Contents
1 Geometrical Optics
1.1 Rays or waves
1.1.1 Camera obscura
1.1.2 Newton's corpuscular theory of light
1.1.3 Huygens' wave theory
1.1.4 Graphical ray tracing
1.2 Fermat's principle
1.2.1 Modern formulation of Fermat's principle
1.2.2 Rays and wavefronts
1.2.3 Image from a point source
1.3 Refracting surfaces
1.3.1 Modeling the cornea of a human eye
1.3.2 Refraction at spherical surfaces
1.3.3 Focal lengths and focal points
1.3.4 Focal planes
1.3.5 Paraxial imaging of extended objects
1.3.6 Optical power and vergence
1.4 Reflecting surfaces
1.4.1 Ray tracing for spherical mirrors
1.4.2 The parabolic mirror
1.5 Lenses: thin lens approximation
1.5.1 Ray tracing for thin lenses
1.5.2 Newton's lens equation
1.5.3 Real and virtual images domain
1.5.4 Focal planes in thin lenses
1.5.5 Ray tracing for oblique rays
1.6 Lenses: principal planes
1.6.1 A lens system
1.7 Stops and pupils
1.7.1 Aperture stop
1.7.2 Pupils
1.7.3 Marginal and chief rays
1.7.4 Field stop, field of view, and angle size
1.8 Some optical instruments
1.8.1 The human eye (schematic representation)
1.8.2 Magnifiers
1.8.3 The telescope
1.8.4 The microscope
1.9 Monochromatic optical aberrations
1.9.1 Field curvature
1.9.2 Spherical aberration
1.9.3 Distortion
1.9.4 Astigmatism and coma
References
2 Polarization
2.1 Plane waves and polarized light
2.1.1 Maxwell's equations with plane waves
2.1.2 Irradiance
2.1.3 Natural light and polarized light
2.1.4 Elliptical, circular, and linear polarization
2.1.5 Polarization: general case
2.2 Dichroism polarization
2.2.1 Linear polarizer
2.2.2 Malus' law
2.3 Polarization by reflection
2.3.1 Laws of reflection and refraction
2.3.2 Fresnel equations
2.3.3 Reflectance and transmittance
2.4 Polarization by total internal reflection
2.4.1 Total internal reflection
2.4.2 Reflectance and transmittance
2.5 Polarization with birefringent materials
2.5.1 Phase retarder plates
2.5.2 Birefringent crystals
2.5.3 Refraction in crystals
2.5.4 Polarizing prisms
2.6 Vectors and Jones matrices
References
3 Interference
3.1 Interference and coherence
3.1.1 Degree of coherence
3.1.2 Interference and coherence
3.1.3 Coherence length
3.2 Interference of two plane waves
3.2.1 Interference with inclined plane waves
3.2.2 Displacement of interference fringes
3.2.3 Interferogram visibility
3.3 Interference of two spherical waves
3.3.1 Circular fringes with the Michelson interferometer
3.3.2 Parallel fringe approximation with the Michelson interferometer
3.4 Practical aspects in the Michelson interferometer
3.4.1 Laboratory interferometer
3.5 Interference in a plate of parallel faces
3.5.1 Stokes relations
3.5.2 Multiple-wave interference
3.5.3 Two-wave interference
3.6 Interference from N point sources
3.6.1 Plane wave approximation
3.7 Interference with extended light sources
3.7.1 Artificial extended sources
3.8 Young interferometer I
3.8.1 Division of wavefront and division of amplitude
3.9 Other interferometers
3.9.1 Fabry–Pérot interferometer
3.9.2 Antireflective thin film
3.9.3 Newton and Fizeau interferometers
References
4 Diffraction
4.1 Huygens–Fresnel principle
4.1.1 Fresnel zones
4.1.2 Fresnel treatment results
4.2 Diffraction integral
4.2.1 Kirchhoff integral theorem
4.2.2 Fresnel–Kirchhoff diffraction
4.2.3 Sommerfeld diffraction
4.3 Fresnel and Fraunhofer diffraction
4.3.1 Fraunhofer diffraction
4.3.2 Fresnel diffraction
4.3.3 Some examples
4.4 Young Interferometer II
4.4.1 Effect of the size of the diffraction aperture
4.4.2 Effect of light source size
4.5 Image formation with diffraction
4.5.1 Image of a point (source) object
4.5.2 Resolution in the image (two points)
4.5.3 Image of an extended object
4.6 Diffraction gratings
References
A Ray tracing
References
B Refractive index
References
C Optical glasses
References
D Chromatic aberrations
References
E Prisms
References
F Polarization ellipse
This book presents lectures on classical optics, based on the Fundamentals of Optics course
that I have been teaching for 12 years in the Physics Department of the Universidad
Nacional de Colombia (UNAL) at Bogotá. At first, I occasionally taught these lectures
as an elective course in the Physics undergraduate program. Beginning in the fall of
2009 through the fall of 2017, I taught the same lectures each semester as an optative
regular course of four hours per week in a 16-week semester format. The content of the
course was based on my own research experience in the field of applied optics, which was
enriched at the Centro de Investigaciones en Óptica, México, where I pursued my Ph.D. in
Optics (1998–2001). This book comprises four chapters: Geometrical Optics, Polarization,
Interference, and Diffraction, each consisting of several sections. Each section corresponds to a
lecture of two hours. The book includes 30 sections and six appendices.
I have written this book to provide students of physics, optics, and engineering with
a basic understanding of the main topics related to geometrical and physical optics. For
further reading on classical optics, students may consult other well-known textbooks such as
Fundamentals of Optics, Fourth Edition, by Jenkins and White (McGraw-Hill Education,
2001), Optics, Fifth Edition, by Hecht (Pearson, 2016), and Principles of Optics, Sixth
Edition, by Born and Wolf (Pergamon Press, 1980).
I would like to thank UNAL for granting me a sabbatical year (February 2018 to
February 2019), during which I was able to write this book.
Yobani Mejía-Barbosa
Bogotá, D. C., Colombia
March 2021
