Elementary Wave Optics

286 Pages·1997·13.599 MB·English

by  Webb, Robert H.

Elementary
Wave Optics
Robert H. Webb
Dover Publications, Inc.
Mineola, New York
Copyright
Copyright 0 1969,1997 by Robert H.W ebb
All rights reserved.
Bibliographical Note
This Dover edition, fist published in 2005, is an unabridged republication of
the work originally published by Academic Press, New York, in 1969. The red-
dish brown color found in the figures and diagrams of the original edition has
been reproduced here in gray.
Library of Congress Cataloging-in-PublicationD ata
Webb, Robert H.,1 934-
Elementary wave optics I Robert H. Webb.
p cm.
Origmally published: New York : Academic Press, 1969.
Includes bibliographical references and index.
ISBN 0-486-43935-6 (pbk.)
1. Light, Wave theory of. I. Title.
QC403.W4 2004
535'. 1z c 2 2
2004059346
Manufactured in the United States of America
Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501
Preface
Wave optics is the study of the various phenomena associated with
the wave properties of light-and by extension, with any waves.
A knowledge of this subject is necessary for an understanding of
optical devices, but more important, a study of wave optics pro-
vides a way to introduce many of the phenomena of modern
quantum physics. The feature which distinguishes modern physics
from classical physics is the occurrence of wave (interference)
effects in the interactions of all kinds of matter and energy. This
book is designed to explain these phenomena in terms of electro-
magnetic waves (including visible light) and of other wave systems
closer to common experience. Extensively described are super-
position, scattering, and the concept of coherence. Coherent optics
(so-called “modern optics”) has newly become accessible to ex-
perimentation, and the approach to modern physics which is em-
phasized here permits the treatment of this subject in some detail.
In order to maintain the thread of the argument, the main part
of the text uses as little formid mathematics as possible. For more
xi
xii Preface
advanced students, the appendices will supply the missing deriva-
tions, after the subject has been introduced in the text.
Problems are an integral part of this text. Detailed solutions are
given to half of them, so that the student can use solved problems
as a learning device. Self-restraint in looking up the solution is
important, since the value of a problem lies in trying to solve it
and in understanding its dficulties. Subsequent use of the solution
then makes pedagogic sense. The unsolved problems are roughly
paired with the solved ones in most cases. Short exercises of a
more conventional sort are also included.
I am grateful for the many contributions of problems, criti-
cisms, and insights from my colleagues in the courses which gen-
erated this book. Professors R. F. Walker, J. T. Tessrnan, and A. E.
Everett, in particular; will recognize their efforts-I hope faith-
fully included. Finally, and in dedication, this is for my most im-
portant luminary-Charme.
ROBERTH . WEBB
Lexington, Massachusetts
Contents
Preface, xi
1 Geometrical optics: summary
EXERCISES, 8
PROBLEMS, 8
2 Waves: description
2.1 Physical description, 16
2.2 Mathematical description, I8
2.3 Sine wave, 21
2.4 Momentum and energy, 25
EXERCISES, 28
PROBLEMS, 29
3 Superposition: reflection, standing waves, group velocity
3.1 Superposition, 31
3.2 Reflection, 32
3.3 Standing waves, 35
vii
Contents
3.4 Phasors, 37
3.5 Harmonics, 39
3.6 Beats, 40
3.7 Group velocity, 41
EXERCISES, 44
PROBLEMS, 45
4 Electromagnetic waves, energy and momentum,
doppler eflect
4.1 Electromagnetic waves, 48
4.2 Energy, 50
4.3 Momentum, 50
4.4 Photons, 53
4.5 Doppler effect,5 4
EXERCISES, 57
PROBLEMS, 57
5 Scattering: index of refraction
5.1 Scattering, 60
5.2 Refraction, 61
5.3 Index of refraction, 62
5.4 Birefringence, 66
5.5 Dichroism, 68
EXERCISES, 68
PROBLEMS, 69
6 Polarized light
6.1 Linear and circular polarization, 71
6.2 Production and analysis of linearly polarized light, 74
6.3 Wave plates, 76
6.4 Colors, 79
6.5 Circularly polarized light, 79
6.6 Angular momentum of light, 80
6.7 Other polarizing interactions, 83
EXERCISES, 87
PROBLEMS, 87
7 Interference
7.1 Two identical sources-in line, 91
7.2 Two identical sources-ofl axis, 94
7.3 Average over detection time, 96
7.4 Coherence, 100
Contents ix
7.5 Huygens’ principle, 102
EXERCISES, 102
PROBLEMS, 103
8 Interference from two sources
8.1 Identical sources, I05
8.2 Sources differingi n phase, 108
8.3 Paths differingi n index, I08
8.4 Sources differingi n frequency, 109
8.5 White light, 109
8.6 Phasors, I I0
EXERCISES, 111
PROBLEMS, 112
9 Interference from many sources
9.1 Three slits, I 27
9.2 Grating, I20
9.3 Line width, 121
9.4 Grating equation, 122
9.5 Wavelength resolution, 123
9.6 Broadening, 125
EXERCISES, 126
PROBLEMS, 127
10 Multiple images: interference of light from
an extended source
10.1 Amplitude separation, 130
10.2 Michelson interferometer, 132
10.3 Fabry-Perot interferometer, 134
10.4 Wedge, 135
10.5 Transmitted light, 136
10.6 Phase change on reflection, 137
10.7 Wavelength dependence, 138
EXERCISES, I39
PROBLEMS, 140
11 Diflraction
11.1 Single slit, 143
11.2 Diffraction-limited optics, I45
11.3 Resolution, 146
11.4 Babinet’s principle, 149
X Contents
11.5 I(p)--single slit, 150
EXERCISES, 252
PROBLEMS, 253
12 Modern optics
12.1 Fourier transformsa s diffractionp atterns, 156
12.2 Image retrieval, 158
12.3 Holography-recovery of phase information, I60
12.4 Holography-"gratings" approach, 162
PROBLEMS, I65
Appendixes
A Miscellaneous mathematical notes, I66
B Derivation of the wave equation, 169
C Strings, I75
D Summary on electricity and magnetism
-derivation of electromagnetic wave equation, 180
E Resonance, I86
F Index of refraction-macroscopic approach, I90
G Fresnel diflraction, 192
A Fourier transforms, 196
Bibliography, 203
Solutions to selected problems, 207
Index, 263
Geometrical
optics:
summary
Geometrical optics deals with light (and more generally with waves)
in situations where it is possible to ignore the wave character of the
phenomenon. This usually means that the wavelengths involved are
very much smaller than the dimensions of anything with which the
waves interact. Later we will see that geometrical optics is a limiting
case of wave optics. The usual value in limiting cases is their sim-
plicity, and geometrical optics shares this asset, with reservations.
All of geometrical optics may be deduced from three simple
empirical rules :
1. Light travels in straight lines in homogeneous media.
2. The angle at which light is reflected from a surface is equal to
the angle at which it is incident.
3. When light passes from one medium to another, its path is
described by the equation n, sin 8, = n2 sin 02.
1
2 Geometrical optics
Figure 1.1 summarizes these rules and defines the various angles.
A “ray” is a line along the path the light follows. We think of this as
a very narrow beam of light.
I
Medium 1
Medium 2
I
Refractdray
F&we 1.1: Reflection We may regard rule 3, which describes refraction, as defining the
and refraction. relative index of refraction: n,/n,.
If we follow custom and define the index of vacuum to be nvPc= 1,
then n, and n, are the indices of each medium relative to vacuum,
and are so listed in handbooks. Later we will see that this ability to
characterize each medium by a single number is extremely impor-
tant. Among other consequences, it will lead us to regard nk as the
ratio of the speed of light in vacuum (c) to (ck), the speed of light in
medium k: nk = c/ck.T his in turn allows us to deduce the three rules
from the more general Fermat’s principle. The main asset of this
principle is the esthetic one of unification. It is not essential to the
conclusions of geometrical optics, although occasional simplifica-
tions are possible. But the three rules suffice.
A further statement limits the kinds of media usually considered.
This is the reciprocity principle, which requires that if light can follow
a certain path from A to Byt hen it can follow the same path from
B to A. Some media do not support this principle, but they seldom
occur in questions pertaining to geometrical optics.
If we apply our rules directly to plane surfaces, they describe the
behavior of mirrors and prisms (1.1-1.3)*. Rule 3 also predicts the
phenomenon of total internal reflection. When light passes from
a medium with a larger index to one with a smaller index (as, for
* Numbers in parentheses indicate relevant problems at the end of the chapter.