Introduction to Geometrical Optics

328 Pages·2003·6.721 MB·English

by  Milton Katz

I n t r o d u c t i o n to
Geometrical Optics
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I n t r o d u c t i on to
Geometrical Optics
Milton Katz
state university of New York
US* World Scientific
«• NNeeww J Jeersrseeyy • •L Loonnddoonn • •S Simin gapore • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
First published in 1994 by Penumbra Publishing Co.
Illustrations: Russel Hayes and George Zikos
INTRODUCTION TO GEOMETRICAL OPTICS
Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
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ISBN 981-238-202-X
ISBN 981-238-224-0 (pbk)
Printed by Fulsland Offset Printing (S) Pte Ltd, Singapore
TABLE OF CONTENTS
PREFACE xiii
ACKNOWLEDGMENTS xiv
CHAPTER 1: LIGHT
1.1 Introduction 1
1.2 The Electromagnetic Spectrum 1
1.2.1 Wave Motion 1
1.2.2 Wavelength and Frequency Range 2
1.2.3 Measurement of the Velocity of Light 3
1.3 Light Sources 4
1.3.1 Self-Luminous 4
1.3.1.1 Incandescent Sources 4
1.3.1.2 Electric Arcs and Discharges 4
1.3.1.3 Fluorescent Lamps 4
1.3.1.4 Lasers 4
1.3.2 Light Reflecting Sources 4
1.4 Optical Media 4
1.4.1 Transparent, Colored and Translucent Materials 5
1.4.2 Reflecting and Opaque Materials 5
1.5 Point and Extended Sources 5
1.6 Rectilinear Propagation of Light 6
1.6.1 Pinhole Camera 6
1.6.2 Propagation of Light in Nonhomogeneous Media 6
1.7 The Corpuscular and Wave Theory of Light 7
1.8 Umbra, Penumbra and Eclipses 8
1.9 Real and Virtual Objects and Images 10
1.10 Stops 10
1.10.1 Field Stop 10
1.10.2 Aperture Stop 10
1.10.3 Baffles 11
1.11 Optical System 11
1.11.1 Vergence and Diopters 11
1.12 Pencils and Beams of Light 12
1.12.1 Point Source 12
1.12.2 Extended Source 12
1.13 Visual Angle 12
CHAPTER 2: REFLECTION AT PLANE MIRRORS
2.1 Reflection 15
2.2 The Law of Reflection 15
2.2.1 Mirror Rotation 16
2.2.1.1 The Galvanometer 16
2.2.1.2 Measurement of Mirror Rotation Angles 16
v
vi Contents
2.2.1.3 Hadley's Sextant 17
2.3 Image of a Point Formed by a Plane Mirror 17
2.3.1 Image of an Extended Object 18
2.3.2 Inversion and Reversion of Reflected Images 18
2.4 Constant Deviation by Two Inclined Mirrors 19
2.4.1 Applications of Constant Angles of Deviation 20
2.5. Multiple Images Produced by Two Inclined Mirrors 21
2.5.1 Construction of Images 21
2.5.1.1 Image Series J 21
2.5.1.2 Image Series K 23
2.5.2 Number of J and K Images 23
2.5.3 The Kaleidoscope 25
2.6. Ray Paths to the Eye 26
2.7. Field of View of a Plane Mirror 26
2.8 Reflection According to Newton's Corpuscular Theory 28
2.9. Reflection According to Huygens' Wave Theory 29
CHAPTER 3: REFRACTION OF LIGHT
3.1 The Law of Refraction 33
3.2 The Reversibility of Light 33
3.3 Refraction and Particle Motion 33
3.3.1 Vector Diagram - Perpendicular Component Increased by Refraction 34
3.3.2 Vector Diagram - Tangential Component Decreased by Refraction 34
3.3.3 Huygens'Construction for Refraction 35
3.4 Absolute Index of Refraction and Snell's Law 36
3.5 Construction of Refracted Ray 37
3.6 Deviation of the Refracted Ray 38
3.7 Dispersion 38
3.8 Total Internal Reflection 38
3.9 Optical Path Length 39
3.10 Fermat's Principle 40
CHAPTER 4: REFRACTION BY PLANES, PLATES AND PRISMS
4.1 Exact Ray Tracing Through a Plane Refracting Surface 43
4.2 Exact Ray Tracing Through a Parallel Plate 44
4.3 Displacement of Rays Obliquely Incident on a Tilted Plate 46
4.4 Refraction Through Prisms 47
4.5 Prism Geometry 48
4.6 Limits to Prism Transmission: Grazing Incidence and Emergence 48
4.7 Minimum Deviation by a Prism 49
4.8 Calculation of the Path of a Ray Through a Prism 50
4.9 Calculation of the Total Deviation by a Prism 50
CHAPTER 5: PARAXIAL REFRACTION AT PLANES, PLATES AND PRISMS
5.1 Paraxial Refraction at a Plane Surface 53
5.2 Paraxial Image Formation by Parallel Plates 54
5.3 Reduced Thickness 56
Contents vii
5.4 Thin Prisms 56
5.5 Ophthalmic Prisms, Centrads and the Prism-Diopter 57
5.7 Obliquely Combined Prisms 59
5.8 Risley Prisms 61
CHAPTER 6: REFRACTION AND REFLECTION AT SPHERICAL SURFACES
6.1 Sign Convention 65
6.2 Refraction at a Single Spherical Refracting Surface 66
6.2.1 The Paraxial Image Equation 66
6.2.2 Focal Points and Focal Lengths 67
6.2.3 Refracting Power 69
6.2.4 Construction of On-Axis Image Points 69
6.2.5 Construction of the Focal Points 70
6.2.6 Construction of Off-Axis Image Points 71
6.2.7 Image Positions as an Object Approaches the Surface 72
6.2.8 Possible Positions of the Image 73
6.2.9 Lateral Magnification 73
6.3 The Image Equation for Plane Surfaces 74
6.4 Newtonian Equations 74
6.5 The Focal Planes and Focal Images of a Spherical Refracting Surface 75
6.6 The Smith-Helmholtz Formula or Lagrange Invariant 76
6.7 Reflection by Spherical Mirrors 76
6.7.1 The Paraxial Image Equation 76
6.7.2 The Focal Points of a Spherical Mirror 78
6.7.3 Construction of Axial Image Points for Spherical Mirrors 79
6.7.4 Construction of Focal Points of a Spherical Mirror 79
6.7.5 Construction of Off-Axis Image Points Formed by a Mirror 79
6.7.6 Image Positions as an Object Approaches a Spherical Mirror 80
6.7.7 Possible Positions of the Image Formed by a Spherical Mirror 81
6.7.8 Lateral Magnification by Spherical Mirrors 81
6.7.9 Newtonian Equations for a Spherical Mirror 81
6.7.10 The Field of View of a Spherical Mirror 82
6.8 Angular Magnification 83
6.9 Vergence, Power and Curvature 84
6.9.1 Vergence and Power 84
6.9.2 Curvature and Vergence 85
6.9.3 Curvature and Sagitta 86
6.9.4 The Correction of Lens Measure Readings 87
CHAPTER 7: THIN LENSES
7.1 Convex and Concave Lenses 93
7.2 Lens Nomenclature 94
7.3 The Optical Center of a Lens 94
7.4 The Thin Lens 95
7.5 The Thin Lens Equation 95
7.6 Focal Lengths 97
7.7 Construction of the Off-Axis Image Point 97
viii Contents
7.8 Lateral Magnification 98
7.9 Vergence Equations and Power of a Thin Lens 99
7.9.1 Thin Lens Power in Non-Uniform Medium 99
7.10 Object and Image Formation by a Thin Lens 100
7.10.1 Positive Lenses 100
7.10.2 Negative Lenses 100
7.10.3 Applications of Lenses with Various Conjugates 102
7.10.4 The Minimum Separation Between a Real Object and Its Real Image 102
7.11 Newtonian Equations 103
7.12 The Focal Planes and Focal Images of a Thin Lens 103
7.13 Prismatic Power of a Thin Lens 104
7.14 Stops and Pupils of Lens Systems 105
7.14.1 Procedure for Finding the Stops, Pupils and Field of View of a Thin Lens 106
CHAPTER 8: ROTATIONALLY SYMMETRICAL SYSTEMS
8.1 Introduction 111
8.2 Paraxial Construction of the Image 111
8.3 Paraxial Calculation of Images Through an Optical System 112
8.4 The Vergence Form of the Refraction and Transfer Equations 115
8.4.1 Iterative Use of the Vergence Equations 115
CHAPTER 9: ASTIGMATIC LENSES
9.1 Astigmatic Images 119
9.2 Curvature and Power in Principal and Normal Sections 121
9.3 Power in Oblique Meridians of a Cylinder 123
9.3.1 The Oblique Power Equation 123
9.4 Thin Astigmatic Lenses 124
9.4.1 Forms of Astigmatic Lenses 125
9.5 Transposition of Flat Prescriptions 127
9.6 The Circle of Least Confusion and the Spherical Equivalent Lens 128
9.7 The Circle of Least Confusion for Any Object Distance 129
9.8 The Lengths of the Focal Lines and the Diameter of the CLC 130
9.9 Obliquely Combined Cylinders 130
CHAPTER 10: THICK LENS SYSTEMS: PART I
10.1 Introduction 139
10.2 The Cardinal Points 139
10.2.1 The Principal Planes and Points 139
10.2.2 The Nodal Points 140
10.2.3 Construction of the Nodal Points 141
10.2.4 Other "Cardinal" Points 143
10.3 The Newtonian Equations for a Thick System 143
10.4 The Refraction Equations for a Thick System 144
10.5 The Lateral Magnification of a Thick Lens 144
10.6 Summary of Vergence Equations for a Thick Lens System 145
10.7 Lateral, Axial and Angular Magnification 145
10.7.1 Lateral Magnification: Y 145
Contents ix
10.7.2 Axial Magnification: X 145
10.7.3 Angular Magnification: Ma 146
CHAPTER 11: THICK LENS SYSTEMS: PART II
11.1 The Gullstrand Equations 149
11.1.1 Equivalent Power 149
11.1.2 The Position of the Second Focal Point F' 151
11.1.3 The Position of the Second Principal Point H' 151
11.1.4 The Positions of the First Focal and Principal Points F and H 151
11.2 Distances Referred to Principal Planes 152
11.2.1 Summary of the Gullstrand Equations 152
11.2.1. IThe Positions of the Nodal Points N and N' 153
11.2.2 The Effect of Lens Thickness on the Positions of the Principal Planes 154
11.2.3 The Effect of Lens Shape on the Position of the Principal Planes 155
11.2.4 Telephoto and Wide-Angle Lenses 155
11.3 Vertex Power 157
11.4 Vertex Power and Ophthalmic Lenses 157
11.5 Effective Power 158
11.5.1 The Relationship of Effective Power to Vertex Power 159
11.6 Combination of Two Thick Lens 159
11.7 The Gullstrand Schematic Eye 161
11.7.1 Procedure for Calculating Cardinal Points of the Schematic Eye 161
11.8 Purkinje Images 164
11.8.1 Calculation of Purkinje Image I 164
11.8.2 Calculation of Purkinje Image II 165
11.8.3 Calculation of Purkinje Image III 166
CHAPTER 12: STOPS, PUPILS AND PORTS
12.1 Types of Stops 173
12.2 Pupils 173
12.3 The Field Stop and the Entrance and Exit Ports 174
12.4 Field of View and Vignetting 175
12.5 Procedure for Finding the Stops, Pupils, Ports and Field of View 176
CHAPTER 13: NUMERICAL APERTURE, f-NUMBER, AND RESOLUTION
13.1 Numerical Aperture 183
13.2 f-Number 183
13.3 Angular Resolution 185
13.4 Linear Resolution 187
13.5 Resolution Charts 187
13.6 Snellen Charts 188
13.7 Modulation Transfer Function 189
13.8 The Numerical Aperture of a Fiber Optic 191
CHAPTER 14: MAGNIFIERS AND MICROSCOPES
14.1 Introduction 195
14.2 Visual Angle and Angular Magnification 195