- Title Pages
- Epigraph
- Preface
- Acknowledgments
- Chapter One Introduction
- Chapter Two Introduction to the “Physics” of Rays
- Chapter Three Introduction to the Mathematics of Rays
- Chapter Four Ray Optics: The Classical Rainbow
- Chapter Five An Improvement over Ray Optics: Airy’s Rainbow
- Chapter Six Diffraction Catastrophes
- Chapter Seven Introduction to the WKB(J) Approximation: All Things Airy
- Chapter Eight Island Rays
- Chapter Nine Seismic Rays
- Chapter Ten Elastic Waves
- Chapter Eleven Surface Gravity Waves
- Chapter Twelve Ocean Acoustics
- Chapter Thirteen Tsunamis
- Chapter Fourteen Atmospheric Waves
- Chapter Fifteen The Classical Connection
- Chapter Sixteen Gravitational Scattering
- Chapter Seventeen Scattering of Surface Gravity Waves by Islands, Reefs, and Barriers
- Chapter Eighteen Acoustic Scattering
- Chapter Nineteen Electromagnetic Scattering: The Mie Solution
- Chapter Twenty Diffraction of Plane Electromagnetic Waves by a Cylinder
- Chapter Twenty-One The Classical-to-Semiclassical Connection
- Chapter Twenty-Two The WKB(J) Approximation Revisited
- Chapter Twenty-Three A Sturm-Liouville Equation: The Time-Independent One-Dimensional Schrödinger Equation
- Chapter Twenty-Four The <i>S</i>-Matrix and Its Analysis
- Chapter Twenty-Five The Jost Solutions: Technical Details
- Chapter Twenty-Six One-Dimensional Jost Solutions: The <i>S</i>-Matrix Revisited
- Chapter Twenty-Seven Morphology-Dependent Resonances: The Effective Potential
- Chapter Twenty-Eight Back Where We Started
- Appendix A Order Notation: The “Big <i>O</i>,” “Little <i>o</i>,” and “∼” Symbols
- Appendix B Ray Theory: Exact Solutions
- Appendix C Radially Inhomogeneous Spherically Symmetric Scattering: The Governing Equations
- Appendix D Electromagnetic Scattering from a Radially Inhomogeneous Sphere
- Appendix E Helmholtz’s Theorem
- Appendix F Semiclassical Scattering: A Précis (and a Few More Details)
- Bibliography
- Index
- Princeton Series in Applied Mathematics

# Ray Optics: The Classical Rainbow

# Ray Optics: The Classical Rainbow

- Chapter:
- (p.76) Chapter Four Ray Optics: The Classical Rainbow
- Source:
- Rays, Waves, and Scattering
- Author(s):
### John A. Adam

- Publisher:
- Princeton University Press

This chapter focuses on the ray optics of the rainbow. Some of the most powerful tools of mathematical physics were developed explicitly to address the problem of the rainbow and closely related problems. Indeed, the rainbow has served as a benchmark for testing theories of optics. The more successful of those theories now make it possible to describe the rainbow in mathematical terms—that is, to predict the distribution of light in the sky. The chapter first provides an overview of the physical features and historical details relating to the rainbow before discussing the ray theory of the rainbow from an elementary mathematics standpoint. In particular, it considers some relevant numerical values, polarization of the rainbow, and the divergence problem. It also explores related topics in meteorological optics, including the glory, coronas (simplified), and Rayleigh scattering.

*Keywords:*
ray optics, rainbow, ray theory, elementary mathematics, polarization, divergence problem, meteorological optics, glory, corona, Rayleigh scattering

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- Title Pages
- Epigraph
- Preface
- Acknowledgments
- Chapter One Introduction
- Chapter Two Introduction to the “Physics” of Rays
- Chapter Three Introduction to the Mathematics of Rays
- Chapter Four Ray Optics: The Classical Rainbow
- Chapter Five An Improvement over Ray Optics: Airy’s Rainbow
- Chapter Six Diffraction Catastrophes
- Chapter Seven Introduction to the WKB(J) Approximation: All Things Airy
- Chapter Eight Island Rays
- Chapter Nine Seismic Rays
- Chapter Ten Elastic Waves
- Chapter Eleven Surface Gravity Waves
- Chapter Twelve Ocean Acoustics
- Chapter Thirteen Tsunamis
- Chapter Fourteen Atmospheric Waves
- Chapter Fifteen The Classical Connection
- Chapter Sixteen Gravitational Scattering
- Chapter Seventeen Scattering of Surface Gravity Waves by Islands, Reefs, and Barriers
- Chapter Eighteen Acoustic Scattering
- Chapter Nineteen Electromagnetic Scattering: The Mie Solution
- Chapter Twenty Diffraction of Plane Electromagnetic Waves by a Cylinder
- Chapter Twenty-One The Classical-to-Semiclassical Connection
- Chapter Twenty-Two The WKB(J) Approximation Revisited
- Chapter Twenty-Three A Sturm-Liouville Equation: The Time-Independent One-Dimensional Schrödinger Equation
- Chapter Twenty-Four The <i>S</i>-Matrix and Its Analysis
- Chapter Twenty-Five The Jost Solutions: Technical Details
- Chapter Twenty-Six One-Dimensional Jost Solutions: The <i>S</i>-Matrix Revisited
- Chapter Twenty-Seven Morphology-Dependent Resonances: The Effective Potential
- Chapter Twenty-Eight Back Where We Started
- Appendix A Order Notation: The “Big <i>O</i>,” “Little <i>o</i>,” and “∼” Symbols
- Appendix B Ray Theory: Exact Solutions
- Appendix C Radially Inhomogeneous Spherically Symmetric Scattering: The Governing Equations
- Appendix D Electromagnetic Scattering from a Radially Inhomogeneous Sphere
- Appendix E Helmholtz’s Theorem
- Appendix F Semiclassical Scattering: A Précis (and a Few More Details)
- Bibliography
- Index
- Princeton Series in Applied Mathematics