above the bottom also cancel one another. Thus, a ray from the center travels a distance λ / 2 λ / 2 less than the one at the bottom edge of the slit, arrives out of phase, and interferes destructively. In part (b), the ray from the bottom travels a distance of one wavelength λ λ farther than the ray from the top. However, when rays travel at an angle θ θ relative to the original direction of the beam, each ray travels a different distance to a common location, and they can arrive in or out of phase. When they travel straight ahead, as in part (a) of the figure, they remain in phase, and we observe a central maximum. (Each ray is perpendicular to the wave front 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 wave front in the slit emits wavelets, as we discussed in The Nature of Light. We then consider light propagating onwards from different parts of the same slit. Here, the light arrives at the slit, illuminating it uniformly and is in phase across its width. The analysis of single-slit diffraction is illustrated in Figure 4.4. (b) The diagram shows the bright central maximum, and the dimmer and thinner maxima on either side. The central maximum is six times higher than shown. (a) 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 ( Diffraction Gratings) produces evenly spaced lines that dim slowly on either side of the center.įigure 4.3 Single-slit diffraction pattern. Note that the central maximum is larger than maxima on either side and that the intensity decreases rapidly on either side. Figure 4.3 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, which we discussed in the chapter on interference. For example, if you place your middle and index fingers close together and look through the opening at a light bulb, you can see a rather clear diffraction pattern, consisting of light and dark lines running parallel to your fingers. However, situations do occur in which apertures are small enough that the diffraction of light is observable. Since the wavelengths of visible light range from approximately 390 to 770 nm, most objects do not diffract light significantly. The diffraction of sound waves is apparent to us because wavelengths in the audible region are approximately the same size as the objects they encounter, a condition that must be satisfied if diffraction effects are to be observed easily. (credit: modification of map data from Google Earth) ![]() Figure 4.2 Because of the diffraction of waves, ocean waves entering through an opening in a breakwater can spread throughout the bay. ![]()
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