Index Absorption , 25, 117 Cornu spiral , 64 Amplitude , complex , 29 Crystal optics, 16, 84- 108 Aperture , 48 , 49 , 53 , 55 , 60 , 62 Crystals, 20 numerical , 61 optically active, 137 Axes , uniaxial , 90 optical ( optic ) , 90, 101 Current density, 109 principal , 85 ray , 105 Damped oscillations , 118 Damping , radiation , 121 Babinet ' s theorem , 49 Damping constant , 79 Bessel function , 57 Damping for ('e, 117 Bessel 's inequality , 32 Diaphragm , 49, 51, 52, 55. See also Binormals , 101 Aperture lliradials , 105 Dielectric constant , Birefringence , 108, 147 complex , 78- 82 Boundary conditions , 46, 47, 48, 50 principal , 86 Brewster ' s law , 75 Dielectric constant tensor , 84 - 86 Brun ' s law , 11 Differential equations for light rays , 10 , 19 , 22 Canonical equations , 15, 18, 20 Diffraction , inhomogeneous form of , 22 from circular aperture , 55 - 57 Charged particles , 109 Fraunhofer , 53 Circular frequency , 28 f ' resnel , 53 , 62 - 66 Clausius .Mosotti equation , 112 from grating , 57- 59 Coherent light sources , 61, 151 by slit , 54- 55 Coherent wave trains , 43 Diffraction angle , 48, 51, 55, 57, 59 Completeness relation , 32 Diffraction pattern , 58 , 59 , 61 Conductivity , electrical , 77, 80 Dipole moment , Cone , electric , 109 ray , 104 electric , of optically active wave , 105 crystals , 140 Conservation of energy , 16 magnetic , of optically active for electromagnetic waves , 69, crystals , 142 85 , 114 Discontinuity of E at surface , 70, 71 155 156 INDEX Dispersion law . 34 . 35 . 38 . 117 Frequency, for xrays , 128 circular , 28 Doppler effect , 133 Larmor , 145 Dual equations , 95, 96 I-sum rule , 152- 153 Dual variables , 92 Grating , 57, 58, 60, 61 step ., 62 Eikonal , 8 Green ' s theorem , 46 angular , 25 Group velocity , 37, 98, 115, 116 Eikonal equationt 8 Electrons , 113 , 119 , 121 - 131 , 145 Ha milton , W . R ., 10 Electron , spin of , 146 Ha miltons theory , Emission , 25 homogeneous form of , 14 Energy , scattered , 125 inhomogeneous form of , 21 Energy conservation , 16 Harmonic oscillation , 28 for electromagnetic waves , 69, 85, Hertz oscillator , 123 114 energy radiation of , 124 Energy density , Hertz vector , 122 of electromagnetic field , 85 Huygens , C., 106 of material oscillators , 115 Huygens ' s principle , 9, 20 total , 116 Energy transport , direction of , 93 Illuminance , 26, 42 Euler , L ., 28 Image plane , 61 Euler 's homogenity relation , 16, 99 Image space, 11 Extremal curve , 5 Index of refraction (refractive Extremal principle in canonical index ) , 2, 40, 111 form , 15 of crystals ( double root ) , 88, Extremal property , 2 100, 101 in Faraday effect , 146 of metals ( complex ) , 77- 83, 120 Faradayeffec4146 - 148 in optical activity , 133, 136 Fermat 's principle , 3, 4, 6, 7, 14 variable , 4, 28 Fluctuations , Intensity , 29, 43, 57, 58, 74, 125 density , 124 incident , 75, 130, 131 theory of , 126 of illumination , 26 Focal plane , 61 reflected , 75, 80 Fourier inversion formula , 35 refracted , 75 Fourier ' s theorem , 31 , 35 of scattered xrays , 130 Fraunhofer diffraction , 53 , 54 - 62 specific , of light , 26 Fresnel , A . I -, 28 time -averaged , 30 Fresnel diffraction , 53 , 62 - 66 Intensity maxima , 44 Fresnel formulas , 6 Intensity ratio , 65 Fresnel integral , 63 Interference , 28, 42, 44, 45, 67 Fresnel mirror -experiment , 43 Fresnel ' s formulae , Kepler , la \v of , 25. See also for absorbing media , 79- 83 Lambert , law of for nonabsorbing media , 73- 77 Kirchhoff .Clausius law , 12 INDEX 157 Kirchhoff , solution of , 45 - 53 Microscope , 59 Kuhn , I .sum rule of Thomas and , Mirror , 152 - 153 Fresnel , 43 Kuhn ' s model , 138 - 143 perfect , 82 Molecules , not mirror -symmetric , Lagrangian multipliers , method 133 of , 3, 15 , 90 Lambert , la \" of , 25 , 26 Ne \vton ' s rings , 45 Larmor frequency , 145 Nodes of E and H in standing Lasers , 151 waves , 83 Legend re transformation , 151 Nonlinear optics , 151 Lenses , 13 , 53 Light , Object , , circularly polarized , 133, 134, 146 illuminated , 60 corpuscular theory of , 28 luminous , 59 elliptically polarized , 77, 81 Object space, 11 linearly polarized , 75, 76, 77, 80 Optical activity , 133 polarized , 67 Optical axes, 90, 101 unpolarized , 67, 75, 131 Optical constant for metals , 82, 120 Light intensity , specific , 26 Optical instruments , 62 Light vector , 67, 68 Optically active crystals , 137 Lorentz force , 144 Optically active molecule , 138 Lorentz 's theory of scattering , 124 Optically uniaxial crystals , 90 Optical path , 3, 4, 6, 107 Magnetic field ( static ) , 143, 146 Oscillation , Malus ' s la "" 9 damped , 118 Mass absorption coefficient , 128 harmonic , 28 Maxwell equations , 68, 110, 134 7r ( para ] ] el to 11 ) , 145 in crystal optics , 84 0" (perpendicular to 11) , 145 for periodic process es, 71, 77, vectorial , 30 86 , 121 Oscillator , Mechanical momentum , 16 Hertz , 123 Mechanical problem , associated , 14 quasi -elastic , 110 Mechanical waves , 34 Oscillator strength , 113 Media , absorbing (metals ) , 77- 83, 119- 121 Parseval ' s formula . 33 . 36 . See also anisotropic , 141 Completeness relation dispersion -free , 39 Pedal surface . 97 homogeneous , 1, 124 Phase . inhomogeneous , 41 continuity of . 40. 72 isotropic , I , 34, 39, 41, 42, 45, 71, propagation of . 93 116 , 138 , 141 Phase velocity . 34. 40. 68. 71. 86. nonabsorbing , 71- 77 88 . 110 Metals . See Media , absorbing Photometric brightness . See Light ( metals ) intensity . specific Michelson ' s transmission echelon . Plane . See Grating , step - of inciden (~e. 2. 72 , 73 , 79 . 80 . 81 , 82 158 INDEX Plane ( continued ) index of (refractive index ) , 2, 4, of polarization , 68, 76, 81, 83, 151 28 , 40 , 79 , 86 , Ill , 120 , 133 , 136 , Polarization , 67 , 77 , 79 146 circular , 133 , 145 , 151 law of , 2, 4 , 41 electric , 111 , 124 Refractivity , molar , 113 plane of , 68, 76 Resolving power , 59- 62, 152 for plane waves , 69, 79 Rotation of plane of oscillation , Potentials , angle of , 133, 147 scalar , 121 in Faraday effect , 146 vector , 121 in optical activity , 133, 136 Poynting vector , 74, 77, 84, 91, 93 , 114 Scattered energy , 125 Principal angle of incidence , 81 Scattering, light-light, 151 Principal axes, 85 Scattering angle , 132 Principal dielectric constants , 86 Scattering coefficient , 126, 127 Principal maxima , 58, 59, 61, 152 Screens , 46 , 48 , 49 Principal section , 88, 89 Shado ' v boundary , 51, 65 Sine condition , 12 , 60 Quantum -mechanical model , 120, Singular directions , 99, 105 131 Slit , 54 , 63 Quantum (wave ) mechanics, 146, Snell ' s law , 1, 7 153 Spectral lines , splitting of , 145, 146 Statistical average , 132 Radiation , energy, 124 Statistical mechanics , 124 , 126 Radiation condition , 47 Structure factor , 130 Radiation damping, 121 in quantum theory , 132 Radiator , isotropic , 26 Superposition principle , linear , Ray, 29 , 34 , 35 , 38 extraordinary , 89 Surface , ordinary , 88, 89 of constant phase , 86, 107 parallel , 53 pedal , 97, 98 reflected, 2, 75 ray , 98 refracted , 2, 75 wave , 20 , 97 Ray axes, 105 Surface wave , 77 Ray cone, 104 Ray direction , 20, 93, 97- 107 Tensor , Ray equation , 10, 16, 19, 22 permutation , .137 Ray index , 91, 97, 98 skew -symmetric , 134, 137 Ray surface, 98 Thomas and Kuhn , I -sum rule of , Ray variables, 91 153 Ray vector, 91 Thomson , J . J ., 128 Ray velocity , 91 Total reflection , 75 , 76 , 77 Reflection , limiting angle of , 76 law of, 2, 4, 41 Transversality condition , 18 total , 75, 76, 77 Transversality of light waves , 28, 67 Refraction , double, 108 Variational principle , 11, 16, 17, 21 INDEX 159 Vectors , axial , 134 polar , 134 Verdet ' s constant , 147 Wave equation , 38 general solution of , 39 Kirchhoff ' s solution of , 48 , 49 time -independent , 71 Wave , damped , 79 electromagnetic , 69, 74 harmonic , 43 , 45 incident , 71 , 72 , 73 , 74 mechanical , 34 outgoing , 47 plane , 33, 39, 69, 71, 72, 80, 86, 107 , 135 reflected , 72 , 73, 74 , 76 , 82 refracted , 73 , 74 , 76, 79 , 80 scalar , 67 spherical , 39 standing , 82 surface , 77 transverse vector , 67 Wave concept , 28 Wave cone , 105 Wave kinematics , 28 , 38 Wavelength , 42, 45, 59, 124, 152 Wave normal , 20 , 34 Wave packet , 35, 37, 45, 93 Wave surface , 20 , 97 Xrays , Ill , 124, 128 scattering of , 127- 133 Young , T ., 28 Zeeman effect , 143 - 146.