1st Edition

# Concise Optics Concepts, Examples, and Problems

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This introductory text is a reader friendly treatment of geometrical and physical optics emphasizing problems and solved examples with detailed analysis and helpful commentary. The authors are seasoned educators with decades of experience teaching optics. Their approach is to gradually present mathematics explaining the physical concepts. It covers ray tracing to the wave nature of light, and introduces Maxwell’s equations in an organic fashion. The text then moves on to explains how to analyze simple optical systems such as spectacles for improving vision, microscopes, and telescopes, while also being exposed to contemporary research topics.

**Ajawad I. Haija** is a professor of physics at Indiana University of Pennsylvania.

**M. Z. Numan** is professor and chair of the department of physics at Indiana University of Pennsylvania.

**W. Larry Freeman** is Emeritus Professor of Physics at Indiana University of Pennsylvania.

**Part I. Introduction**

1. Light: Its Nature and History of Study

1.1 Introduction

1.2 Light-The Core of Optics

1.3 Plane Waves

1.4 Energy And Momentum of Electromagnetic Waves

Part II. Geometrical Optics of Light

2. Reflection and Refraction

2.1 Introduction

2.2 Reflection

2.3 Image Formation Via Reflection

2.4 Refraction

2.5 Image Formation Via Refraction

3. Paraxial Rays and Lenses

3.1 Introduction

3.2 Thin lenses - Kinds and Shapes

3.3 Image Formation in Thin Lenses

3.4 Lens Equation

3.5 Newtonian Form for an Object-Image Relationship in Thin lenses

3.6 Power and Vergence of a Thin Lens

3.7 Combination of Lenses

4. Matrix Optics for Paraxial Rays

4.1 Introduction

4.2 Translation Matrix

4.3 Refraction Matrix

4.4 Multi Operation Matrix- Lenses

4.5 Thick Lens - Revisited

4.6 Effective Matrix of an Optical System– Further Analysis

Part III. Wave Optics

5. Light Waves, Properties, and Propagation

5.1 Introduction

5.2 Maxwell’s Equations

5.3 Wave Equation

5.4 Types and Properties of Electromagnetic Wave Equations

5.5 Electromagnetic Wave Equation in Dielectrics

5.6 The Photon Flux Density

6. Light Waves, Coherence, Superposition, and Interference

6.1 Introduction

6.2 Superposition of Two Waves

6.3 Superposition of Multiple Waves of Arbitrary Phases

6.4 Superposition of Two Waves of a slightly Different Frequency – Group Velocity

6.5 Coherence, a Must Condition For Sustainable Interference

7. Double and Multiple Light Beam Interference

7.1 Introduction

7.2 Young’s Double Slit Experiment

7.3 Lloyd’s Mirror

7.4 Newton’s rings

7.5 Interference of Light in Thin Films

7.6 Multiple Beam Interference

7.7 Fringes of Equal Inclination – Fizeau Fringes

7.8 Michelson Interferometer

8. Diffraction I. Fraunhofer Diffraction

8.1 Introduction

8.2 Setup of Single Slit Diffraction

8.3 Double Slit Diffraction

8.4 Diffraction Gratings

8.5 Resolution and Resolving Power

9. Diffraction II: Fresnel Diffraction

9.1 Introduction

9.2 Lay Out and Assumptions - Obliquity Factor

9.3 Huygens – Fresnel Diffraction

9.4 Fresnel Diffraction for a Rectangular Aperture – Fresnel Zone Structure

10. Optics of Multilayer Systems

10.1 Introduction

10.2 Basic Theory - Dielectric Layer

10.3 Extension to Mutlilayer Structures- Characteristic Matrix Technique, CMT

10.4 Ultra-Thin Single Film

10.5 Analytic Formulas for Reflectivity and Transmissivity of Absorbing Layers

11. Polarization

11.1 Introduction

11.2 Basic Theory

11.3 States of Polarization

11.4 Various processes of Polarization

11.5 Propagation of Light Waves in Double Refracting Materials

11.6 Wavefronts and Refraction of Rays in Birefringent Materials

12. Fourier Optics

12.1 Introduction

12.2 Periodic Functions and Fourier Series

12.3 Important Integrals

12.4 Complex Form of Fourier Series

12.5 Fourier Transform

12.6 Relevance of Fourier Transform to Diffraction

13. Photonics

13.1 Introduction

13.2 Classical Physics and Radiation – The Foundation of Modern Photonics

13.3 Some Natural Photonics

13.4 Human Engineered Photonic Systems

**Appendices**

A –Trigonometry

B – Complex Numbers

C – Mathematical Operators-Cartesian and Spherical Coordinates

D – Matrices

E – Physical Constants

F– Examples on Fresnel Diffraction Done on MathematicaF

G- Solution of Selected Examples from Ch. 10 Using Excel. Linear Algebra-Matrices

H – Mathematical Expansions and Series

### Biography

**Ajawad I. Haija** attended the University of Alexandria in Egypt, where he received his B.Sc. degree in 1968 with distinction, first honor. He received his Ph.D. (1971-1977) at Pennsylvania State University in 1977. In 2000, he moved to the United States and joined the Indiana University of Pennsylvania. He is currently on the physics faculty, where he conducts research on the properties of thin multilayer structures and super-lattices. In 2014 Dr. Haija was awarded the Distinguished Faculty Award for Teaching, 2013–2014, Indiana University of Pennsylvania, IUP. A. J. Haija is a former member of New York Academy of Sciences and a current member of the American Physical Society.

**M. Z. Numan** hails from Bangladesh, where he received his B.Sc. (Hons.) and M.Sc. degrees in physics from Dhaka University. He received his Ph.D. from The College of William and Mary in Virginia in 1982. He taught at Virginia Commonwealth University in Richmond, Virginia, University of North Carolina at Chapel Hill, and Indiana University of Pennsylvania, where he is currently the chair of the department of physics. His research focused on materials modification and characterization using ion implantation, back scattering and channeling; optical and electrical characterization of metallic multi-layers and semiconductor materials; light harvesting through silicon micro and nano structures.

**W. Larry Freeman** was born and grew up in South Carolina, USA, and earned his B.Sc. in physics from Appalachian State University in 1969. Dr. Freeman received his Ph.D. From Clemson University in 1976 where his dissertation explored quantum size effects in thin Bismuth films at low temperatures. After leaving Clemson University and teaching high school and technical college, he returned to Clemson on a post-doctoral position. He joined the US Naval Intelligence service in 1978, and was moved to the US Army Night Vision and Electro-Optics Laboratory in 1980 where he was heavily involved with the development of solid-state materials used for the detection of radiation in the infrared radiation wavelength range. He was instrumental in developing nondestructive testing and characterization as well as fabrication techniques for the manufacturing of solid-state infrared detector arrays.

Dr. Freeman moved to Indiana University of Pennsylvania in 1984 where he taught graduate and undergraduate courses in physics. He retired from IUP in 2010 and currently holds the position of Emeritus Professor of Physics. He maintains his memberships in the American Physical Society and American Association of Physics Teachers.

"a comprehensive text… at the right level for our students and brings together ideas from other undergraduate courses to explain the basic fundamentals of optics…. There are quite a few helpful worked out examples as well as good homework problems included."

--Matthew M. Waite, West Chester University of PA"There are a number of introductory/undergraduate optics books in the market...What is different about this book is that the whole gamut of introductory optics can be covered in one semester, as only the basic essentials of each topic are covered. The prerequisites assumed are rather minimal—introductory physics and basic calculus. The appendices cover other requisite math such as complex numbers, volume integrals and matrices. What is surprising (and not usually found in introductory texts) is the rather extensive discussion on calculating the Cornu spiral. Also presented is the appropriate Mathematica code. The other topic not usually encountered is the characteristic-matrix technique for dealing with thin films and layer stacks...The book is ideal either for use in the classroom or for self-study."

--Vengu Lakshminarayanan, University of Waterloo, Canada