Optics (eBook)

Front Cover 1
Optics, Part 1 and 2 4
Copyright Page 5
Table of Contents 6
Preface to the English Edition 8
Principal Physical Constants 10
Principal symbols and variables 11
PART 1: 
12 
CHAPTER 
14 
1.1. The object of optics 14
1.2. Sources of light 14
1.3. Transmission of light—light rays—diffraction 15
1.4. Monochromatic and complex radiation 17
1.5. Speed of light and index of refraction 18
1.6. Wave surfaces — optical trajectories 19
1.7. Huygens and Snell constructions 20
1.8. Energy definitions relative to electromagnetic radiation 23
1.9. Properties of objects with respect to radiant energy 27
1.10. Theories of the nature of light 29
1.11. Wave properties of light 29
1.12. Interference 31
1.13. Transverse light waves—polarization of light 37
1.14. Particle properties of light—photons 39
1.15. Validity of certain fundamental ideas 40
Problems 41
CHAPTER 2. 
44 
2.1. Maxwell's equations 44
2.2. Electromagnetic waves in free-space 47
2.3. Sinusoidal electromagnetic waves in free-space 51
2.4. Electromagnetic waves in homogeneous, isotropic dielectrics 53
2.5 Electromagnetic waves in a homogeneous ohmic conductor 54
2.6. Movement of an electromagnetic wave from one medium to another 56
2.7. Radiation pressure 57
2.8. Electromagnetic theory of light 59
Problems 60
CHAPTER 3. 
62 
3.1. Geometric laws of reflection and refraction 62
3.2. Calculation of reflection and transmission coefficients 63
3.3. Discussion of the Fresnel formulas 65
3.4. Reflection and transmission of energy 70
3.5. Reflection on absorbing isotropic media 72
3.6. Experimental verification and applications 74
3.7. Stationary waves from normal reflection on plane mirrors 76
3.8. Progressive waves from oblique reflection 80
3.9. Wave guides 81
3.10. Resonant cavities 84
3.11. Applications of stationary and guided waves 85
Exercises 88
CHAPTER 4. 
90 
4.1. Geometric optics of anisotropic media 90
4.2. Wave normals and rays 91
4.3. Electromagnetic plane waves in anisotropic media 94
4.4. Indicial equation—indicial surface 96
4.5. Experimental verification 99
4.6. Wave surface 100
4.7. Special cases of the Huygens construction 101
4.8. Polarization by birefringence 103
4.9. Indicial ellipsoid 105
4.10. Total reflection—measurement of the refractive indices 109
4.11. Indicial ellipsoid and crystalline symmetry 110
4.12. Polarizing prisms 111
4.13. Absorbing crystals 112
4.14. Reflection factor of crystals 112
Exercises 113
CHAPTER 5. 
116 
5.1. The wave equation and the equation of geometric optics 116
5.2. Focused waves 118
5.3. Huygens, Fresnel, and Kirchhoff methods for the study of wave propagation 119
5.4. Propagation of a free wave—Fresnel zones 121
5.5. Classification of diffraction phenomena 124
5.6. Babinet's theorem 126
5.7. Shadowing of an infinite straight edge 127
5.8. Illumination along the axis of a circular opening and a circular disc 129
5.9. Diffraction on optical images 131
5.10. Diffraction by a rectangular opening 133
5.11. Diffraction by a circular opening 138
5.12. Applications 140
5.13. Resolving power of optical instruments 141
5.14. Use of the Fourier transform for diffraction at infinity 145
5.15. Application of diffraction to the detection of phase structures 148
5.16. Diffraction by multiple identical apertures or obstacles 151
5.17 Holography 153
Problems 154
CHAPTER 6. 
156 
A. INTERFERENCE IN NATURAL LIGHT 156
6.1. Non-localized interference fringes 156
6.2. Localized interference fringes 159
6.3. Interference from transparent plates with plane parallel faces. Fringes of equal inclination 160
6.4. Interference by transparent films of variable thickness. Fringes of equal thickness. 165
6.5. Fringes of equal thickness given by films of air 167
6.6. Generalizations as to the localization of interference fringes 171
6.7. The concept of the point source 172
6.8. Coherence 174
6.9. The Michelson interferometer 176
6.10. Wave trains—longitudinal coherence 178
6.11. Interference in white light 181
6.12. Spectral analysis of the white light interference fringes 185
6.13. The use of interference for the measurement of optical trajectories and their variations 185
6.14. Study of the structure of surfaces 188
6.15. Measurement of the index of refraction 189
6.16. Measurement of small length variations 191
B. INTERFERENCE IN POLARIZED LIGHT 191
6.17. Fresnel-Arago experiments 191
6.18. The passage of light through a plane, parallel birefringent plate without doubling 192
6.19. The interference given by a birefringent plate set in parallel light between a polarizer and analyser 193
6.20. White light phenomena 196
6.21. Applications of interferences in polarized light 197
6.22. Interference given by a birefringent plate in converging polarized light 198
Exercises 200
CHAPTER 7. 
203 
7.1. The general characteristics of the phenomena 203
7.2. Multiple reflections in transparent plates 203
7.3. The modification of the reflection factor of transparent surfaces 205
7.4. Interference fringes from air layers. The Fabry-Perot interferometer 207
7.5. Interference filters 211
7.6. Stratified structures—dielectric mirrors 211
7.7. Diffraction at infinity due to a series of identical equidistant slits 212
7.8. Line gratings 216
7.9. The use of gratings for the separation of wavelengths 220
7.10. Radiointerferometers 222
7.11. The constitution of white light 223
7.12. The formation of images of objects having a periodic structure 224
7.13. Two-dimensional gratings 226
7.14. Three-dimensional gratings—X-ray diffraction by crystals 228
7.15. Methods for measuring the spacing of crystal planes 232
7.16. The intensity of the diffraction maxima given by crystals 233
7.17. Lippmann colour photography 235
Problems 236
CHAPTER 8. 
239 
8.1. Definitions 239
8.2. Elliptical light 239
8.3. Special cases 242
8.4. Determination of the orientation of a linear vibration 245
8.5. Application to rotatory power 248
8.6. The analysis of an elliptical vibration with known orientation 250
8.7. The anal/sis of a general elliptical vibration 253
8.8. Partially polarized light 257
Problems 258
CHAPTER 9. 
260 
9.1. Phase velocity and signal velocity 260
9.2. Measurement of the phase velocity 260
9.3. Measurement of the signal velocity 261
9.4. Results 261
9.5. The velocity of light in a moving medium 262
9.6. The effect of the relative motion of the source and the observer 263
9.7. Absolute motion—the Michelson-Morley experiment 264
9.8. The relativity of space and time. The Lorentz transformation 266
9.9. Kinematic consequences of the Lorentz transformation 267
9.10. Applications to optics 270
9.11. Dynamic consequences of special relativity 272
Problems 274
APPENDIX A. 
276 
A.1. Periodic functions 276
A.2. The use of complex variables 278
A.3. The sum of sinusoidal functions with the same period 279
A.4. Fourier series 280
A.5. Fourier transforms and integrals 282
A.6. The sum of two sinusoidal functions with closely adjacent periods 284
A.7. The function sin x/x 286
Problems 286
APPENDIX B. 
287 
B.1. The wave equation 287
B.2. Sinusoidal plane waves 287
B.3. Groups of waves. Group velocity 290
Problems 292
APPENDIX C. 
293 
C.1. Symmetry of physical phenomena 293
C.2. The laws of symmetry 294
C.3. Invariance of the laws of symmetry 295
C.4. Applications to optics 295
APPENDIX D. 
297 
Solutions and hints for the problems 300
PART 2: 
308 
CHAPTER 10. 
310 
10.1. Electromagnetic waves and molecular structure 310
10.2. Electromagnetic effects created by a charged particle 311
10.3. Radiation from a Hertzian dipole 315
10.4. Scattering of electromagnetic waves by free electrons 317
10.5. Extinction as a result of scattering. X-ray case 319
10.6. Propagation of electromagnetic waves in an ionized gas 320
10.7. Propagation of electromagnetic waves in metals 321
10.8. Radiation forces and torques 324
10.9. Artificially dispersive media 325
10.10. Optical properties of classical atomic and molecular models 327
Problems 331
CHAPTER 11. 
333 
11.1. The photoelectric effect in metals 333
11.2. Quantization of light energy. Photons 336
11.3. X-ray production 337
11.4. The Compton effect 339
11.5. Creation and annihilation of electron pairs 341
11.6. Photons and waves 342
11.7. The uncertainty relationships 345
11.8. Complementarity 346
11.9. Wave groups. Spectral decomposition 347
11.10. Polarization of light and photons 349
Problems 349
CHAPTER 12. 
351 
12.1. Emission and absorption spectrum of hydrogen 351
12.2. The Bohr postulates 353
12.3. Electron excitation of atoms 356
12.4. lonization energy of atoms 358
12.5. Thermal excitation of atoms 360
12.6. Excitation and ionization of atoms by radiation 361
12.7. Some general statements about transitions occurring between quantizedsystems 362
12.8. Mean lifetime 364
12.9. Width of spectral lines 364
12.10. Production of atomic spectra 366
12.11. Coherence and structure of light sources 367
Problems 369
CHAPTER 13. 
370 
13.1. Diffraction of material particles 370
13.2. Matter waves or de Broglie waves 372
13.3. The equation for matter waves or the Schrodinger equation 373
13.4. The probabilistic interpretation of the wave function 375
13.5. The wave associated with the motion of a free particle 376
13.6. The principle of spectral decomposition 377
13.7. The uncertainty relationships 378
13.8. The relationships between wave mechanics and newtonian mechanics 380
13.9. Particles in fields of force 381
13.10. The particle in a box 387
13.11. Matter waves and electromagnetic waves 388
Problems 390
CHAPTER 14. 
392 
14.1. The two-body problem in wave mechanics 392
14.2. The rigid diatomic rotor 393
14.3. Angular momentum in quantum mechanics 397
14.4. The linear harmonic oscillator 400
14.5. The hydrogen atom 404
14.6. An examination of several of the energy states of the hydrogen atom 408
14.7. Stationary states of many-electron atoms 412
14.8. Determination of the atomic electron density 414
Problems 416
CHAPTER 15. 
418 
15.1. Non-stationary states. Spontaneous transitions 418
15.2. The radiant flux emitted by an atom 420
15.3. Selection rules 421
15.4. The spectrum of hydrogen-like atoms and ions 422
15.5. Spectra of the alkali atoms. Spectral evidence for the quantum number 424
15.6. The magnetic properties of the electron 429
15.7. Fine structure of spectral lines and electron spin 432
15.8. Total angular momentum. The internal quantum number j 434
15.9. The hyperfine structure of spectral lines 437
15.10. The normal Zeeman effect. The effect of the quantum number m 438
15.11. Anomalous Zeeman effects. The Lande factor 442
15.12. The electronic structure of atoms 444
15.13. X-ray spectra 448
15,14. Scattering of X-rays by atoms 452
15.15. y-rays 453
Problems 453
CHAPTER 16. 
456 
16.1. Various kinds of molecular spectra 456
16.2. Pure rotational spectra of diatomic molecules 456
16.3. Vibration-rotation spectra of diatomic molecules 458
16.4. Fundamentals of the electronic spectra of diatomic molecules 462
16.5. Scattering of X-rays and electrons by molecules 464
Problems 465
CHAPTER 17. 
467 
17.1. The action of an electromagnetic wave on an atom or a molecule 467
17.2. Atomic or molecular polarizability 469
17.3. Refraction of light by a transparent gas 471
17.4. Reflection of light by a transparent gas 473
17.5. Molecular scattering of light by a transparent gas 474
17.6. Refractive dispersion of gases and vapours 477
17.7. Permittivity of polar gases 479
17.8. Refraction and absorption by condensed bodies 481
17.9. The Kramers-Kronig relations 485
17.10. Scattering of light by condensed media 486
Problems 488
CHAPTER 18. 
490 
18.1. Anisotropy of molecules 490
18.2. Scattering spectra 493
18.3. Crystal birefringence 495
18.4. Dichroism of crystals 496
18.5. Induced birefringence 496
18.6. Birefringence in crystals resulting from compression or stretching 497
18.7. Electrical birefringence (Kerr, 1877) 498
18.8. Magnetic birefringence (Cotton and Mouton, 1905) 501
18.9. The dynamic birefringence of liquids 502
18.10. Artificial dichroisms 502
18.11. The structure of optically active media 503
18.12. Rotatory dispersion and circular dichroism 504
18.13. The atomic theory of the rotatory power 505
18.14. Magnetic rotatory power (Faraday, 1845) 507
Problems 509
CHAPTER 19. 
511 
19.1. Stimulated transitions 511
19.2. Thermal equilibrium between matter and radiation. The black-body. 513
19.3. The laws of thermal radiation 515
19.4. Kirchhoffs law 517
19.5. The quantum theory of thermal radiation. Planck's equation 518
19.6. The comparative properties of spontaneous and induced emission 520
19.7. Applications of stimulated emission phenomena 521
Problems 524
CHAPTER 20. 
527 
20.1. The aims and methods of spectrometry 527
20.2. Radiation sources 527
20.3. The separation of the radiation 529
20.4. Radiation detection 531
20.5. Prism and grating spectroscopes 535
20.6. The properties of a dispersing instrument 537
20.7. Fourier transform spectrometry 539
20.8. High-resolution spectrometry 540
20.9. Wavelength measurement 541
20.10. An application 541
Problems 542
APPENDIX E. 
544 
E.1. Numerical quantities 544
E.2. Thermal agitation 544
E.3. The statistical character of molecular theories 545
E.4. Molecular Beams 547
APPENDIX F. 
548 
F.1. The idea of an operator 548
F.2. Axiomatic quantum theory 549
Problems 550
Solutions and hints for the problems 551
Index 558
Other titles in the series in natural philosophy 564