Geometrical And Trigonometric Optics

Optics has recently evolved into one of the most flourishing fields in physics, with photonics finding increasing application in products such as optical thermometers, camera monitors and LED lighting, plus numerous military applications. This book covers the geometrical aspects of optics, the fundamental level of understanding the technology. Beginning with how light is generated and how fast it travels, the book discusses how materials interact with light, how various materials affect the velocity of light, and the ramifications of change in the speed of light. The concept of the index of refraction, and how it is used with Snell's law to produce image forming systems, is developed. An ideal textbook for advanced undergraduate level courses in geometrical optics, this book will also interest those wanting to learn the concepts and theory of geometrical optics. Each chapter contains worked examples, and there are exercises to reinforce the reader's understanding of material.

Preface	p. ix
Light propagation	p. 1
Background history	p. 1
Nature of light	p. 2
Wavefronts and rays	p. 8
Index of refraction	p. 10
Optical path length (OPL) and reduced thickness	p. 12
Coordinate system	p. 16
Solid angle	p. 17
Polarization	p. 19
Problems	p. 22
Bibliography	p. 28
Reflections and refractions at optical surfaces	p. 30
Rays	p. 30
Fermat's principle	p. 31
Snell's law	p. 34
Reflection versus refraction at an interface	p. 37
Handedness/parity	p. 39
Plane parallel plate (PPP) and reduced thickness	p. 40
Problems	p. 45
Bibliography	p. 48
Image formation	p. 49
Pinhole camera	p. 49
Object representation	p. 52
Lenses	p. 54
Image types	p. 58
Problems	p. 59
Bibliography	p. 60
Mirrors and prisms	p. 61
Plane mirrors	p. 61
Deviating prisms	p. 65
Dispersing prisms	p. 69
Glass	p. 80
Plastic optical materials	p. 87
Problems	p. 88
Bibliography	p. 95
Curved optical surfaces	p. 96
Optical spaces	p. 96
Sign convention	p. 97
Ray tracing across a spherical surface	p. 98
Sag of spherical surfaces	p. 104
Paraxial ray propagation	p. 105
Gaussian equation of a single surface	p. 111
Focal lengths and focal points	p. 112
Transverse magnification	p. 113
Problems	p. 116
Bibliography	p. 121
Thin lenses	p. 122
Lens types and shape factors	p. 122
Gaussian optics - cardinal points for a thin lens	p. 123
Mapping object space to image space	p. 125
Magnification	p. 132
F-number	p. 136
ZZ' diagram	p. 139
Thick lens equivalent of thin lens	p. 145
Newtonian optics	p. 148
Cardinal points of a thin lens	p. 149
Thin lens combinations	p. 150
Problems	p. 158
Bibliography	p. 163
Thick lenses	p. 164
Principal points	p. 164
Focal points	p. 167
Nodal points	p. 168
Determining cardinal points	p. 170
Thick lens combinations	p. 175
Problems	p. 187
Bibliography	p. 191
Mirrors	p. 193
Plane mirrors	p. 194
Spherical mirrors	p. 197
Volume of material in a spherical dome	p. 208
Aspheric surfaces	p. 210
Aspheric surface sag	p. 218
Problems	p. 220
Bibliography	p. 225
Optical apertures	p. 226
Aperture stop	p. 227
Field stop	p. 236
F-number and numerical aperture	p. 238
Depth of focus and depth of field	p. 244
Hyperfocal distance	p. 246
Problems	p. 248
Bibliography	p. 254
Paraxial ray tracing	p. 255
Ray tracing worksheet	p. 256
Chief and marginal rays	p. 263
Optical invariants	p. 265
Marginal and chief ray trace table	p. 269
Scaling of chief and marginal rays	p. 277
Whole system scaling	p. 279
Problems	p. 282
Bibliography	p. 291
Aberrations in optical systems	p. 292
Diffraction	p. 292
Diffraction and aberrations	p. 295
Monochromatic lens aberrations	p. 295
Aberration induced by a PPP	p. 310
Chromatic aberration	p. 313
Summary of aberrations	p. 322
Problems	p. 323
Bibliography	p. 326
Real ray tracing	p. 328
Approach	p. 328
Skew real ray trace	p. 330
Refraction at the spherical surface	p. 335
Meridional real ray trace	p. 340
Q-U method of real ray trace	p. 341
Problems	p. 346
Bibliography	p. 346
Linear prism dispersion design	p. 347
Wedge approximation	p. 347
Two-material prism	p. 347
Least-squares solution	p. 349
Three-material prism	p. 349
Concluding remarks	p. 349
Linear mixing model	p. 351
Nature's optical phenomena	p. 379
Rainbows	p. 379
Secondary rainbows	p. 382
Halos	p. 385
Mirages	p. 386
Nomenclature for equations	p. 388
Fundamental physical constants and trigonometric identities	p. 391
Glossary	p. 396
Index	p. 402
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Geometrical And Trigonometric Optics

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