Fig 38-CO The Hubble Space Telescope does its viewing above the atmosphere and does not suffer from the atmospheric blurring, caused by air turbulence, that plagues ground-based telescopes. Despite this advantage, it does have limitations due to diffraction effects. In this chapter we show how the wave nature of light limits the ability of any optical system to distinguish between closely spaced objects. (©Denis Scott/CORBIS) Fig 38-CO, p.1205

Figure 38.1 The diffraction pattern that appears on a screen when light passes through a narrow vertical slit. The pattern consists of a broad central fringe and a series of less intense and narrower side fringes. Fig 38-1, p.1206

Figure 38.2 Light from a small source passes by the edge of an opaque object and continues on to a screen. A diffraction pattern consisting of bright and dark fringes appears on the screen in the region above the edge of the object. Fig 38-2, p.1207

Figure 38.3 Diffraction pattern created by the illumination of a penny, with the penny positioned midway between screen and light source. Note the bright spot at the center. Fig 38-3, p.1207

Active Figure 38.4 (a) Fraunhofer diffraction pattern of a single slit. The pattern consists of a central bright fringe flanked by much weaker maxima alternating with dark fringes. (Drawing not to scale.) Fig 38-4a, p.1207

Active Figure 38.4 (b) Photograph of a single-slit Fraunhofer diffraction pattern. Fig 38-4b, p.1207

Figure 38.5 Paths of light rays that encounter a narrow slit of width a and diffract toward a screen in the direction described by angle q. Each portion of the slit acts as a point source of light waves. The path difference between rays 1 and 3, rays 2 and 4, or rays 3 and 5 is (a/2) sin q. (Drawing not to scale.) Fig 38-5, p.1208

Figure 38.6 Intensity distribution for a Fraunhofer diffraction pattern from a single slit of width a. The positions of two minima on each side of the central maximum are labeled. (Drawing not to scale.) Fig 38-6, p.1209

Figure 38. 7 Fraunhofer diffraction pattern for a single slit Figure 38.7 Fraunhofer diffraction pattern for a single slit. The light intensity at a distant screen is the resultant of all the incremental electric field magnitudes from zones of width Dy. Fig 38-7, p.1210

Figure 38.8 Phasor diagrams for obtaining the various maxima and minima of a single-slit diffraction pattern. Fig 38-8, p.1210

Figure 38.8 Phasor diagrams for obtaining the various maxima and minima of a single-slit diffraction pattern. Fig 38-8a, p.1210

Figure 38.8 Phasor diagrams for obtaining the various maxima and minima of a single-slit diffraction pattern. Fig 38-8b, p.1210

Figure 38.8 Phasor diagrams for obtaining the various maxima and minima of a single-slit diffraction pattern. Fig 38-8c, p.1210

Figure 38.8 Phasor diagrams for obtaining the various maxima and minima of a single-slit diffraction pattern. Fig 38-8d, p.1210

Figure 38. 9 Phasor diagram for a large number of coherent sources Figure 38.9 Phasor diagram for a large number of coherent sources. All the ends of the phasors lie on the circular arc of radius R. The resultant electric field magnitude ER equals the length of the chord. Fig 38-9, p.1211

Figure 38.10 (a) A plot of light intensity I versus b/2 for the single-slit Fraunhofer diffraction pattern. (b) Photograph of a single-slit Fraunhofer diffraction pattern. Fig 38-10, p.1212

Figure 38.10 (a) A plot of light intensity I versus b/2 for the single-slit Fraunhofer diffraction pattern. Fig 38-10a, p.1212

Figure 38.10 (b) Photograph of a single-slit Fraunhofer diffraction pattern. Fig 38-10b, p.1212

Active Figure 38.11 The combined effects of two-slit and single-slit interference. This is the pattern produced when 650-nm light waves pass through two 3.0- mm slits that are 18 mm apart. Notice how the diffraction pattern acts as an “envelope” and controls the intensity of the regularly spaced interference maxima. Fig 38-11, p.1213

Figure 38.12 Two point sources far from a narrow slit each produce a diffraction pattern. (a) The angle subtended by the sources at the slit is large enough for the diffraction patterns to be distinguishable. (b) The angle subtended by the sources is so small that their diffraction patterns overlap, and the images are not well resolved. (Note that the angles are greatly exaggerated. The drawing is not to scale.) Fig 38-12, p.1214

Figure 38.12 Two point sources far from a narrow slit each produce a diffraction pattern. (a) The angle subtended by the sources at the slit is large enough for the diffraction patterns to be distinguishable. Fig 38-12a, p.1214

Figure 38.12 Two point sources far from a narrow slit each produce a diffraction pattern. (b) The angle subtended by the sources is so small that their diffraction patterns overlap, and the images are not well resolved. (Note that the angles are greatly exaggerated. The drawing is not to scale.) Fig 38-12b, p.1214

Figure 38.13 Individual diffraction patterns of two point sources (solid curves) and the resultant patterns (dashed curves) for various angular separations of the sources. In each case, the dashed curve is the sum of the two solid curves. (a) The sources are far apart, and the patterns are well resolved. (b) The sources are closer together such that the angular separation just satisfies Rayleigh’s criterion, and the patterns are just resolved. (c) The sources are so close together that the patterns are not resolved. Fig 38-13, p.1215

Figure 38.13 Individual diffraction patterns of two point sources (solid curves) and the resultant patterns (dashed curves) for various angular separations of the sources. In each case, the dashed curve is the sum of the two solid curves. (a) The sources are far apart, and the patterns are well resolved. (b) The sources are closer together such that the angular separation just satisfies Rayleigh’s criterion, and the patterns are just resolved. (c) The sources are so close together that the patterns are not resolved. Fig 38-13a1-c1, p.1215

Figure 38.14 (Example 38.4) Two point sources separated by a distance d as observed by the eye. Fig 38-14, p.1217

Figure 38.15 (a) The photograph on which Charon, the moon of Pluto, was discovered in 1978. From an Earth-based telescope, atmospheric blurring results in Charon appearing only as a subtle bump on the edge of Pluto. Fig 38-15a, p.1218

Figure 38.15 (b) A Hubble Space Telescope photo of Pluto and Charon, clearly resolving the two objects. Fig 38-15b, p.1218

Figure 38. 16 Side view of a diffraction grating Figure 38.16 Side view of a diffraction grating. The slit separation is d, and the path difference between adjacent slits is d sin q. Fig 38-16, p.1218

Active Figure 38. 17 Intensity versus sin q for a diffraction grating Active Figure 38.17 Intensity versus sin q for a diffraction grating. The zeroth-, first-, and second-order maxima are shown. Fig 38-17, p.1219

Active Figure 38. 18 Diagram of a diffraction grating spectrometer Active Figure 38.18 Diagram of a diffraction grating spectrometer. The collimated beam incident on the grating is spread into its various wavelength components with constructive interference for a particular wavelength occurring at the angles qbright that satisfy the equation d sin qbright ml, where m 0, 1, 2, . . . . Fig 38-18, p.1219

Figure 38. 19 A small portion of a grating light valve Figure 38.19 A small portion of a grating light valve. The alternating reflective ribbons at different levels act as a diffraction grating, offering veryhigh- speed control of the direction of light toward a digital display device. Fig 38-19, p.1220

Figure 38. 20 (Conceptual Example 38 Figure 38.20 (Conceptual Example 38.6) A compact disc observed under white light. The colors observed in the reflected light and their intensities depend on the orientation of the disc relative to the eye and relative to the light source. Fig 38-20, p.1221

Figure 38.21 In this hologram, a circuit board is shown from two different views. Notice the difference in the appearance of the measuring tape and the view through the magnifying lens. Fig 38-21a, p.1223

Figure 38.21 In this hologram, a circuit board is shown from two different views. Notice the difference in the appearance of the measuring tape and the view through the magnifying lens. Fig 38-21b, p.1223

Figure 38.22 Experimental arrangement for producing a hologram. Fig 38-22, p.1223

Figure 38. 23 Two light rays strike a hologram at normal incidence Figure 38.23 Two light rays strike a hologram at normal incidence. For each ray, outgoing rays corresponding to m = 0 and m = ±1 are shown. If the m = -1 rays are extended backward, a virtual image of the object photographed in the hologram exists on the front side of the hologram. Fig 38-23, p.1223

Figure 38.24 Schematic diagram of the technique used to observe the diffraction of x-rays by a crystal. The array of spots formed on the film is called a Laue pattern. Fig 38-24, p.1224

Figure 38.25 (a) A Laue pattern of a single crystal of the mineral beryl (beryllium aluminum silicate). Each dot represents a point of constructive interference. Fig 38-25a, p.1224

Figure 38.25 (b) A Laue pattern of the enzyme Rubisco, produced with a wide-band x-ray spectrum. This enzyme is present in plants and takes part in the process of photosynthesis. The Laue pattern is used to determine the crystal structure of Rubisco. Fig 38-25b, p.1224

Figure 38. 26 Crystalline structure of sodium chloride (NaCl) Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm. Fig 38-26, p.1225

Figure 38.27 A two-dimensional description of the reflection of an x-ray beam from two parallel crystalline planes separated by a distance d. The beam reflected from the lower plane travels farther than the one reflected from the upper plane by a distance 2d sin q. Fig 38-27, p.1225

Figure 38.28 Schematic diagram of an electromagnetic wave propagating at velocity c in the x direction. The electric field vibrates in the xy plane, and the magnetic field vibrates in the xz plane. Fig 38-28, p.1225

Figure 38.29 (a) A representation of an unpolarized light beam viewed along the direction of propagation (perpendicular to the page). The transverse electric field can vibrate in any direction in the plane of the page with equal probability. (b) A linearly polarized light beam with the electric field vibrating in the vertical direction. Fig 38-29, p.1226

Active Figure 38.30 Two polarizing sheets whose transmission axes make an angle q with each other. Only a fraction of the polarized light incident on the analyzer is transmitted through it. Fig 38-30, p.1226

Figure 38.31 The intensity of light transmitted through two polarizers depends on the relative orientation of their transmission axes. (a) The transmitted light has maximum intensity when the transmission axes are aligned with each other. (b) The transmitted light has lesser intensity when the transmission axes are at an angle of 45with each other. (c) The transmitted light intensity is a minimum when the transmission axes are perpendicular to each other. Fig 38-31, p.1227

Figure 38.32 (a) When unpolarized light is incident on a reflecting surface, the reflected and refracted beams are partially polarized. (b) The reflected beam is completely polarized when the angle of incidence equals the polarizing angle qp, which satisfies the equation n tan qp. At this incident angle, the reflected and refracted rays are perpendicular to each other. Fig 38-32, p.1228

Figure 38.32 (a) When unpolarized light is incident on a reflecting surface, the reflected and refracted beams are partially polarized. Fig 38-32a, p.1228

Figure 38.32 (b) The reflected beam is completely polarized when the angle of incidence equals the polarizing angle qp, which satisfies the equation n tan qp. At this incident angle, the reflected and refracted rays are perpendicular to each other. Fig 38-32b, p.1228

Figure 38.33 Unpolarized light incident on a calcite crystal splits into an ordinary (O) ray and an extraordinary (E) ray. These two rays are polarized in mutually perpendicular directions. (Drawing not to scale.) Fig 38-33, p.1229

Figure 38.34 A point source S inside a double-refracting crystal produces a spherical wave front corresponding to the ordinary ray and an elliptical wave front corresponding to the extraordinary ray. The two waves propagate with the same velocity along the optic axis. Fig 38-34, p.1229

Table 38-1, p.1230

Figure 38.35 A calcite crystal produces a double image because it is a birefringent (double-refracting) material. Fig 38-35, p.1230

Figure 38.36 (a) Strain distribution in a plastic model of a hip replacement used in a medical research laboratory. The pattern is produced when the plastic model is viewed between a polarizer and analyzer oriented perpendicular to each other. Fig 38-36a, p.1230

Figure 38.36 (b) A plastic model of an arch structure under load conditions observed between perpendicular polarizers. Such patterns are useful in the optimal design of architectural components. Fig 38-36b, p.1230

Figure 38. 37 The scattering of unpolarized sunlight by air molecules Figure 38.37 The scattering of unpolarized sunlight by air molecules. The scattered light traveling perpendicular to the incident light is plane-polarized because the vertical vibrations of the charges in the air molecule send no light in this direction. Fig 38-37, p.1231

This photograph of a rocket launch from Vandenburg Air Force Base, California, shows the effects of scattering of light by air molecules. The lower portion of the trail left by the rocket appears red, due to the scattering of wavelengths at the violet end of the spectrum as the light from the Sun travels through a large portion of the atmosphere to light up the trail. The upper portion of the trail is illuminated by light that has traveled through much less atmosphere and appears white. p.1231

Fig Q38-6, p.1233

Fig P38-17, p.1235

Fig P38-30, p.1236

Fig P38-42, p.1237

Fig P38-50, p.1238

Fig P38-54, p.1238

Fig P38-56a, p.1238

Fig P38-56b, p.1238

Fig P38-58, p.1239

Fig P38-69, p.1240

Fig P38-69a, p.1240

Fig P38-69b, p.1240

Fig A38-3, p.1241