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.

Reviews 1

Choice Review

Most standard optics books (e.g., works by F. Jenkins and H. White, M. Born and E. Wolf, E. Hecht and A. Zajac, and F. Pedrotti and L. Pedrotti) routinely divide the subject into geometric optics and physical optics, with geometric covered in a third the space of physical optics. On the other hand, a working knowledge of optical communications, lasers, and imaging requires a firm understanding of geometric optics. Eustace Dereniak (Univ. of Arizona) and Teresa Dereniak effectively fulfill this need at a level accessible to undergraduates as well as practitioners. The rigorous mathematical treatment is restricted to geometry and algebra. The authors cover the conventional topics, e.g., reflection, refraction, image formation, mirrors, lenses, and aberrations, but the practical detail they provide is normally only found in more specialized and less accessible advanced works. The book's great virtue is the extensive number of problems and worked examples that accompany the text. However, the book has the feel of transcribed lectures and sometimes lacks coherence. The work lacks the matrix treatment of imaging optics and reference to widely available ray tracing computer programs (e.g., CODE V). For such a practical volume, appendix B's 18 pages of numbers and several specialized graphs seem unnecessary. Summing Up: Recommended. Lower-division undergraduate through professional collections. M. Coplan Institute for Physical Science and Technology

Preface	p. ix
1 Light propagation	p. 1
1.1 Background history	p. 1
1.2 Nature of light	p. 2
1.3 Wavefronts and rays	p. 8
1.4 Index of refraction	p. 10
1.5 Optical path length (OPL) and reduced thickness	p. 12
1.6 Coordinate system	p. 16
1.7 Solid angle	p. 17
1.8 Polarization	p. 19
Problems	p. 22
Bibliography	p. 28
2 Reflections and refractions at optical surfaces	p. 30
2.1 Rays	p. 30
2.2 Fermat's principle	p. 31
2.3 Snell's law	p. 34
2.4 Reflection versus refraction at an interface	p. 37
2.5 Handedness/parity	p. 39
2.6 Plane parallel plate (PPP) and reduced thickness	p. 40
Problems	p. 45
Bibliography	p. 48
3 Image formation	p. 49
3.1 Pinhole camera	p. 49
3.2 Object representation	p. 52
3.3 Lenses	p. 54
3.4 Image types	p. 58
Problems	p. 59
Bibliography	p. 60
4 Mirrors and prisms	p. 61
4.1 Plane mirrors	p. 61
4.2 Deviating prisms	p. 65
4.3 Dispersing prisms	p. 69
4.4 Glass	p. 80
4.5 Plastic optical materials	p. 87
Problems	p. 88
Bibliography	p. 95
5 Curved optical surfaces	p. 96
5.1 Optical spaces	p. 96
5.2 Sign convention	p. 97
5.3 Ray tracing across a spherical surface	p. 98
5.4 Sag of spherical surfaces	p. 104
5.5 Paraxial ray propagation	p. 105
5.6 Gaussian equation of a single surface	p. 111
5.7 Focal lengths and focal points	p. 112
5.8 Transverse magnification	p. 113
Problems	p. 116
Bibliography	p. 121
6 Thin lenses	p. 122
6.1 Lens types and shape factors	p. 122
6.2 Gaussian optics - cardinal points for a thin lens	p. 123
6.3 Mapping object space to image space	p. 125
6.4 Magnification	p. 132
6.5 F-number	p. 136
6.6 ZZ' diagram	p. 139
6.7 Thick lens equivalent of thin lens	p. 145
6.8 Newtonian optics	p. 148
6.9 Cardinal points of a thin lens	p. 149
6.10 Thin lens combinations	p. 150
Problems	p. 158
Bibliography	p. 163
7 Thick lenses	p. 164
7.1 Principal points	p. 164
7.2 Focal points	p. 167
7.3 Nodal points	p. 168
7.4 Determining cardinal points	p. 170
7.5 Thick lens combinations	p. 175
Problems	p. 187
Bibliography	p. 191
8 Mirrors	p. 193
8.1 Plane mirrors	p. 194
8.2 Spherical mirrors	p. 197
8.3 Volume of material in a spherical dome	p. 208
8.4 Aspheric surfaces	p. 210
8.5 Aspheric surface sag	p. 218
Problems	p. 220
Bibliography	p. 225
9 Optical apertures	p. 226
9.1 Aperture stop	p. 227
9.2 Field stop	p. 236
9.3 F-number and numerical aperture	p. 238
9.4 Depth of focus and depth of field	p. 244
9.5 Hyperfocal distance	p. 246
Problems	p. 248
Bibliography	p. 254
10 Paraxial ray tracing	p. 255
10.1 Ray tracing worksheet	p. 256
10.2 Chief and marginal rays	p. 263
10.3 Optical invariants	p. 265
10.4 Marginal and chief ray trace table	p. 269
10.5 Scaling of chief and marginal rays	p. 277
10.6 Whole system scaling	p. 279
Problems	p. 282
Bibliography	p. 291
11 Aberrations in optical systems	p. 292
11.1 Diffraction	p. 292
11.2 Diffraction and aberrations	p. 295
11.3 Monochromatic lens aberrations	p. 295
11.4 Aberration induced by a PPP	p. 310
11.5 Chromatic aberration	p. 313
11.6 Summary of aberrations	p. 322
Problems	p. 323
Bibliography	p. 326
12 Real ray tracing	p. 328
12.1 Approach	p. 328
12.2 Skew real ray trace	p. 330
12.3 Refraction at the spherical surface	p. 335
12.4 Meridional real ray trace	p. 340
12.5 Q-U method of real ray trace	p. 341
Problems	p. 346
Bibliography	p. 346
Appendix A Linear prism dispersion design	p. 347
A.1 Wedge approximation	p. 347
A.2 Two-material prism	p. 347
A.3 Least-squares solution	p. 349
A.4 Three-material prism	p. 349
A.5 Concluding remarks	p. 349
Appendix B Linear mixing model	p. 351
Appendix C Nature's optical phenomena	p. 379
C.1 Rainbows	p. 379
C.2 Secondary rainbows	p. 382
C.3 Halos	p. 385
C.4 Mirages	p. 386
Appendix D Nomenclature for equations	p. 388
Appendix E Fundamental physical constants and trigonometric identities	p. 391
Glossary	p. 396
Index	p. 402

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