Contents 2-Basics of Light and Propagation 14 Light Phenomena & Properties 14 Light as a Particle 14 Light as an EM wave 14 Some Properties of Wave 14 Propagation of Light: Huygens’ Principle 15 Light Rays and Pencils 16 Definitions 16 Wavefronts & Rays 16 Light Rays 16 Pencil of Rays 17 Beam of Light 17 Vergence of Light 17 Vergence 17 Vergence: Sign Convention Rule 18 Vergence Unit: Dioptre 18 Symbols 19 Vergence: Pictorial Presentation 19 Rectilinear Propagation of Light 19 Shadow Formation 19 Shadows 19 Shadow Formation due to a Point Source 20 Pinhole Camera 21 3-Refraction at the Plane Surfaces 21 Refraction of Light at Plane Surfaces (Part 1) 21 Refraction 21 Refraction: Eye 21 Refraction (cont.) 21 Index of Refraction & Terminology 22 Refraction at Plane Surfaces 22 Refraction: Terminology 22 Refraction at Plane Surfaces (cont.) 22 Absolute & Relative Refractive Index 23 Refractive Index or Index of Refraction 23 Refractive Indices for Some Common Optical Material 23 Relative Refractive Index 23 What Happens to Wavelength & Frequency of Light Waves… 23 Snell’s Law of Refraction 24 The Principle of Reversibility 24 The Principle of Reversibility of Light 24 Refraction by a Rectangular Glass Block 25 Lateral Displacement Calculation 25 Refraction by Multilayer Parallel Glass Surfaces 25 Apparent & Real Depth 26 Critical & Total Internal Reflection 26 Relationship: Critical Angle & Refractive Index 27 Summary 27 Formula: Refraction at Plane Surfaces 27 4-Refraction of Prisms 28 Refraction by Prism 28 Triangular Prism 28 Prism Application 28 Ray Diagrams & Notations 28 Angle of Deviation of a Prism 29 Deviation of Light Ray Through Prism for a Large Apical Angle 29 Derivation 30 Thick Prism Deviation Formula 30 Prism Deviation Calculation 30 Angle of Minimum Deviation 31 Prism Spectrometer 31 Angle of Minimum Deviation of Prism 31 Relationship between Apical Angle, Deviation & Refractive Index 32 How to Calculate Refractive Index of a Prism 32 Formula: Refractive Index of Prism 32 Critical Angle & Total Internal Reflection 33 Prism: Critical Angle 33 Prism: Total Internal Reflection 33 Dispersion 33 Abbe Number 34 Thin Prism, Deviation Prism Power 34 Ophthalmic Prism 34 Angle of Deviation of Glass Prism 34 Deviation Angle for a Series of Apex Angles 35 Thin Prism 35 Thin Prism: Deviation 35 Formulae: Deviation for Thick & Thin Prism 36 Thin Prism PowerΔ 36 Thin Prism Power: Generalised Formula 36 Prism: Summary 37 5-Refraction by Spherical Surfaces 37 Identify the Difference between Converging & Diverging Refracting Surfaces 37 Converging Refracting Surfaces 37 Converging Refracting Surfaces 37 Diverging Refracting Surfaces 38 Apply Sign Conventions 38 Sign Convention 38 Sign Rules: Distance Measurement 38 Sign Rules: Height 38 Sign Rules: Angles & Radius of Curvature 38 Fundamental Paraxial Approximation – Equation for the Image Position 39 Fundamental Paraxial Equation 39 The Power of a Refracting Surface 39 Understand Reduce Vergence Concept 40 Reduced Vergence 40 Derive Gauss Law & its Implementation 40 Gauss Law: Reduced Vergence 40 Calculate Linear Magnification of the Image 41 Linear Magnification 41 Linear Magnification of the Image 41 Understand Focal Point, Focal Length & Refractive Power 41 Focal Points & Focal Lengths 41 Secondary Focal Points & Focal Lengths 41 Primary Focal Points & Focal Lengths 41 Focal Lengths & Focal Points: Converging Surface 42 Focal Lengths & Focal Point: Negative Surface 42 Convex Surface: F’ & f’ 42 Convex Surface F & f 42 Concave Surface: F’ & f’ 43 Concave Surface: F & f 43 Secondary Focal Power & Focal Length: Converging Surface 43 Refracting Power & Focal Length 44 Focal/Refractive Powers 44 Key Formulae: Spherical Refracting Surfaces 44 6-Refraction by Spherical Surfaces (Part 2) 45 Graphical Construction – Image Formations for Convex Refracting Surfaces & Concave Refracting Surfaces 45 Image Formation by a Spherical Surface 45 Key Points for Image Formation 45 Graphical Technique for Image Construction 45 Graphical Technique Procedure 45 Basic Properties of Real & Virtual Images 46 Real & Virtual Image 46 Characteristics of Images 46 Newton’s Equations for a Single Spherical Surface 46 Newton’s Equations: A Single Refracting Spherical Surface 46 Newton’s Equations 47 7-Thin Lenses 47 Types of Lenses & Lens Specifications 47 Types of Lens 47 Convex (Converging) Lenses 47 Concave (Diverging) Lenses 47 Wavefront Reshaping by Convex Lens 48 Wavefront Reshaping by Concave Lens 48 Sphericalens Specification 48 Spherical Len Notation 48 Thin Lens: Definition 48 Focal Lengths & Focal Points 49 Focal Lengths & Power: Thin Lens 49 Image Formation by Thin Lens: Graphical Construction of Images using Thin Convex & Concave Lenses 49 Thin Lens Image Formation 49 Graphical Construction: Image Formation Converging Lens 50 Graphical Construction: Image Formation Diverging Lens 50 Ray Diagram: Object Outside 2F 50 Ray Diagram: Object at 2F 50 Ray Diagram: Object Between F & 2F 51 Ray Diagram: Object at F 51 Ray Diagram: Object Inside F 51 Thin Lenses: Summary Ray Tracing 51 Thin Lens Equations (Conjugate Foci Formula) 52 Thin Lens Equation: Derivation 52 Simplified Version: Thin Lens 52 Thin Lens Formula 53 Lens Makers Formula 53 Image Magnification 54 Image Magnification: Thin Lens 54 Effectivity of Thin Lens 54 Lens Effectivity: Concept 54 Effectivity 54 Lens Effectivity 55 Newton’s Equations 55 Newton’s Equations: Single Refracting Spherical Surface 55 Newton’s Equation: Thin Lens 56 Spherometer & Sag Formula 56 Spherometers 56 The Sag Formula 56 8-Lens Systems 57 2 Thin Lenses in Contact 57 2 Thin Lenses in Contact: Equivalent Power 57 2 Thin Lenses in Separation 58 Ray Tracing: 2 Lens System 58 Simple Lens Systems 58 Vertex Powers & Vertex Focal Lengths 58 Back Vertex Power (BVP) 59 Back Vertex Focal Length 59 Front Vertex Power (FVP) 59 Front Vertex Focal Length 60 Key Formulae & Notations 60 Equivalent Lens System 60 Equivalent Lens System: Principal Points 60 Equivalent Power & Focal Lengths 61 Derivation of the Equivalent Power Formula for a Simple 2 Thin Lens System in Air: Notation 61 Image Formation 62 Image Information: A Simple Thin Lens System 62 Recall: Newton’s Formulae – A Single Thin Lens 62 Newton’s Formulae: A Simple 2 Thin Lens System 62 The Conjugate Foci Relationship 63 Step-Along Vergence 63 Recall: Vergence Effectivity 64 Step-Along Method for Image Information 64 Step-Along Image Information: Magnification 64 9-Thick Lenses 65 Thick Lens Notations 65 Surface Powers of a Thick Lens 65 Thick Lenses 65 A Simple Thin Lens System 65 Back & Front Vertex Powers 66 Equivalent Power of a Thick Lens 66 Difference Between Vertex, Surface & Equivalent Powers 66 Thick Lens Powers 67 Equivalent Thick Lens System 67 Equivalent Thick Lens System: Focal Lengths 67 Cardinal Points 67 2nd Principal Point & 2nd Focal Point 68 1st Principal Point & 1st Focal Point 68 Principal Planes as a Reference 69 Nodal Points 70 Nodal Points & Principal Planes 70 Location of Principal Points & Planes 70 1st Principal Plane Location 70 2nd Principal Plane Location 71 Graphical Construction 71 Graphical Construction: Image Formation 71 Image Formation: Positive Thick Lens 71 Newton’s Formulae 72 10-Thick Lenses (Part 2) 72 Recap 72 Recap Thick Lens: Power & Focal Length Equations 73 Concept of Undeviated Ray 74 Image Formation: Positive Thick Lens 74 Undeviated Ray when Pass through Principal Points 74 Gauss’s Law – Magnification 75 Gauss’s Law: Thick Lens 75 Gauss’s Law: Thick Lens Magnification 75 The Effect of Lens Shape/Form on Principal Plane Location 75 Effect of Lens Shape on Principal Plane Location 76 Image Formation of Thick Lens Using Various Methods 76 Practice Problem (10.4) 76 Practice Problem (10.6) 78 11-Reflection & Mirrors 80 Reflection of Light at Plane Surfaces 80 Law of Reflection of Light 81 Image Formation by a Plane Mirror 81 Image of a Point Object Formed by a Plane Mirror 81 How do we see an Extended Object by a Plane Mirror? 81 What is the Minimum Size of a Plane Mirror Required by a Person to see Their Entire Length? 82 Image Reversion in a Plane Mirror 82 Characteristics of the Image Formed by Reflection at a Plane Mirror 82 Application 82 Reflection of Light at Curved Surfaces: Mirrors 83 Spherical Mirrors 83 Narrow Aperture Concave Mirror 84 Narrow Aperture Convex Mirror 84 A Wide Aperture Effect on Both Concave & Convex Mirrors 84 Wide Aperture Concave Mirror 84 Spherical Aberration in Lenses 85 Reflection of Light at Curved Surfaces 85 Key Distinction between Reflection & Refraction 85 Relationship between Focal Length & Radius of Curvature 85 Focal Points 86 Powers of a Spherical Reflecting Surface (mirrors) 86 Image Formation by Spherical Mirrors – Graphical Construction 86 Image Formation of Concave Mirror: Graphical Construction 86 Image Formation of Concave Mirror: Object Located at C 87 Image Formation of Concave Mirror: Object Located Between C & F 87 Image Formation of Concave Mirror: Object Located at F 87 87 Image Formation of Convex Mirror: Graphical Construction 88 Image Formation of Concave Mirror: Real Object Located Inside Focus 88 Calculations for Images 89 The Conjugate Foci Relationship for Spherical Mirrors 89 Sign Rules: Distance Measurement 89 Sign Rules: Focal Length & Radius of Curvature of Spherical Mirrors 90 Fresnel’s Law 90 12-Simple Magnifiers 91 Magnification 91 Retinal Image Size 91 Magnifiers 91 Definitions 92 Accommodation 92 Near Point or LDDV 92 Far Point & Range of Vision 92 Emmetropic Eye & Ametropic Eye 92 Ametropia Classification 93 Spherical Ametropia 93 Magnification of an Eye 94 Visual Angle 94 Why Magnifier is Needed? 94 Low Vision Aid 95 Angular Magnification (M) 95 Angular Magnification: Derivation 95 Two Extreme Magnifications – Nominal & Maximum Angular Magnification 96 What happens if the object is placed at the first principal focal point of the simple magnifier lens? 96 What happens when the image is formed at the least distance of distinct vision (LDDV)? 97 Effect of magnification when eye is at the second focal length of a simple magnifier 97 Different Types of Magnifiers 97 Field of View of a Simple Magnifier 98 Distance Magnification 99 M-Equation 99 Magnification Formulae: Summary 100 13-Compound Magnifiers Telescopes 100 Compound Magnifiers 100 Telescopes 100 Telescope Types 101 Keplerian Telescope 101 Keplerian Telescope: Image Formation 101 Keplerian Telescopes: Afocal System 101 Keplerian Telescope: Magnification (M) 102 Keplerian Telescope: Key Points 103 Galilean Telescope 103 Galilean Telescope: Afocal Configuration 104 Galilean Telescope: Derivation for Angular Magnification in Afocal Setting 104 Galilean Telescope Application: Low Vision Aid (Telescopic Spectacle Unit) 105 Telemicroscope 105 Summary 105 Keplerian Telescope 105 Galilean Telescope 105 14-Microscopes 106 Compound Microscope 106 Microscope: Image Formation Ray Tracing 106 Microscope: Magnification 106 Microscope: Image Formation in Different Operating Conditions 107 Microscopes: Image Formation in Maximum Magnification 107 Microscope: Magnification Derivation in Normal Use Condition 107 Microscope Setting 108 Microscope Setting: Image Formation at Infinity 108 Microscope: Magnification Derivation when Image Formation is at Infinity 109 15-Apertures & Field Stops 109 Definition of Terms 110 Aperture Stops 110 Aperture Stop (Physical Aperture Stop) 111 Aperture Stop & Entrance Pupil 111 Entrance Pupil 111 How to Locate Entrance Pupil of Multi-Element Optical System? 112 Entrance Pupil 112 Entrance Pupil & Actual Iris of the Human Eye 112 Distinguish the figure in which entrance pupil is same as the aperture stop 112 Exit Pupil 113 Entrance & Exit Pupils 113 Chief Ray (C-Ray) & Marginal Ray (M-Ray) 113 Aperture & Field Stops 114 Field Stops & Windows 114 How to Calculate Field of View 114 Entrance & Exit Pupils with Telescopes 115 Field Stop, Entrance & Exit Pupils with Telescopes 115 Entrance & Exit Pupils with Telescopes 115 Entrance & Exit Pupils in Galilean Telescope 116 Problem (1): Illustration to represent the superposition of stops, pupil, & window on the optical system 116 Numerical Aperture 116 F-number 117 Depth of Focus 117 Depth of Field 117 16-Wave Nature of Light Superposition & Interference 118 Waves 118 Light: Electromagnetic Waves 118 Relationship Between B & E 118 Characteristics of Waves 118 Characteristics of Waves: Time Period 119 Characteristics of Waves: Velocity/Speed 119 Relationship Between v, f, λ 119 Mathematical Description of a Wave: Wave Function 119 Mathematical Description of a Sinusoidal Waves 121 Mathematical Description of a Sine Wave: Another Form 121 Equivalent Moving Wave Equations 122 Phase & Initial Phase 122 Phase or Phase Velocity of a Wave 123 Phase or Wave Velocity: Alternative Approach 123 Super Position of Light Waves & Interference 124 Super Position of Light Waves 124 Wave Equation 124 Superposition of Waves 124 Addition of Waves 124 Intensity of 2 Overlapping Waves 126 Phase Differences 126 Phase Difference & Path Difference 127 Interference 127 Interference of Equal Intensity 128 Intensity Variation 128 Condition for Interference 128 17-Interference 129 Young’s Double Slit Experiment 129 Young Double Slit Experiment: Interference Pattern 130 Young Double Slit Experiment: Intensity Equation 130 Young Double Slit Experiment: Position of Bright Fringes or Maxima 131 Young Double Slit Experiment: Fringe Separation or Fringe Width 131 Young Double Slit Experiment: Position of Dark Fringes or Minima 131 Young’s Double Slit Experiment: Formulae 132 Fresnel Biprism: Wave front Splitting 132 Thin Film Interference 133 Phase Change Due to Reflection 133 Phase Shift on Reflection 134 When 1 Reflection is External & 1 Reflection is Internal 134 When Both the Reflections are External or Both the Reflections are Internal 135 Thin Film Interference for Nonreflective Coating 135 Michelson Interferometer: Amplitude Splitting 135 Interferometer: Application in OCT 136 Newton’s Rings 136 18-Diffraction 136 Diffraction 136 Diffraction Pattern & Huygens’s Theory 137 Diffraction: Effect of Slit Width 137 Diffraction Types 137 Fraunhofer Diffraction: Single Slit 138 Fraunhofer Diffraction Pattern of a Single Slit 138 Fraunhofer Diffraction from a Single Slit: Locating the Minima 138 Fraunhofer Diffraction by a Single Slit: Locating the Minima 139 Locating Subsequent Minima 139 Single Slit Diffraction-Dark Fringes 140 Quantitatively Measurement of Intensity in Single Slit Diffraction 140 Intensity in Single Slit Diffraction 141 Quantitatively Measurement of Intensity in Single Slit Diffraction 141 Diffraction: Maxima 141 Single Slit Diffraction Irradiances: Effect of Slit Width 142 Fraunhofer Diffraction by a Circular Aperture 142 Resolution 143 Rayleigh’s Criterion for Resolution 143 Fraunhofer Diffraction at Double Slits 144 Fraunhofer Diffraction at Double Slits 145 19-Polarization 146 Definition Polarization 146 Classification of Polarization 147 Linear Polarization: Mathematical Description 148 Linear Polarization: Summary 149 Circular Polarization 150 Elliptical Polarization 152 Techniques for Producing Polarized Light 152 Dichroism (Selective Absorption) 152 Polaroids (Dichroism) 153 Polaroids 153 What happens when light pass through crossed polarizers? 154 Polarizers & analyzers 154 What happens when the linearly polarized light emerging from a polarizer passes through a second polarizer or analyzer 154 Polarizers & Analyzers (cont.) 155 Malus Law 155 Malus’s law, polarized light passing through analyzer 156 Polarization: Birefringence 156 Polarization by Birefringence 156 Polarization by Reflection 157 Polarization by Reflection: Brewster’s Law 157 Polarization by Scattering 158 Retarders 158 Retarders: Half Wave Plate 159 Retarders: Quarter Wave Plate 159 Retarders: Achromatic Retarders 159