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LIGHT AND MATTER
Fullerton,California
www.lightandmatter.com
Copyrightc2002-2004BenjaminCrowell
Allrightsreserved.
rev.April1,2006
ISBN0-9704670-8-7
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Brief Contents
1 The Rules of the Rules 7
2 The Ray Model of Light 21
3 Images 45
4 Conservation of Mass and Energy 61
5 Conservation of Momentum 89
6 Relativity 121
7 Electricity and Magnetism 143
3
Contents
1 The Rules of the Rules
1.1 Symmetry . . . . . . . . . . . 9
1.2 A Preview of Noether’s Theorem . . 11
1.3 What Are The Symmetries?. . . . 12
Problems . . . . . . . . . . . . . 16
Lab 1a: Scaling. . . . . . . . . . . 18
3 Images
3.1 Location and Magnification . . . . 46
Aflatmirror,46.—Acurvedmirror,47.
3.2 Real and Virtual Images . . . . . 48
3.3 Angular Magnification . . . . . . 49
Problems . . . . . . . . . . . . . 50
Lab 3a: Images. . . . . . . . . . . 52
Lab 3b: A Real Image . . . . . . . . 54
Lab 3c: Lenses . . . . . . . . . . . 56
Lab 3d: The Telescope . . . . . . . 58
2 The Ray Model of Light
2.1 Rays Don’t Rust . . . . . . . . 21
2.2 Time-Reversal Symmetry. . . . . 21
2.3 Applications . . . . . . . . . . 24
Theinverse-squarelaw,24.—Parallax,25.
2.4 The Speed of Light . . . . . . . 28
Theprincipleofinertia,28.—Measuring
thespeedoflight,28.
2.5 Reflection . . . . . . . . . . . 30
Seeingby reflection, 30.—Specular
reflection,30.
Problems . . . . . . . . . . . . . 32
Lab 2a: Time-Reversal and Reflection
Symmetry . . . . . . . . . . . . . 36
Lab 2b: Models of Light . . . . . . . 40
Lab 2c: The Speed of Light in Matter . . 43
4 Conservation of Mass and
Energy
4.1 Conservation of Mass . . . . . . 62
4.2 Conservation of Energy . . . . . 63
Kineticenergy,63.—Gravitationalenergy,
64.—Emissionandabsorptionoflight,
66.—Howmanyformsofenergy?,67.
4.3 Newton’s Law of Gravity . . . . . 69
4.4 Noether’s Theorem for Energy. . . 72
4.5 Equivalence of Mass and Energy . 74
Mass-energy, 74.—Thecorrespondence
principle,75.
Problems . . . . . . . . . . . . . 77
Lab 4a: Conservation Laws. . . . . . 80
Lab 4b: Conservation of Energy . . . . 84
5 Conservation of Momentum
5.1 Translation Symmetry . . . . . . 90
5.2 The Strong Principle of Inertia . . . 91
Symmetryandinertia,91.—Inertialand
noninertialframes,93.
5.3 Momentum . . . . . . . . . . . 96
Conservation ofmomentum, 96.—
4
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Momentumcomparedtokineticenergy,
100.—Force, 101.—Motion in two
dimensions,103.
Problems . . . . . . . . . . . . . 108
Lab 5a: Interactions . . . . . . . . . 110
Lab 5b: Frames of Reference . . . . . 114
Lab 5c: Conservation of Momentum . . 116
Lab 5d: Conservation of Angular Momen-
tum . . . . . . . . . . . . . . . . 118
7.2 Circuits . . . . . . . . . . . . 149
Current,149.—Circuits,151.—Voltage,
152.—Resistance,153.—Applications,155.
7.3 Electromagnetism . . . . . . . . 159
Magneticinteractions,159.—Relativityre-
quiresmagnetism,160.—Magneticfields,
163.
7.4 Induction. . . . . . . . . . . . 166
Electromagneticsignals,166.—Induction,
169.—Electromagneticwaves,171.
7.5 What’s Left? . . . . . . . . . . 173
Problems . . . . . . . . . . . . . 176
Lab 7a: Charge. . . . . . . . . . . 180
Lab 7b: Electrical Measurements . . . 182
Lab 7c: Is Charge Conserved? . . . . 184
Lab 7d: Circuits . . . . . . . . . . 186
Lab 7e: Electric Fields . . . . . . . . 192
Lab 7f: Magnetic Fields . . . . . . . 194
Lab 7g: Induction . . . . . . . . . . 198
Lab 7h: Light Waves . . . . . . . . 200
Lab 7i: Electron Waves . . . . . . . 204
6 Relativity
6.1 The Principle of Relativity. . . . . 123
6.2 Distortion of Time and Space . . . 125
Time,125.—Space,126.—Nosimultaneity,
126.—Applications,128.
6.3 Dynamics . . . . . . . . . . . 133
Combination of velocities, 133.—
Momentum,134.—Equivalenceofmass
andenergy,137.
Problems . . . . . . . . . . . . . 139
7 Electricity and Magnetism
7.1 Electrical Interactions . . . . . . 143
Newton’squest,144.—Chargeandelectric
field,145.
Appendix 1: Photo Credits 207
5
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