Contents
Preface .......................................................................................................................xi 1. Basic Terms and Concepts..................................................................................1
Sources, Light Rays, and Pencils .......................................................................3 Vergence .............................................................................................................4 Refraction and Snell’s Law .................................................................................7 Summary ..........................................................................................................10 Self-Assessment Problems ...............................................................................13
2. Refraction at Spherical Surfaces .................................................................... 15 Converging and Diverging Spherical Surfaces ...............................................15 A Word on Sign Conventions ..........................................................................19 Primary and Secondary Focal Points ...............................................................19 A Very Handy Formula ....................................................................................21 Image Formation by Spherical Surfaces ..........................................................24
Real Images ..................................................................................................24 Virtual Images ..............................................................................................26
Summary ..........................................................................................................27 Self-Assessment Problems ...............................................................................28
3. The Vergence Relationship .............................................................................. 29 More on Vergence ............................................................................................29 Linear Sign Convention...................................................................................33 Vergence Relationship .....................................................................................34 Sample Problems ..............................................................................................35
Sample Problem 1: Converging Surface ......................................................36 Sample Problem 2: Diverging Surface ........................................................38 Sample Problem 3: Locating the Object .....................................................40 Sample Problem 4: A Flat (Plane) Refracting Surface ................................41
Summary ..........................................................................................................44 Self-Assessment Problems ...............................................................................45

4. Thin Lenses ...................................................................................................... 47 Ray Tracing ......................................................................................................49 Vergence Relationship .....................................................................................54 Newton’s Relation ............................................................................................59 Summary ..........................................................................................................60 Self-Assessment Problems ...............................................................................60
5. Optical Systems with Multiple Surfaces ......................................................... 63 Multiple Thin Lens Systems............................................................................63 Virtual Objects .................................................................................................68 Thick Lenses ....................................................................................................70 Summary ..........................................................................................................75 Self-Assessment Problems ...............................................................................75
6. Thick Lenses ..................................................................................................... 77 Definitions ........................................................................................................77 Back and Front Vertex Power ..........................................................................79 Equivalent Lenses ............................................................................................81
Equivalent Power .........................................................................................81 Locating the Principal Planes ......................................................................81 Sample Problem ...........................................................................................83 Nodal Points .................................................................................................85
Summary ..........................................................................................................86 Self-Assessment Problems ...............................................................................87
7. Ametropia ........................................................................................................ 89 Myopia ..............................................................................................................91 Hyperopia .........................................................................................................95 Lens Effectivity ................................................................................................98 Correction of Ametropia with Laser and Surgical Procedures .....................103 Summary ........................................................................................................105 Self-Assessment Problems .............................................................................105
8. Accommodation ............................................................................................ 107 Vergence Relationship for Accommodation ..................................................109 Accommodation in Ametropia .......................................................................110 Near Point of Accommodation ......................................................................114 Accommodation when Ametropia is Corrected with Spectacles ..................117 Correction of Presbyopia ...............................................................................122 Summary ........................................................................................................124 Self-Assessment Problems .............................................................................124
9. Cylindrical Lenses and the Correction of Astigmatism ................................ 127 Lens Crosses ...................................................................................................127 Lens Formulae/Prescriptions ........................................................................130 Image Formation: Point Sources ...................................................................133 Image Formation: Extended Sources ............................................................135

Power in an Oblique Meridian of a Cylindrical Lens ...................................136 Astigmatism: Definitions and Classifications ................................................138 Jackson Crossed-Cylinder Test ......................................................................141 Spherical Equivalency ....................................................................................144 What Does a Person with Astigmatism See? ................................................145 Summary ........................................................................................................146 References ......................................................................................................147 Self-Assessment Problems .............................................................................147
10. Prisms ............................................................................................................ 149 Thick and Thin Prisms ..................................................................................149 Prism Diopters ...............................................................................................151 Prismatic Effects of Lenses ............................................................................151 Clinical Applications ......................................................................................158 Summary ........................................................................................................162 Reference ........................................................................................................162 Self-Assessment Problems .............................................................................162
11. Depth of Field ................................................................................................ 165 Blur Circles, Visual Acuity, and Pinholes ......................................................165 Diffraction Caused by Apertures ...................................................................168 Depth of Field and Depth of Focus ...............................................................171 Hyperfocal Distance ......................................................................................176 Summary ........................................................................................................178 Self-Assessment Problems .............................................................................178
12. Magnification and Low Vision Devices ........................................................ 179 Angular Magnification Produced by Plus Lenses .........................................180 Use of Plus Lenses for Low Vision ................................................................183
Magnifying Lens and Bifocal Add
in Combination ..........................................................................................186 Fixed-Focus Stand Magnifiers ...................................................................187 Effective Magnification ..............................................................................191
Electronic Magnifiers for Near .....................................................................193 Telescopes .......................................................................................................194
Galilean Telescopes ....................................................................................194 Keplerian Telescopes ..................................................................................196 An Alternative Formula to Determine a Telescope’s
Angular Magnification ...............................................................................197 A Convenient Clinical Method to Determine a Telescope’s
Angular Magnification ...............................................................................197 Telescope Use in Ametropia ......................................................................199 Telemicroscopes .........................................................................................201
Summary ........................................................................................................203 Further Reading .............................................................................................204 Self-Assessment Problems .............................................................................204

 13. Retinal Image Size ........................................................................................ 207 Spectacle Magnification .................................................................................207 Retinal Image Size in Uncorrected Ametropia .............................................210 Retinal Image Size in Corrected Ametropia .................................................211 Summary ........................................................................................................215 Self-Assessment Problems .............................................................................215
14. Reflection ....................................................................................................... 217 Ray Tracing: Concave, Convex, and Plane Mirrors ......................................217
Concave Mirrors ........................................................................................217 Convex Mirrors ..........................................................................................220 Plane Mirrors .............................................................................................220
Power of Mirrors ............................................................................................221 The Vergence Relationship ...........................................................................225 Reflections and Antireflection Coatings ........................................................231 Purkinje Images ..............................................................................................233 Corneal Topography ......................................................................................237 Summary ........................................................................................................239 Self-Assessment Problems .............................................................................240
15. Aberrations .................................................................................................... 241 The Paraxial Assumption and Seidel Aberrations .........................................241
Longitudinal Spherical Aberration ............................................................242 Coma ..........................................................................................................245 Oblique Astigmatism ..................................................................................246 Curvature of Field ......................................................................................249 Distortion ...................................................................................................250
Wavefront Sensing and Adaptive Optics .......................................................250 Measurement of the Eye’s Monochromatic Aberrations ..........................250 Supernormal Vision ....................................................................................253 Imaging the Fundus ...................................................................................256
Chromatic Aberration ....................................................................................257 Dispersive Power and Constringence ........................................................257 Lateral (Transverse) Chromatic Aberration ..............................................258 Longitudinal Chromatic Aberration ..........................................................260 Chromatic Aberration in the Human Eye .................................................261 The Red–Green Refraction Technique .....................................................263
Summary ........................................................................................................264 References ......................................................................................................265 Self-Assessment Problems .............................................................................266
Answers to Self-Assessment Problems ................................................................ 267 Chapter 1: Basic Terms and Concepts .........................................................267 Chapter 2: Refraction at Spherical Surfaces ................................................268 Chapter 3: The Vergence Relationship .......................................................270 Chapter 4: Thin Lenses ...............................................................................275

Chapter 5: Optical Systems with Multiple Surfaces ...................................279 Chapter 6: Thick Lenses ..............................................................................284 Chapter 7: Ametropia ..................................................................................290 Chapter 8: Accommodation .........................................................................292 Chapter 9: Cylindrical Lenses and the Correction of Astigmatism ...........298 Chapter 10: Prisms .........................................................................................302 Chapter 11: Depth of Field ............................................................................304 Chapter 12: Magnification and Low Vision Devices ....................................305 Chapter 13: Retinal Image Size .....................................................................308 Chapter 14: Reflection ...................................................................................309 Chapter 15: Aberrations .................................................................................314
Appendix A: Entrance and Exit Pupils of Telescopes .......................................... 317 Appendix B: Location of Purkinje Image III ........................................................ 323 Appendix C: Fluid Lenses ..................................................................................... 329 Appendix D: Javal’s Rule ..................................................................................... 335 Appendix E: Derivation of the Paraxial Relationship ......................................... 337 Appendix F: Correction of Chromatic Aberration ............................................... 339
Longitudinal Chromatic Aberration .............................................................339 Lateral (Transverse) Chromatic Aberration ..................................................343
Practice Examinations .......................................................................................... 345 Practice Examination 1 ..................................................................................345 Practice Examination 2 ..................................................................................349
Answers to Practice Examinations ....................................................................... 355 Practice Examination 1 ..................................................................................355 Practice Examination 2 ..................................................................................357
Index .......................................................................................................................361

Jan Vredeman De Vries
1527–c.1604
This book is intended as an approachable and appropriately rigorous introduction to geometrical and visual optics. It is meant to be a concise and learner-friendly resource for clinicians as they study optics for the first time and as they subsequently prepare for licensing examinations. The emphasis is on those optical concepts and problem-solving skills that underlie contemporary clinical eye care.
Because of its clinical utility, a vergence approach is stressed. While formulae are an inevitable part of optics, an attempt has been made to keep these to a mini- mum by emphasizing underlying concepts. Plentiful schematic figures and clinical examples are used to engage reader interest and foster understanding. Every effort is made to provide the reader with an intuitive and clinical sense of optics that will allow him or her to effectively care for patients.
To develop facility in geometrical and visual optics, it is necessary to solve prob- lems. Each chapter includes self-assessment problems of varying complexity with detailed worked-out solutions given at the end of the book. These problems are an integral part of the text.
The second edition has several new features intended to improve student learn- ing. Figures have been upgraded and are now in color. Summaries, sample prob- lems, and tables within chapters are color highlighted. At the conclusion of each chapter, there is a brief summary and list of formulae. New self-assessment prob- lems have been added to many chapters. To meet student demand for additional self-assessment tools, two comprehensive practice examinations (with answers) are