Fundamentals of Geometrical Optics

474 Pages·2014·4.447 MB·English

by  Virendra N. Mahajan

FUNDAMENTALS OF
GEOMETRICAL OPTICS
VIRENDRA N. MAHAJAN
FUNDAMENTALS OF
GEOMETRICAL OPTICS
Virendra N. Mahajan

FUNDAMENTALS OF
GEOMETRICAL OPTICS
Virendra N. Mahajan
THE AEROSPACE CORPORATION
AND
COLLEGE OF OPTICAL SCIENCES - THE UNIVERSITY OF ARIZONA
SPIE PRESS
Bellingham, Washington USA

Library of Congress Cataloging-in-Publication Data

Mahajan, Virendra N.
Fundamentals of geometrical optics / Virendra N. Mahajan.
pages cm
Includes bibliographical references and index.
ISBN 978-0-8194-9998-1
1. Geometrical optics--Study and teaching. 2. Optical instruments--Reliability--Study
and teaching. 3. Diffraction--Study and teaching. I. Title.
QC382.M34 2014
535'.32--dc23
2014010949

Published by
SPIE
P.O. Box 10
Bellingham, Washington 98227-0010 USA
Phone: [phone]
Fax: [phone]
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Copyright © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

All rights reserved. No part of this publication may be reproduced or distributed in any
form or by any means without written permission of the publisher.

The content of this book reflects the work and thought of the author(s). Every effort has
been made to publish reliable and accurate information herein, but the publisher is not
responsible for the validity of the information or for any outcomes resulting from reliance
thereon.

Printed in the United States of America.
Second printing
To my wife
SHASHI PRABHA

FOREWORD
We are living in the most exciting time, so far, in the use and application
of the phenomenon of light, as we understand it. Optics is now an
important subject in many disciplines, and so competence in optics is at
issue. This volume provides the interested reader with a solid resource to
embark on learning about geometrical optics, which is the foundation of
imaging and non-imaging optics. Professor Virendra N. Mahajan provides
a clear and detailed discussion of essential topics for the understanding of
image formation.
Dr. Mahajan has significant experience teaching and writing about the
subject. He is well known in the optics community and has traveled
around the world, lecturing about optical imaging and aberrations; one of
his favorite topics is the use of Zernike polynomials in optics.
I have known Dr. Mahajan ever since he started teaching at the College of
Optical Sciences in 2005. He flew back and forth from Los Angeles to
Tucson every week to share his knowledge with students. I have also
enjoyed noticing the fine interest and polite interaction he has with his
optics colleagues.
From interacting with Dr. Mahajan over the years, it is apparent that
he is concerned with clearly connecting topics in geometrical optics to
provide students with a solid foundation. One example is his detailed
style in describing and deriving, say, the laws of geometrical optics and ray
tracing in 3D, and the evolution of Gaussian optics from them. Another
example is his insightful explanation of how the individual primary
aberration coefficients of a system of surfaces can be added directly
to form the overall system’s coefficients.

I wish that readers will benefit from Vini Mahajan's Fundamentals of
Geometrical Optics and treasure it as a favorite reference.
May 2014 José Sasián
College of Optical Sciences
University of Arizona
Tucson, Arizona
vii
TABLE OF CONTENTS
FUNDAMENTALS OF
GEOMETRICAL OPTICS
Preface ............................................................................................................................xix
Acknowledgment ............................................................................................................xxi
Symbols and Notation ..................................................................................................xxiii
CHAPTER 1: FOUNDATIONS OF GEOMETRICAL OPTICS
1.1 Introduction ..............................................................................................................3
1.2 Sign Convention .......................................................................................................4
1.3 Fermat’s Principle ....................................................................................................5
1.4 Rays and Wavefronts ...............................................................................................8
1.5 Laws of Geometrical Optics ..................................................................................10
1.5.1 Rectilinear Propagation .............................................................................10
1.5.2 Refraction in 2D ........................................................................................10
1.5.3 Reflection in 2D ........................................................................................12
1.5.4 Refraction in 3D ........................................................................................13
1.5.5 Reflection in 3D ........................................................................................15
1.6 Exact Ray Tracing .................................................................................................17
1.6.1 Ray Incident on a Spherical Surface ..........................................................17
1.6.2 Rectilinear Propagation from the Object Plane to the
First Refracting Surface .............................................................................18
1.6.3 Refraction of a Ray by a Spherical Refracting Surface .............................19
1.6.4 Rectilinear Propagation from the First Refracting Surface to the Second 20
1.6.5 Reflection of a Ray by a Spherical Reflecting Surface .............................21
1.6.6 Conic Surface and Surface Normal ..........................................................22
1.6.7 Refraction of a Ray by a Conic Refracting Surface ..................................22
1.6.8 Reflection of a Ray by a Conic Reflecting Surface ...................................23
1.6.9 Tracing a Tangential Ray ..........................................................................24
1.6.10 Determining Wave and Ray Aberrations ..................................................24
(cid:76)(cid:91)