Christian Huygens Dutch Physicist and Astronomer (1629–1695) Huygens is best known for his contributions to the fields of optics and dynamics. To Huygens, light was a type of vibratory motion, spreading out and producing the sensation of light when impinging on the eye. On the basis of this theory, he deduced the laws of reflection and refraction and explained the phenomenon of double refraction. (Courtesy of Rijksmuseum voor de Geschiedenis der Natuurwetenschappen and Niels Bohr Library.) p.1108

Fig 35-CO This photograph of a rainbow shows a distinct secondary rainbow with the colors reversed. The appearance of the rainbow depends on three optical phenomena discussed in this chapter—reflection, refraction, and dispersion. (Mark D. Phillips/Photo Researchers, Inc.) Fig 35-CO, p.1095

Figure 34. 12 The electromagnetic spectrum Figure 34.12 The electromagnetic spectrum. Note the overlap between adjacent wave types. The expanded view to the right shows details of the visible spectrum. Fig 34-12, p.1081

Active Figure 34.3 Representation of a sinusoidal, linearly polarized plane electromagnetic wave moving in the positive x direction with velocity c. (a) The wave at some instant. Note the sinusoidal variations of E and B with x. Fig 34-3a, p.1071

Figure 35.5 Schematic representation of (a) specular reflection, where the reflected rays are all parallel to each other, and (b) diffuse reflection, where the reflected rays travel in random directions. Fig 35-5ab, p.1098

Figure 35.13 Overhead view of a barrel rolling from concrete onto grass. Fig 35-13, p.1104

Table 35-1, p.1104

Figure 35.14 As a wave moves from medium 1 to medium 2, its wavelength changes but its frequency remains constant. Fig 35-14, p.1104

Active Figure 35.26 (a) Rays travel from a medium of index of refraction n1 into a medium of index of refraction n2, where n2 < n1. As the angle of incidence 1 increases, the angle of refraction 2 increases until 2 is 90° (ray 4). For even larger angles of incidence, total internal reflection occurs (ray 5). Fig 35-26a, p.1112

(Left ) Strands of glass optical fibers are used to carry voice, video, and data signals in telecommunication networks. p.1114

Figure 35.29 Light travels in a curved transparent rod by multiple internal reflections. Fig 35-29, p.1114

A bundle of optical fibers is illuminated by a laser.

Figure 35. 30 The construction of an optical fiber Figure 35.30 The construction of an optical fiber. Light travels in the core, which is surrounded by a cladding and a protective jacket. Fig 35-30, p.1114

Figure 35.20 Variation of index of refraction with vacuum wavelength for three materials. Fig 35-20, p.1109

Figure 35.24 The formation of a rainbow seen by an observer standing with the Sun behind his back. Fig 35-24, p.1110

Figure 35. 22 White light enters a glass prism at the upper left Figure 35.22 White light enters a glass prism at the upper left. A reflected beam of light comes out of the prism just below the incoming beam. The beam moving toward the lower right shows distinct colors. Different colors are refracted at different angles because the index of refraction of the glass depends on wavelength. Violet light deviates the most; red light deviates the least. Fig 35-22, p.1110

Figure 35.21 A prism refracts a single-wavelength light ray through an angle  . Fig 35-21, p.1109

Figure 35.7 (Example 35.2) (b) The geometry for an arbitrary mirror angle. Fig 35-7b, p.1100

Figure 35. 8 Applications of retroreflection Figure 35.8 Applications of retroreflection. (a) This panel on the Moon reflects a laser beam directly back to its source on the Earth. (b) An automobile taillight has small retroreflectors that ensure that headlight beams are reflected back toward the car that sent them. (c) A light ray hitting a transparent sphere at the proper position is retroreflected. (d) This stop sign appears to glow in headlight beams because its surface is covered with a layer of many tiny retroreflecting spheres. What would you see if the sign had a mirror-like surface? Fig 35-8, p.1101

Active Figure 35.10 (a) A ray obliquely incident on an air–glass interface. The refracted ray is bent toward the normal because v2 < v1. All rays and the normal lie in the same plane. (b) Light incident on the Lucite block bends both when it enters the block and when it leaves the block. Fig 35-10, p.1102

Active Figure 35.11 (a) When the light beam moves from air into glass, the light slows down on entering the glass and its path is bent toward the normal. (b) When the beam moves from glass into air, the light speeds up on entering the air and its path is bent away from the normal. Fig 35-11, p.1103

Active Figure 35.4 A plane wave of wavelength  is incident on a barrier in which there is an opening of diameter d. (a) When  << d, the rays continue in a straightline path, and the ray approximation remains valid. (b) When   d, the rays spread out after passing through the opening. (c) When  >> d, the opening behaves as a point source emitting spherical waves. Fig 35-4, p.1098

Active Figure 35.4 A plane wave of wavelength  is incident on a barrier in which there is an opening of diameter d. (a) When  << d, the rays continue in a straightline path, and the ray approximation remains valid. Fig 35-4a, p.1098

Active Figure 35.4 A plane wave of wavelength  is incident on a barrier in which there is an opening of diameter d. (b) When   d, the rays spread out after passing through the opening. Fig 35-4b, p.1098

Active Figure 35.4 A plane wave of wavelength  is incident on a barrier in which there is an opening of diameter d. (c) When  >> d, the opening behaves as a point source emitting spherical waves. Fig 35-4c, p.1098

Active Figure 35. 23 Path of sunlight through a spherical raindrop Active Figure 35.23 Path of sunlight through a spherical raindrop. Light following this path contributes to the visible rainbow. Fig 35-23, p.1110

Figure 35.18 (a) Huygens’s construction for proving the law of reflection. At the instant that ray 1 strikes the surface, it sends out a Huygens wavelet from A and ray 2 sends out a Huygens wavelet from B. We choose a radius of the wavelet to be c  t, where  t is the time interval for ray 2 to travel from B to C. (b) Triangle ADC is congruent to triangle ABC. Fig 35-18, p.1108

Figure 35.18 (a) Huygens’s construction for proving the law of reflection. At the instant that ray 1 strikes the surface, it sends out a Huygens wavelet from A and ray 2 sends out a Huygens wavelet from B. We choose a radius of the wavelet to be c  t, where  t is the time interval for ray 2 to travel from B to C. Fig 35-18a, p.1108

Figure 35.18 (b) Triangle ADC is congruent to triangle ABC. Fig 35-18b, p.1108

Figure 35.19 Huygens’s construction for proving Snell’s law of refraction. At the instant that ray 1 strikes the surface, it sends out a Huygens wavelet from A and ray 2 sends out a Huygens wavelet from B. The two wavelets have different radii because they travel in different media. Fig 35-19, p.1109

Figure 35.25 (Example 35.7) A light ray passing through a prism at the minimum angle of deviation  min. Fig 35-25, p.1111

Active Figure 35.26 (a) Rays travel from a medium of index of refraction n1 into a medium of index of refraction n2, where n2 < n1. As the angle of incidence 1 increases, the angle of refraction 2 increases until 2 is 90° (ray 4). For even larger angles of incidence, total internal reflection occurs (ray 5). (b) The angle of incidence producing an angle of refraction equal to 90° is the critical angle c. At this angle of incidence, all of the energy of the incident light is reflected. Fig 35-26, p.1112

Active Figure 35.26 (b) The angle of incidence producing an angle of refraction equal to 90° is the critical angle c. At this angle of incidence, all of the energy of the incident light is reflected. Fig 35-26b, p.1112

Figure 35.27 (Quick Quiz 35.6 and 35.7) Five nonparallel light rays enter a glass prism from the left. Fig 35-27, p.1113

Figure 35.28 (Example 35.8) A fish looks upward toward the water surface. Fig 35-28, p.1113

Figure 35.31 Geometry for deriving Snell’s law of refraction using Fermat’s principle. Fig 35-31, p.1115

Fig Q35-6a, p.1117

Fig Q35-6b, p.1117

Fig Q35-17, p.1117

Fig P35-4, p.1118

Fig P35-6, p.1118

Fig P35-8, p.1119

Fig P35-21, p.1119

Fig P35-23, p.1120

Fig P35-27, p.1120

Fig P35-28, p.1120

Fig P35-33, p.1121

Fig P35-35, p.1121

Fig P35-38, p.1121

Fig P35-40, p.1121

Fig P35-43, p.1122

Fig P35-45, p.1122

Fig P35-50, p.1122

Fig P35-52, p.1123

Fig P35-55, p.1123

Fig P35-59, p.1123

Fig P35-61, p.1124

Fig P35-63, p.1124

Fig P35-66, p.1124

Fig P35-67, p.1124

Fig P35-69, p.1124

Fig P35-70, p.1125

Fig P35-71, p.1125

Figure 35. 1 Roemer’s method for measuring the speed of light Figure 35.1 Roemer’s method for measuring the speed of light. In the time interval during which the Earth travels 90° around the Sun (three months), Jupiter travels only about 7.5° (drawing not to scale). Fig 35-1, p.1096

Figure 35.2 Fizeau’s method for measuring the speed of light using a rotating toothed wheel. The light source is considered to be at the location of the wheel; thus, the distance d is known. Fig 35-2, p.1097

Figure 35. 3 A plane wave propagating to the right Figure 35.3 A plane wave propagating to the right. Note that the rays, which always point in the direction of the wave propagation, are straight lines perpendicular to the wave fronts. Fig 35-3, p.1097

Figure 35.5 Schematic representation of (a) specular reflection, where the reflected rays are all parallel to each other Fig 35-5a, p.1098

Figure 35.5 Schematic representation of (b) diffuse reflection, where the reflected rays travel in random directions. Fig 35-5b, p.1098

Figure 35.5 (c) and (d) Photographs of specular and diffuse reflection using laser light. Fig 35-5c, p.1098

Figure 35.5 (c) and (d) Photographs of specular and diffuse reflection using laser light. Fig 35-5d, p.1098

Active Figure 35. 6 According to the law of reflection, I = i Active Figure 35.6 According to the law of reflection, I = i. The incident ray, the reflected ray, and the normal all lie in the same plane. Fig 35-6, p.1099

Figure 35.7 (Example 35.2) (a) Mirrors M1 and M2 make an angle of 120° with each other. (b) The geometry for an arbitrary mirror angle. Fig 35-7, p.1100

Figure 35.7 (Example 35.2) (a) Mirrors M1 and M2 make an angle of 120° with each other. Fig 35-7a, p.1100

Figure 35. 8 Applications of retroreflection Figure 35.8 Applications of retroreflection. (a) This panel on the Moon reflects a laser beam directly back to its source on the Earth. Fig 35-8a, p.1101

Figure 35. 8 Applications of retroreflection Figure 35.8 Applications of retroreflection. (b) An automobile taillight has small retroreflectors that ensure that headlight beams are reflected back toward the car that sent them. Fig 35-8b, p.1101

Figure 35. 8 Applications of retroreflection Figure 35.8 Applications of retroreflection. (c) A light ray hitting a transparent sphere at the proper position is retroreflected. Fig 35-8c, p.1101

Figure 35. 8 Applications of retroreflection Figure 35.8 Applications of retroreflection. (d) This stop sign appears to glow in headlight beams because its surface is covered with a layer of many tiny retroreflecting spheres. What would you see if the sign had a mirror-like surface? Fig 35-8d, p.1101

Figure 35.9 (a) An array of mirrors on the surface of a digital micromirror device. Each mirror has an area of about 16  m2. Fig 35-9a, p.1101

Figure 35. 9 (b) A close-up view of two single micromirrors Figure 35.9 (b) A close-up view of two single micromirrors. The mirror on the left is “on” and the one on the right is “off.” Fig 35-9b, p.1101

Active Figure 35.10 (a) A ray obliquely incident on an air–glass interface. The refracted ray is bent toward the normal because v2 < v1. All rays and the normal lie in the same plane. Fig 35-10a, p.1102

Active Figure 35.10 (b) Light incident on the Lucite block bends both when it enters the block and when it leaves the block. Fig 35-10b, p.1102

Active Figure 35.11 (a) When the light beam moves from air into glass, the light slows down on entering the glass and its path is bent toward the normal. Fig 35-11a, p.1103

Active Figure 35.11 (b) When the beam moves from glass into air, the light speeds up on entering the air and its path is bent away from the normal. Fig 35-11b, p.1103

Figure 35. 12 Light passing from one atom to another in a medium Figure 35.12 Light passing from one atom to another in a medium. The dots are electrons, and the vertical arrows represent their oscillations. Fig 35-12, p.1103

Figure 35.15 (Example 35.4) Refraction of light by glass. Fig 35-15, p.1105

Figure 35.16 (Example 35.6) (a) When light passes through a flat slab of material, the emerging beam is parallel to the incident beam, and therefore  1 =  3. The dashed line drawn parallel to the red ray coming out the bottom of the slab represents the path the light would take if the slab were not there. (b) A magnification of the area of the light path inside the slab. Fig 35-16, p.1107

Figure 35.16 (Example 35.6) (a) When light passes through a flat slab of material, the emerging beam is parallel to the incident beam, and therefore  1 =  3. The dashed line drawn parallel to the red ray coming out the bottom of the slab represents the path the light would take if the slab were not there. Fig 35-16a, p.1107

Figure 35.16 (Example 35.6) (b) A magnification of the area of the light path inside the slab. Fig 35-16b, p.1107

Fig 35-17, p.1108

Figure 35.17 Huygens’s construction for (a) a plane wave propagating to the right Fig 35-17a, p.1108

Figure 35.17 Huygens’s construction for (b) a spherical wave propagating to the right. Fig 35-17b, p.1108