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Part One Geometrical Optics1

1 Properties of Light3

1.1 The Rectilinear Propagation of Light5

1.2 The Speed of Light6

1.3 The Speed of Light in Stationary Matter8

1.4 The Refractive Index9

1.5 Optical Path10

1.6 Laws of Reflection and Refraction11

1.7 Graphical Construction for Refraction13

1.8 The Principle of Reversibility14

1.9 Fermat's Principle14

1.10 Color Dispersion18

2 Plane Surfaces and Prisms24

2.1 Parallel Beam24

2.2 The Critical Angle and Total Reflection25

2.3 Plane-Parallel Plate28

2.4 Refraction by a Prism29

2.5 Minimum Deviation30

2.6 Thin Prisms32

2.7 Combinations-of Thin Prisms32

2.8 Graphical Method of Ray Tracing33

2.9 Direct-Vision Prisms34

2.10 Reflection of Divergent Rays36

2.11 Refraction of Divergent Rays36

2.12 Images Formed by Paraxial Rays38

2.13 Fiber Optics40

3 Spherical Surfaces44

3.1 Focal Points and Focal Lengths45

3.2 Image Formation46

3.3 Virtual Images47

3.4 Conjugate Points and Planes47

3.5 Convention of Signs50

3.6 Graphical Constructions. The Parallei-Ray Method50

3.7 Oblique-Ray Methods52

3.8 Magnification54

3.9 Reduced Vergence54

3.10 Derivation of the Gaussian Formula56

3.11 Nomography57

4 Thin Lenses60

4.1 Focal Points and Focal Lengths60

4.2 Image Formation62

4.3 Conjugate Points and Planes62

4.4 The Parallel-Ray Method62

4.5 The Oblique-Ray Method63

4.6 Use of the Lens Formula64

4.7 Lateral Magnification64

4.8 Virtual Images65

4.9 Lens Makers' Formula67

4.10 Thin-Lens Combinations68

4.11 Object Space and Image Space70

4.12 The Power of a Thin Lens70

4.13 Thin Lenses in Contact71

4.14 Derivation of the Lens Formula72

4.15 Derivation of the Lens Makers'Formula73

5 Thick Lenses78

5.7 Two Spherical Surfaces78

5.2 The Parallel-Ray Method79

5.3 Focal Points and Principal Points81

5.4 Conjugate Relations82

5.5 The Oblique-Ray Method82

5.6 General Thick-Lens Formulas84

5.7 Special Thick Lenses88

5.8 Nodal Points and Optical Center88

5.9 Other Cardinal Points90

5.10 Thin-Lens Combination as a Thick Lens91

5.11 Thick-Lens Combinations93

5.12 Nodal Slide93

6 Spherical Mirrors98

6.1 Focal Point and Focal Length98

6.2 Graphical Constructions99

6.3 Mirror Formulas102

6.4 Power of Mirrors104

6.5 Thick Mirrors105

6.6 Thick-Mirror Formulas107

6.7 Other Thick Mirrors109

6.8 Spherical Aberration109

6.9 Astigmatism111

7 The Effects of Stops115

7.1 Field Stop and Aperture Stop115

7.2 Entrance and Exit Pupils116

7.3 Chief Ray117

7.4 Front Stop117

7.5 Stop between Two Lenses118

7.6 Two Lenses with No Stop120

7.7 Determination of the Aperture Stop121

7.8 Field of View122

7.9 Field of a Plane Mirror122

7.10 Field of a Convex Mirror124

7.11 Field of a Positive Lens124

8 Ray Tracing130

8.1 Oblique Rays130

8.2 Graphical Method for Ray Tracing131

8.3 Ray-tracing Formulas134

8.4 Sample Ray-tracing Calculations135

9 Lens Aberrations149

9.1 Expansion of the Sine. First-Order Theory150

9.2 Third-Order Theory of Aberrations151

9.3 Spherical Aberration of a Single Surface152

9.4 Spherical Aberration of a Thin Lens153

9.5 Results of Third-Order Theory157

9.6 Fifth-Order Spherical Aberration160

9.7 Coma162

9.8 Aplanatic Points of a Spherical Surface166

9.9 Astigmatism167

9.10 Curvature of Field170

9.11 Distortion171

9.12 The Sine Theorem and Abbe's Sine Condition173

9.13 Chromatic Aberration176

9.14 Separated Doublet182

10 Optical Instruments188

10.1 The Human Eye188

10.2 Cameras and Photographic Objectives191

10.3 Speed of Lenses191

10.4 Meniscus Lenses193

10.5 Symmetrical Lenses193

10.6 Triplet Anastigmats194

10.7 Telephoto Lenses195

10.8 Magnifiers195

10.9 Types of Magnifiers198

10.10 Spectacle Lenses198

10.11 Microscopes200

10.12 Microscope Objectives201

10.13 Astronomical Telescopes202

10.14 Oculars and Eyepieces205

10.15 Huygens Eyepiece205

10.16 Ramsden Eyepiece206

10.17 Kellner or Achromatized Ramsden Eyepiece206

10.18 Special Eyepieces206

10.19 Prism Binoculars207

10.20 The Kellner-Schmidt Optical System208

10.21 Concentric Optical Systems209

Part Two Wave Optics213

11 Vibrations and Waves214

11.1 Simple Harmonic Motion216

11.2 The Theory of Simple Harmonic Motion217

11.3 Stretching of a Coiled Spring218

11.4 Vibrating Spring221

11.5 Transverse Waves223

11.6 Sine Waves224

11.7 Phase Angles225

11.8 Phase Velocity and Wave Velocity228

11.9 Amplitude and Intensity229

11.10 Frequency and Wavelength232

11.11 Wave Packets235

12 The Superposition of Waves238

12.1 Addition of Simple Harmonic Motions along the Same Line239

12.2 Vector Addition of Amplitudes240

12.3 Superposition of Two Wave Trains of the Same Frequency242

12.4 Superposition of Many Waves with Random Phases244

12.5 Complex Waves246

12.6 Fourier Analysis248

12.7 Group Velocity250

12.8 Graphical Relation between Wave and Group Velocity252

12.9 Addition of Simple Harmonic Motions at Right Angles253

13 Interference of Two Beams of Light259

13.1 Huygens' Principle260

13.2 Young's Experiment261

13.3 Interference Fringes from a Double Source263

13.4 Intensity Distribution in the Fringe System265

13.5 Fresnel's Biprism266

13.6 Other Apparatus Depending on Division of the Wave Front268

13.7 Coherent Sources270

13.8 Division of Amplitude. Michelson Interferometer271

13.9 Circular Fringes273

13.10 Localized Fringes275

13.11 White-Light Fringes276

13.12 Visibility of the Fringes277

13.13 Interferometnc Measurements of Length279

13.14 Twyman and Green Interferometer281

13.15 Index of Refraction by Interference Methods282

14 Interference Involving Multiple Reflections286

14.1 Reflection from a Plane-Parallel Film288

14.2 Fringes of Equal Inclination291

14.3 Interference in the Transmitted Light292

14.4 Fringes of Equal Thickness293

14.5 Newton's Rings294

14.6 Nonreflecting Films295

14.7 Sharpness of the Fringes297

14.8 Method of Complex Amplitudes299

14.9 Derivation of the Intensity Function300

14.10 Fabry-Perot Interferometer301

14.11 Brewster's Fringes302

14.12 Chromatic Resolving Power303

14.13 Comparison of Wavelengths with the Interferometer305

14.14 Study of Hyperfine Structure and of Line Shape308

14.15 Other Interference Spectroscopes310

14.16 Channeled Spectra. Interference Filter311

15 Fraunhofer Diffraction by a Single Opening315

15.1 Fresnel and Fraunhofer Diffraction315

15.2 Diffraction by a Single Slit316

15.3 Further Investigation of the Single-Slit Diffraction Pattern319

15.4 Graphical Treatment of Amplitudes. The Vibration Curve322

15.5 Rectangular Aperture324

15.6 Resolving Power with a Rectangular Aperture325

15.7 Chromatic Resolving Power of a Prism327

15.8 Circular Aperture329

15.9 Resolving Power of a Telescope330

15.10 Resolving Power of a Microscope332

15.11 Diffraction Patterns with Sound and Microwaves334

16 The Double Slit338

16.1 Qualitative Aspects of the Pattern338

16.2 Derivation of the Equation for the Intensity339

16.3 Comparison of the Single-Slit and Double-Slit Patterns341

16.4 Distinction between Interference and Diffraction341

16.5 Position of the Maxima and Minima. Missing Orders342

16.6 Vibration Curve346

16.7 Effect of Finite Width of Source Slit347

16.8 Michelson's Stellar Interferometer349

16.9 Correlation Interferometer351

16.10 Wide-Angle Interference352

17 The Diffraction Grating355

17.1 Effect of Increasing the Number of Slits355

17.2 Intensity Distribution from an Ideal Grating357

17.5 Principal Maxima358

17.4 Minima and Secondary Maxima358

17.5 Formation of Spectra by a Grating359

17.6 Dispersion362

17.7 Overlapping of Orders362

17.8 Width of the Principal Maxima363

17.9 Resolving Power364

17.10 Vibration Curve365

17.11 Production of Ruled Gratings368

17.12 Ghosts370

17.13 Control of the Intensity Distribution among Orders370

17.14 Measurement of Wavelength with the Grating373

17.15 Concave Grating373

17.16 Grating Spectrographs374

18 Fresnel Diffraction378

18.1 Shadows378

18.2 Fresnel's Half-Period Zones380

18.3 Diffraction by a Circular Aperture383

18.4 Diffraction by a Circular Obstacle384

18.5 Zone Plate385

18.6 Vibration Curve for Circular Division of the Wave Front386

18.7 Apertures and Obstacles with Straight Edges388

18.8 Strip Division of the Wave Front389

18.9 Vibration Curve for Strip Division. Cornu's Spiral389

18.10 Fresnel's Integrals390

18.11 The Straight Edge393

18.12 Rectilinear Propagation of Light395

18.13 Single Slit397

18.14 Use of Fresnel's Integrals in Solving Diffraction Problems399

18.15 Diffraction by an Opaque Strip400

19 The Speed of Light403

19.1 Romer's Method403

19.2 Bradley's Method. The Aberration of Light405

19.3 Michelson's Experiments406

19.4 Measurements in a Vacuum408

19.5 Kerr-Cell Method408

19.6 Speed of Radio Waves410

19.7 Ratio of the Electrical Units411

19.8 The Speed of Light in Stationary Matter411

19.9 Speed of Light in Moving Matter412

19.10 Fresnel's Dragging Coefficient413

19.11 Airy's Experiment414

19.12 Effect of Motion of the Observer414

19.13 The Michelson-Morley Experiment416

19.14 Principle of Relativity418

19.15 The Three First-Order Relativity Effects419

20 The Electromagnetic Character of Light423

20.1 Transverse Nature of Light Vibrations424

20.2 Maxwell's Equations for a Vacuum424

20.3 Displacement Current425

20.4 The Equations for Plane Electromagnetic Waves427

20.5 Pictorial Representation of an Electromagnetic Wave428

20.6 Light Vector in an Electromagnetic Wave429

20.7 Energy and Intensity of the Electromagnetic Wave429

20.8 Radiation from an Accelerated Charge430

20.9 Radiation From a Charge in Periodic Motion432

20.10 Hertz's Verification of the Existence of Electromagnetic Waves432

20.11 Speed of Electromagnetic Waves in Free Space434

20.12 Cerenkov Radiation434

21 Sources of Light and Their Spectra438

21.1 Classification of Sources438

21.2 Solids at High Temperature439

21.3 Metallic Arcs439

21.4 Bunsen Flame442

21.5 Spark442

21.6 Vacuum Tube443

21.7 Classification of Spectra445

21.8 Emittance and Absorptance445

21.9 Continuous Spectra447

21.10 Line Spectra450

21.11 Series of Spectral Lines452

21.12 Band Spectra453

22 Absorption and Scattering457

22.1 General and Selective Absorption457

22.2 Distinction between Absorption and Scattering458

22.3 Absorption by Solids and Liquids459

22.4 Absorption by Gases461

22.5 Resonance and Fluorescence of Gases461

22.6 Fluorescence of Solids and Liquids464

22.7 Selective Reflection. Residual Rays464

22.8 Theory of the Connection between Absorption and Reflection465

22.9 Scattering by Small Particles466

22.10 Molecular Scattering468

22.11 Raman Effect469

22.12 Theory of Scattering470

22.13 Scattering and Refractive Index471

23 Dispersion474

23.1 Dispersion of a Prism474

23.2 Normal Dispersion475

23.3 Cauchy's Equation479

23.4 Anomalous Dispersion479

23.5 Sellmeier's Equation482

23.6 Effect of Absorption on Dispersion485

23.7 Wave and Group Velocity in the Medium487

23.8 The Complete Dispersion Curve of a Substance488

23.9 The Electromagnetic Equations for Transparent Media489

23.10 Theory of Dispersion491

23.11 Nature of the Vibrating Particles and Frictional Forces494

24 The Polarization of Light497

24.1 Polarization by Reflection498

24.2 Representation of the Vibrations in Light499

24.3 Polarizing Angle and Brewster's Law500

24.4 Polarization by a Pile of Plates501

24.5 Law of Malus503

24.6 Polarization by Dichroic Crystals504

24.7 Double Refraction505

24.8 Optic Axis507

24.9 Principal Sections and Principal Planes507

24.10 Polarization by Double Refraction508

24.11 Nicol Prism510

24.12 Parallel and Crossed Polarizers511

24.13 Refraction by Calcite Prisms511

24.14 Rochon and Wollaston Prisms513

24.15 Scattering of Light and the Blue Sky514

24.16 The Red Sunset515

24.17 Polarization by Scattering516

24.18 The Optical Properties of Gemstones518

25 Reflection523

25.1 Reflection from Dielectrics523

25.2 Intensities of the Transmitted Light526

25.3 Internal Reflection527

25.4 Phase Changes on Reflection527

25.5 Reflection of Plane-polarized Light from Dielectrics529

25.6 Elliptically Polarized Light by Internal Reflection531

25.7 Penetration into the Rare Medium533

25.8 Metallic Reflection534

25.9 Optical Constants of Metals536

25.10 Description of the Light Reflected from Metals538

25.11 Measurement of the Principal Angle of Incidence and Principal Azimuth540

25.12 Wiener's Experiments541

26 Double Refraction544

26.1 Wave Surfaces for Uniaxial Crystals544

26.2 Propagation of Plane Waves in Uniaxial Crystals546

26.3 Plane Waves at Oblique Incidence549

26.4 Direction of the Vibrations550

26.5 Indices of Refraction for Uniaxial Crystals551

26.6 Wave Surfaces in Biaxial Crystals553

26.7 Internal Conical Refraction556

26.8 External Conical Refraction557

26.9 Theory of Double Refraction559

27 Interference of Polarized Light564

27.1 Elliptically and Circularly Polarized Light564

27.2 Quarter- and Half-Wave Plates567

27.3 Crystal Plates between Crossed Polarizers568

27.4 Babinet Compensator569

27.5 Analysis of Polarized Light571

27.6 Interference with White Light572

27.7 Polarizing Monochromatic Filter575

27.8 Applications of Interference in Parallel Light576

27.9 Interference in Highly Convergent Light576

28 Optical Activity and Modern Wave Optics581

28.1 Rotation of the Plane of Polarization581

28.2 Rotary Dispersion582

28.3 Fresnel's Explanation of Rotation584

28.4 Double Refraction in Optically Active Crystals586

28.5 Shape of the Wave Surfaces in Quartz588

28.6 Fresnel's Multiple Prism589

28.7 Cornu Prism590

28.8 Vibration Forms and Intensities in Active Crystals591

28.9 Theory of Optical Activity593

28.10 Rotation in Liquids594

28.11 Modern Wave Optics596

28.12 Spatial Filtering597

28.13 Phase-Contrast Microscope602

28.14 Schlieren Optics604

Part Three Quantum Optics609

29 Light Quanta and Their Origin611

29.1 The Bohr Atom612

29.2 Energy Levels616

29.3 Bohr-Stoner Scheme for Building Up Atoms617

29.4 Elliptical Orbits, or Penetrating Orbitals619

29.5 Wave Mechanics622

29.6 The Spectrum of Sodium625

29.7 Resonance Radiation626

29.8 Metastable States629

29.9 Optical Pumping630

30 Lasers632

30.1 Stimulated Emission633

30.2 Laser Design634

30.3 The Ruby Laser635

30.4 The Helium-Neon Gas Laser636

30.5 Concave Mirrors and Brewster's Windows642

30.6 The Carbon Dioxide Laser643

30.7 Resonant Cavities646

30.8 Coherence Length650

30.9 Frequency Doubling652

30.10 Other Lasers653

30.11 Laser Safety653

30.12 The Speckle Effect653

30.13 Laser Applications654

31 Holography658

31.1 The Basic Principles of Holography659

31.2 Viewing a Hologram664

31.3 The Thick, or Volume, Hologram665

31.4 Multiplex Holograms669

31.5 White-Light-Reflection Holograms670

31.6 Other Holograms672

31.7 Student Laboratory Holography675

32 Magneto-Optics and Electro-Optics678

32.1 Zeeman Effect679

32.2 Inverse Zeeman Effect685

32.3 Faraday Effect686

32.4 Voigt Effect, or Magnetic Double Refraction688

32.5 Cotton-Mouton Effect690

32.6 Kerr Magneto-optic Effect691

32.7 Stark Effect691

32.8 Inverse Stark Effect692

32.9 Electric Double Refraction693

32.10 Kerr Electro-optic Effect693

32.11 Pockels Electro-optic Effect695

33 The Dual Nature of Light698

33.1 Shortcomings of the Wave Theory699

33.2 Evidence for Light Quanta700

33.3 Energy, Momentum, and Velocity of Photons703

33.4 Development of Quantum Mechanics704

33.5 Principle of Indeterminacy705

33.6 Diffraction by a Slit705

33.7 Complementarity707

33.8 Double Slit707

33.9 Determination of Position with a Microscope709

33.10 Use of a Shutter710

33.11 Interpretation of the Dual Character of Light711

33.12 Realms of Applicability of Waves and Photons712

Appendixes715

Ⅰ The Physical Constants716

Ⅱ Electron Subshells717

Ⅲ Refractive Indices and Dispersions for Optical Glasses720

Ⅳ Refractive Indices and Dispersions of Optical Crystals721

Ⅴ The Most Intense Fraunhofer Lines722

Ⅵ Abbreviated Number System723

Ⅶ Significant Figures724

Index727