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`APPLE 1052
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`IPR2021-00208
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`

`

`2 =
`
`OPTICS
`
`SECONDEDITION
`
`EUGENE HECHT
`AdelphiUniversity
`
`With Contributions by Alfred Zajac
`
`av
`
`v
`ADDISON-WESLEY PUBLISHING COMPANY
`Reading, Massachusetts = Mento Park, California » Den Mills, Ontario
`Wokingham, England » Amsterdam = Sydney » Singapore
`Tokyo # Madrid = Bogoia = Santiago = San Juan
`
`

`

`
`
`
`
`!
`
` 4
`
`
`
`Sponsoring editor: Bruce Spatz
`Production supervisors: MargaretPinette and Lorraine Ferrier
`Text designer: Joyce Weston
`Hlustrators: Oxford Wlustrators
`Art consultant: Loretta Bailey
`Manufacturing supervisor: Ann DeLacey
`Library of Congress Cataloging-in-Publication Data
`Hecht, Eugene.
`Optics.
`Bibliography: p.
`Includes indexes,
`Il.Title.
`1. Optics.
`1, Zajac, Alfred.
`
`QC355.2.H42 1987
`535
`86-14067
`ISBN 0-201-11609-X
`
`Reprinted with corrections May, 1990,
`Copyright © 1987, 1974 by Addison-Wesley Publishing Campany. Inc.
`All rights reserved, No partof this publication may be reproduced,
`stored in a retrieval systern, or transmitted, in any form or by any
`means, electronic, mechanical, photocopying, recurding, ar
`
`otherwise, without the prior written permission of the publisher.
`Printed in the United States of America. Published simultaneously
`in Canada.
`1112
`14 15 MA 96959493
`
`To Ca, b, w. 1.
`
`
`
`3
`
`

`

`
`
`Preface
`
`Thecreation of this second edition was guided primarily
`by two distinct imperatives: to incorporate the peda-
`gogical insights gained in the classroom over the past
`dozen years, and to bring the book in step with the
`fast-moving edge of optical technology. Accordingly,
`several sections have been reorganized, some con-
`densed, others extended, and the exposition updated
`and improved throughout. in the process I have added
`a numberof graphs, drawings and photographs, as well
`as a gooddealof new textual material—always with the
`motivation of enlivening and clarifying the treatment.
`As well as the very many small but significant
`refinementsthatare incorporatedin this secondedition,
`there are also some substantive improvements in
`methodology and emphasis. For example, atomic pro-
`cesses associated with radiation and absorption are con-
`sidered earlier and in more detail. The central role of
`scattering in optics (e.g., in reflection, refraction, and
`dispersion) can thereafter he understood more intui-
`tively (Chapter 3). Huygens’s principle, which is so
`useful and yet so contrived, then takes on a physical
`significance that is far moresatisfying. Accordingly,
`several of the original classic derivations (those associ-
`ated with the propagation oflight andits interaction
`with material interfaces) have been recast, and addi-
`tional ones have been included as well (e.g., internal
`reflection as viewed from the perspective of atomic
`scattering, p. 106, Fig. 4.35).
`With the realization that a picture is indeed worth a
`thousand words, newillustrations have been added to
`the discussion of geometrical optics (Chapters 5 and 6),
`
`primarily to facilitate a better understanding of ray
`tracing and image formation. Notsurprisingly, the dis-
`cussion of fiberoptics has been considerably extended
`to include the remarkable developments of the last
`decade. The introduction to Fourier methods (Chapter
`7) has been strengthened, in part, so that these ideas
`can be applied more naturally in the remaining exposi-
`tion. Often unduly troublesome, the notion of waves
`leading and lagging one another is given additional
`attention as it relates to polarization (Chapter 8). The
`ramifications of the limited coherence ofa typicallight
`source are now examined, if only briefly, during the
`study of interference (Chapter 9). Using a new set of
`wavefront diagrams (e.g., Figs. 10.6, 10.10, 10.19) the
`plane-wave Fourier-component
`representation
`of
`diffraction (Chapter 10)
`is unobtrusively introduced
`early on. Enlarged andrefined, the discussion of Four-
`ier optics (Chapter 11) now contains a simpler, more
`pictorial representation that complements the formal
`mathematical treatment (there are 25 new diagramsin
`Chapter 11 alone). The intentionis to makethis material
`increasingly accessible to an ever wider readership.
`Muchof the treatment of coherence theory (Chapter
`12) has been reworked andreillustrated to produce a
`simpler, more accessible version. The discussions of
`Jasers and holography (Chapter 14) have also been
`appropriately extended and broughtup to date,
`The natural tendency in a textbook is to isolate the
`principle ideas, focusing exclusively on each of them in
`turn: Thusthere are the traditional chapters on inter-
`ference, diffraction, polarization, and so forth. Thefirst
`vit
`
`
`
`4
`
`

`

`Over the years many people have been kind enough
`to share their thoughts about the book with me and I
`take this opportunity to express my appreciation to them
`all. In particular I thank Professors R. G. Wilson of
`Illinois Wesleyan University, B. Gottschalk of Harvard
`University, E. W. Jenkins of The University of Arizona,
`W. M. Becker of Purdue University, L. R. Wilcox of
`$.U.N.Y. Stony Brook, R. Talaga of the University of
`Maryland, R. A. Llewellyn of the University of Central
`Florida, R. Schiller of Stevens Institute of Technology,
`S. P. Almeida of Virginia PolytechnicInstitute and State
`University, G.
`Indebetouw of Virginia Polytechnic
`Institute and State University, and J. Higbie of the
`University of Queensland. Wherever possible I have
`incorporated photographsandsuggestions by students
`and encourage their continued participation. Anyone
`wishing to exchange ideas should write to the author
`c/o Physics Department, Adelphi University, Garden
`City, N.Y. 11530.
`1 am especially grateful
`to Lorraine Ferrier, who
`oversaw the production of this second edition. She
`worked long hours, good naturedly bringing to bear a
`rare combination ofskill, patience, and knowledgethat
`madethis book physically as fine asit is. Finally, I nod
`appreciatively to my friend Carolyn Eisen Hecht for
`going throughall this, one more time.
`Freeport, New York
`
`7.2 The Complex Method
`
`Contents
`
`1 A Brief History
`1.1 Prolegomenon ....... 7
`12
`In the Beginning
`1.3. From the Seventeenth Century
`1.4 The Nineteenth Century
`1.5 Twentieth-Century Optics
`2 The Mathematics of Wave Motion
`2.1 One-Dimensional Waves
`2.2 Harmonic Waves
`2.3. Phase and Phase Velocity ....... .
`2.4 The Complex Representation
`2.5 Plane Waves
`2.6 The Three-DimensionalDifferential Wave
`Equation
`2.7 Spherical Wayes
`2.8 Cylindrical Waves
`2.9 Scalar and Vector Waves
`Problems
`
`3 Electromagnetic Theory, Photons, and Light
`3.1 Basic Laws of Electromagnetic Theory... .
`3.2 Electromagnetic Waves
`3.8 Energy and Momentum
`3.4 Radiation
`3.5 Light and Matter
`3.6 The Electromagnetic-Photon Spectrum
`Problems
`
`4 The Propagation of Light
`4.1
`Introduction
`
`4.2 The Laws of Reflection and Refraction
`4.3. The Electromagnetic Approach
`44 Familiar Aspects of the Interaction of Light and
`Matter
`4.5 The Stokes Treatmentof Reflection and
`Refraction
`4.6 Photons and the Laws of Reflection and
`Refraction
`Problems
`
`5 Geometrical Optics—Paraxial Theory
`5.1
`Introductory Remarks... 2...
`5.2
`53
`5.4 Mirrors
`5.5 Prisms
`5.6 Fiberoptics
`5.7 Optical Systems
`
`6 More on Geometrical Optics
`6.1 Thick Lenses and Lens Systems... .
`6.2 Analytical Ray Tracing
`6.3. Aberrations
`Problems
`
`7 The Superposition of Waves
`The Addition of Waves of the Same Frequency
`7.1 The Algebraic Method
`
`vitt
`
`Preface
`
`edition more or less followed that approach, while at
`the same time underscoring conceptualinterrelation-
`ships and the unity of the entire subject—afterall,
`optics,like all of physics, is the study of the interaction
`of matter and energy. This secondedition subtly moves
`a bit further toward a holistic approach. The text now
`introduces manyof the unifyingideas, albeit on a simple
`level, as soon asis appropriate. For example. the concept
`of interference is used qualitatively to understand
`propagation phenomena(p.63) longbeforeit’s studied
`formally in Chapter 9. Amongother benefits, this tech-
`nique of presenting advanced concepts in simplified
`form early in the exposition allows the student
`to
`develop an integrated perspective.
`Respondingto requests from users, I have consider-
`ably increased the amount of material devoted to the
`analysis and solution of problems. The book now con-
`tains an abundanceof problems, roughly twice the num-
`ber that appearedin thefirst edition. Moreover,a por-
`tion of these are specifically designed to develop needed
`analyticalskills. Because a balance was maintained,with
`as many “easy” problems addedas hardones, the exer-
`cises should better serve the needsof the student reader.
`This is especially true because, as in the first edition,
`the complete solutions to many of the problems (those
`withoutasterisks) can be foundat the back of the book.
`
`E.H.
`
`5
`
`

`

`
`OPTICS
`
`11 Fourier Optics
`LL.
`Introduction... ee eee ee ee eee
`11.2. Fourier Transforms . 2. 2 ee ee
`11.3. Optical Applications 5.6... 02 ee
`Problems ....... sew ee
`ne es
`
`nN
`a7
`472
`472
`483
`512
`
`x
`
`Contents
`
`247
`248
`250
`250
`252
`254
`259
`261
`263
`266
`
`7.3 Phasor Addition ©... 2... oe ee
`74 Standing Waves 2...
`The Addition of Waves of Different Frequency
`75 Beats 2.2... ke ee
`7.6 Group Velocity 22.0... 0.00004
`7.7 Anharmonic Periodic Waves—Fourier Analysis
`7.8 Nonperiodic Waves—Fourier Integrals
`.
`.
`.
`-
`7.9 Pulses and Wave Packets... 2.2...
`7.10 Optical Bandwidths 2.2... 1. Le
`Problems
`.- 22... 2.200.208
`.
`8 Polarization
`270
`270
`8.1 The Nature of Polarized Light
`-
`82 Polarizers 2... 2.0... se
`277
`279
`83 Dichroism .. 2... ee ee
`282
`84 Birefringence... 2.2.2... 0.0004
`292
`8.5 Scattering and Polarization ....,....
`296
`8.6 Polarization by Reflection... 2... 2.
`300
`87 Retarders
`- 2... 2.2.0. ..-02.0,
`305
`88 Circular Polarizers
`. 2.2... LL
`306
`
`8.9 Polarization of Polychromatic Light
`309
`8.10 Optical Activity 2.2... 2...
`314
`8.11 Induced Optical Effects—Optical Modulators
`321
`8.12 A Mathematical Description of Polarization .
`.
`326
`Problems. 2... ee ee
`9 Interference
`333
`334
`. 2. .,.....002.
`91 General Considerations
`337
`9.2 Conditions for Interference... 2. 0...
`339
`9.3 Wayefront-Splitting Interferometers
`.
`.
`.
`.
`.
`346
`9.4 Amplitude-Splitting Interferometers
`.
`.
`.
`.
`.
`361
`9.5 Types and Localization of Interference Fringes
`363
`96 Multiple-Beam Interference ........
`373
`9.7 Applications of Single and Multilayer Films
`378
`98 Applications of Interferometry... ... .
`388
`Problems
`. 2-2... . ee. ee ee
`10 Diffraction
`392
`392
`10.f Preliminary Considerations 2... 4 6
`401
`10.2 Fraunhofer Diffraction ..... . see
`434
`10.5 Fresnel Diffraction ........ tee
`459
`10.4 Kirchhoff’s Scalar Diffraction Theory .
`.
`.
`.
`463
`10.5 BoundaryDiffractionWaves 2...) 0
`Problems
`2... 7... 2.2 ee eee
`
`
`
`
`12 Basics of Coherence Theory
`121
`Introduciion 2.0. ee see
`12.2 Visibility 2... 22. cae
`12.3 The Mutual Coherence Theory and the
`Degree of Coherence»... 2... an
`12.4 Coherence andStellar Interferometry.
`«
`Problems 22... 2... 2. ee
`
`13 Some Aspects of the Quantum Nature of
`Light
`13.f Quantum Fields 2.22. 2...
`13.2 Blackbody Radiation—Planck’s Quantum
`Hypothesis 2... 1 oe eee ee
`13.3. The Photoelectric Effect—Einstein’s Photon
`Concept... ee ee
`13.4 Particlesand Waves 2
`2 2 2
`2 2
`18.5 Probability and Wave Optics
`. 2... 2.
`13.6 Fermat, Feynman, and Photons ..... ~
`13.7 Absorption, Emission, and Scattering
`Problems
`. 2-2-7. ee ee ee ee
`
`14 Sundry Topics from Contemporary Optics
`14.1
`imagery—The Spatial Distribution of Optical
`Information «1... eee ee ee
`14.2 Lasers and Laserlight ...........
`14.3 Holography
`.......00....00.
`14.4 Nonlinear Optics 2...
`Problems
`
`Appendix 1
`Appendix 2
`Table 1
`Solutions to Selected Problems
`Bibliography
`Index of Tables
`Index
`
`Second Edition
`
`516
`516
`519
`523
`530
`535
`
`538
`538
`5389
`541
`544
`548
`550
`552
`556
`
`559
`559
`577
`593
`610
`616
`
`620
`623
`624
`629
`661
`665
`
`6
`
`

`

`i A BRIEF HISTORY
`
`
`1.1
`PROLEGOMENON
`In chapters to come we will evolve a formal treatment
`of muchof the scienceof optics with particular emphasis
`on aspects of contemporary interest. The subject
`embraces a vast body of knowledge accumulated over
`roughly three thousand years of the human scene.
`Before embarking on a study of the modern view of
`things optical, let's briefly trace the road that led us
`there, if for no other reason than to putit all in per-
`spective.
`The complete story has myriad subplots and charac-
`ters, heroes, quasi-heroes, and an occasionalvillain or
`two, Yet from our vantage in time, we cansift out of
`the tangle of millennia perhaps four main thermes—the
`optics of reflection and refraction, and the wave and
`quantum theories oflight.
`
`1.2
`IN THEBEGINNING
`
`Theorigins of optical technology date back to remote
`antiquity. Exodus 38:8 (ca. 1200n.c.) recounts how
`Bezaleel, while preparing the ark and tabernacle,recast
`“the looking-glasses of the women” into a brass laver
`(a ceremonial]basin). Early mirrors were made of pol-
`ished copper, bronze, and later on of speculum, a cop-
`per alloy rich in tin. Specimens have survived from
`ancient Egypt—-a mirror
`in perfect condition was
`unearthed along with some tools from the workers’
`
`quarters near the pyramid of Sesostris II (ca. 1900 B.c.)
`in the Nile valley. The Greek philosophers Pythagoras,
`Democritus, Empedocles, Plato, Aristotle, and others
`evolved several theories of the nature of light (that of
`the last narned being quite similar to the aether theory
`of the nineteenth century). Therectilinear propagation
`oflight was known,as was the law of reflection enunci-
`ated by Euclid (300 B.c.) in his book Cetoptrics. Hero of
`Alexandria attempted to explain both these phenomena
`by asserting that light traverses the shortest allowed
`path between two points. The burningglass {a positive
`lens} was alluded to by Aristophanes in his comic play
`The Clouds (424 s.c.). The apparent bendingof objects
`partly immersedin water is mentioned in Plato’s Repub-
`lic. Refraction was studied by Cleomedes(50 a.p.) and
`later by Claudius Ptolemy(130 a.p.) of Alexandria, who
`tabulated fairly precise measurementsof the angles of
`incidence and refraction for several media.It is clear
`from the accounts of the historian Pliny (23-79 a.p.)
`that the Romansalso possessed burningglasses. Several
`glass and crystal spheres, which were probably used to
`start fires, have been found among Romanruins, and
`a planar convex lens was recovered in Pompeii. The
`Roman philosopher Seneca (3 8.c-65 a.D.) pointed out
`that a glass globe filled with water could be used for
`magnifying purposes. Andit is certainly possible that
`some Romanartisans may have used magnifyingglasses
`to facilitate very fine detailed work.
`After
`the fall of
`the Western Roman Empire
`(475 a.p.), which roughly marksthestart of the Dark
`
`i
`
`7
`
`

`

`Ages,little or noscientific progress was made in Europe
`for a great while, The dominance of the Greco-Roman-
`Christian culture in the lands embracing the Mediter-
`ranean soon gaye way by conquest to the rule of Allah.
`Alexandria fell to the Moslemsin 642 A.p., and by the
`endofthe seventh century,the landsof Islam extended
`from Persia across the southern coast of the Medizer-
`ranean to Spain. Thecenter of scholarship shifted to
`the Arab world, wherethescientific and philosophical
`treasures of the past were translated and preserved.
`Rather than lying intact but dormant,as much ofscience
`did, optics was extended at the hands of Alhazen (ca.
`1000 a.p.). He elaborated on the law ofreflection, put-
`ting the angles of incidence and reflection in the same
`plane normalto the interface; he studied spherical and
`parabolic mirrors and gave a detailed description of the
`humaneye.
`By the latter part of the thirteenth century, Europe
`was only beginningto rouse from its intellectual stupor.
`Alhazen’s work was translated into Latin. and it had a
`greateffect on the writings of Robert Grosseteste (1175—
`1253), Bishop of Lincoln,
`and on
`the
`Polish
`mathematician Vitello (or Witelo), both of whom were
`influential in rekindling thestudyof optics. Their works
`were known to the Franciscan Roger Bacon (1215-
`1294), whois considered by manyto bethefirst scientist
`in the modern sense. He seems to have initiated the
`idea of using lenses for correcting vision and even
`hinted at the possibility of combining Jenses to form a
`telescope. Bacon also had some understanding of the
`way in which rays traverse a lens. After his death, optics
`again languished, Evenso, by the mid-1300s, European.
`paintings were depicting monks wearing eyeglasses.
`And alchemists had come up with a liquid amalgam of
`tin and mercury thatwas rubbed onto the back ofglass
`Plates to make mirrors, Leonardo da Vinci (1452-1519)
`described the camera obscura, later popularized by the
`work ofGiovanni Battista Della Porta (1585-1615), who
`discussed multiple mirrors and combinationsofpositive
`aud negative lenses in his Magia natwralis (1589).
`This, for the most part, modest array of events con-
`stitutes what might becalled the first period of optics.
`It was undoubtedly a beginning—but on the whole a
`dull one. It was more a time for learning howto play
`the game than actually scoring points. The whirlwind
`
`the various colors excited the aether into characteristic
`
`Chapter 1 A Brief History
`
`1.3 From the Seventeenth Century
`
`3
`
`of accomplishmentand excitement was to comelater,
`in the seventeenth century.
`
`>1
`
`mission angles are proportional. He evolved a treatment
`of first-orderoptics for thin-lens systems andin his book
`describes the detailed operation of both the Keplerian
`(positive eyepiece) and Galilean (negative eyepiece) tele-
`scopes. Willebrord Snell (1591-1626), professor at Ley-
`den, empirically discovered the long-hidden law of
`refraction in 1621—this was one of the great moments
`in optics. By learning precisely how rays oflight are
`redirected on traversing a boundary hetween two
`media, Snell in one swoop swung open the door to
`modern appliedoptics. René Descartes (1596-1650) was
`the first to publish the now familiar formulation of the
`law of refraction in termsof sines. Descartes deduced
`the law using a model in whichlight was viewed as a
`pressure transmitted by an elastic medium:as he putit
`in his La Dioptrique (1637)
`, +. recall the natnre that [ have attributed to light, when
`I said thatit is nothing other than a certain motion or
`an action conceived in a very subtle matter, which fills
`the poresofall other bodies...
`The universe was a plenum. Pierre de Fermat (1601-
`1665),
`taking exception to Descartes’s assumptions,
`rederived thelaw of reflection from his own principle
`ofleast time (1657). Departing from Hero’s shortest-path
`statement, Fermat maintained that
`light propagates
`from one point to anotheralong the route taking the
`least time, evenif it has to vary from the shortest actual
`path to doit.
`The phenomenon of diffraction, i.e., the deviation
`from rectilinear propagation that occurs when light
`advances beyond an obstruction, was first noted by
`Professor Francesco Maria Grimaldi (1618-1663)at the
`Jesuit College in Bologna. He had observed bands of
`light within the shadowofa rodilluminated by a small.
`source. Robert Hooke (1635-1703), curator of experi-
`ments for the RoyalSociety, London,later also observed
`diffraction effects. He was the first to study the colored
`interference patterns generated by thin films (Micro-
`graphia, 1665) and correctly concluded that they were
`due to an interaction betweenthe light reflected from
`the front and back surfaces. He proposed the idea that
`light was a rapid vibratory motion of the medium propa-
`ating at a very great speed. Moreover “every pulse or
`vibration of
`the luminous body will generate a
`
`Figure 1.2 René Descartes (1596-1650).
`
`sphere’”—this was the beginning of the wave theory.
`Within a year of Galileo’s death, Isaac Newton (1642—
`1727) was born. Thethrust of Newton's scientific effort
`is clear from his own description of his work in optics
`as experimental philosophy. It was his intent to build on
`direct observation and avoid speculative hypotheses.
`Thus he remained ambivalent for a long while about
`the actualnature oflight. Wasit corpuscular—a stream
`of particles, as some maintained? Or waslight a wave
`in an all-pervading medium,the aether? At the age of
`23, he began his now famous experiments ondispersion.
`I procured mea triangularglass prism to try therewith
`the celebrated phenomenaofcolours,
`Newton concluded that white light was composed of a
`mixture of a whole range of independentcolors. He
`maintained that the corpusclesof light associated with
`
`.3
`
`FROM THE SEVENTEENTH CENTURY
`
`It is not clear who actually invented the refracting
`telescope, but records in the archives at The Hague
`show that on October2, 1608, Hans Lippershey (1587-
`1619), a Dutch spectacle maker, applied for a patent
`on the device, Galileo Galilei (1564-1642), in Padua,
`heard aboutthe invention and within several months
`had built his own instrument, grinding the lenses by
`hand. The compound microscope wasinventedatjust
`about
`the same time, possibly by the Dutchman
`Zacharias Janssen (1588-1632). The microscope’s con-
`cave eyepiece was replaced with a convex lens by Fran-
`cisco Fontana (1580-1656) of Naples, and a similar
`change in the telescope was introduced by Johannes
`Kepler (1571-1630). In 1611, Kepler published his
`Dioptrice. He had discovered total internal reflection
`and arrived at the small angle approximationto the law
`of refraction,
`in which case the incident and trans-
`
`Figure 1.1
`
`Johannes Kepler (1571-1630).
`
`8
`
`

`

`
`
`
`
`
`4
`
`Chapter 1 A Brief History
`
`
`
`Figure 1.3 Sir Isaac Newton (1642-1727),
`
`the sensation of red corre-
`vibrations. Furthermore,
`sponded to the longest vibration of the aether, and
`violet to the shortest. Even though his work shows a
`curious propensity for simultaneously embracing both
`the wave and emission (corpuscular) theories, he did
`become more committedto thelatter as he grew older.
`Perhaps his main reason for rejecting the wave theory
`asit stood then was the blatant problem of explaining
`rectilinear propagation in terms of waves that spread
`outin all directions,
`After someall-too-limited experimenta, Newton gave
`up trying to remove chromatic aberration from refract-
`ing telescope lenses, Erroneously concluding that it
`could not be done, he turned to the design ofreflectors.
`Sir Isaac’s first reflecting telescope, completed in 1668,
`was only 6 inches long and 1 inch in diameter, but it
`magnified some 30 times.
`At aboutthe sametimethatSir Isaacwas emphasizing
`the emission theory in England, Christiaan Huygens
`(1629-1695), on the continent, was greatly extending
`the wave theory. Unlike Descartes, Hooke, and Newton,
`
`light effectively
`Huygens correctly concluded that
`slowed down on entering more dense media. He was
`able to derive the Jawsofreflection and refraction and
`even explained the doublerefraction of calcite, using
`his wave theory, Andit was while working with calcite
`that he discovered the phenomenonofpolarization.
`Asthere are two different refractions, I conceived also
`that there are two different emanations of the waves of
`light... .
`Thuslight was either a scream of particles or a rapid
`undulation of aethereal matter. In any case,
`it was
`
`
`
`Figure 1.4 Christiaan Huygens(1629-1695).
`
`its speed of propagation was
`generally agreed that
`exceedingly large. Indeed, many believed that light
`propagatedinstantaneously, a notion ibat went back at
`least as far as Aristotle. The fact chat it was finite was
`determinedby the Dane Ole Christensen Rémer(1644-
`1710). Jupiter's nearest moon, Jo, bas an orbit about
`that planetthat is nearly in the plane of Jupiter's own
`orbit around the Sun. Rémer made a careful study of
`the eclipses of Io as it moved throughthe shadow hehind
`Jupiter. In 1676 he predicted that on November9th Io
`would emerge from the dark some 10 minutes later
`than would have been expected onthe basisofits yearly
`averaged motion, Precisely on schedule, Io performed
`as predicted, a phenomenon Rémercorrectly explained
`as arising from thefinite speed oflight. He was able to
`determinethat light took about 22 minutesto traverse
`the diameter of the Earth’s orbit around the Sun—a
`distance of about 186 million miles. Huygens and
`Newton, among others, were quite convinced of the
`validity of Romer's work. Independently estimating the
`Earth’s orbital diameter,
`they assigned values to ¢
`equivalent to 2.3 X 10° mjs and 2.4 x 10° m/s, respec-
`tively.Still others, especially Hooke, remained skeptical,
`arguing that any speedso incredibly high actually had
`to be infinite.*
`The great weight of Newton's opinion hunglike a
`shroud over the wave theory during the eighteenth
`century, all butstifling its advocates. There were too
`many content with dogma and too few nonconformist
`enough to follow their own experimental philosophy,
`as surely Newton would have had them do. Despite this,
`the prominent mathematician Leonhard Euler (1707—
`1783) was a devotee of the wave theory, even if an
`unheeded one. Euler proposed that the undesirable
`color effects seen ina lens were absentin the eye (which
`is an erroneous assumption)because the different media
`present negated dispersion. He suggested that achro-
`matic lenses might be constructed in a similar way.
`Enthused by this work, Sarnuel Klingenstjerna (1698-
`1765), a professor at Upsala, reperformed Newton's
`experiments on achromatism and determined them to
`be in error. Klingenstjerna was in communication with
`
`* A. Wrdblewski, Am. J. Phys. 53 (7), July 1985, p. 620.
`
`1.4 The Nineteenth Century
`
`5
`
`a Londonoptician, John Dollond (1706-1761), who was
`observing similar results. Dollond finally, in 1758, com-
`bined two elements, one of crown andthe otherofflint
`glass, to form a single achromatic lens. This was an
`accomplishment of very great practical
`importance.
`Incidentally, Dollond’s vention was actually preceded
`by the unpublished work of the amateur scientist
`Chester MoorHall (1703-1771) of Moor Hall in Essex.
`
`1.4
`
`THE NINETEENTH CENTURY
`
`The wave theory of light was reborn at the hands of
`Dr. Thomas Young (1773-1829), one of the truly great
`mindsof the century. On November 12, 1801, July 1,
`1802, and November 24, 1803, he read papers before
`the RoyalSociety extolling the wave theory and adding
`to it a new fundamentalconcept, the so-called principle
`of interference:
`Whentwo undulations, from diflerentorigins, coincide
`either perfectly or very nearly in direction, their joint
`effect is a combinationof the motions belonging to each.
`Hewas able to explain the colored fringes of thin films
`and determined wavelengths of various colors using
`Newton’s data. Even though Young, time and again,
`maintained thathis conceptions had their very origins
`in the research of Newton, he wasseverely attacked. In
`a seriesof articles, probably written by Lord Brougham,
`in the Edinburgh Review’, Young's papers were said to
`be ‘destitute of every species of merit”—and that’s
`going pretty far. Underthepall of Newton's presumed
`infallibility, the pedants of England were not prepared
`for the wisdom of Young, who in turn becamedisheart-
`ened.
`Augustin Jean Fresnel (1788-1827), born in Broglie,
`Normandy, beganhisbrilliant revival of the wave theory
`in France, unaware of the efforts of Young some 13
`years earlier. Fresnel synthesized the concepts of
`Huygens’s wave description andthe interference prin-
`ciple. The mode of propagation of a primary wave was
`viewed as a succession of stimulated spherical secondary
`wavelets, which overlapped and interfered to reform
`the advancing primary wave as it would appear an
`instant later. In Fresnel’s words:
`
`
`
`9
`
`

`

`7
`
`Figure 1.6
`
`James Clerk Maxwell (1831-1879).
`
`1.4 The Nineteenth Century
`
`order to measure the duration of an electric spark.
`to the interference principle, a somewhat disappointed
`
`Using this scheme, Arago had proposed to measure the
`Fresnel nonetheless wrote to Youngtelling him that he
`
`was consoled by finding himself in such good com-
`speed of light in dense media but was never able to
`pany—the two great men becameallies.
`carry out the experiment. Foucault took up the work,
`
`which was later to provide material for his doctoral
`Huygens was aware of the phenomenonof polariz-
`thesis. On May 6, 1850, he reported to the Academy of
`ation arising in calcite crystala, as was Newton.Indeed,
`Sciences that the speed oflight in water was less than
`the latter in his Opticks stated,
`
`that in air. This result was, of course, in direct conflict
`Every Rayof Light has therefore two opposite Sides...
`with Newton's formulation of the emission theory and
`
`a hard blow to its few remaining devotees.
`Hefurther developedthis conceptof Jateral asymmetry
`While all of this was happening in optics, quite
`even though avoiding any interpretation in terms of
`
`independently, the study of electricity and magnetism
`the hypothetical nature of light. Yet it was not until
`wasalso bearing fruit. In 1845 the master experimen-
`
`1808 that Etienne Louis Malus (1775-1812) discovered
`talist Michael Faraday (1791~1867) established aninter-
`that this two-sidedness of light became apparent upon
`
`relationship between electromagnetism andlight when
`reflection as well; it was not inherent co crystalline
`he foundthatthepolarization direction of a beam could
`media. Fresnel and Arago then conducted a series of
`
`bealtered by a strong magnetic field applied to the
`experiments to determinethe effect of polarization on
`medium. James Clerk Maxwell (1831-1879) brilliantly
`interference, but the results were utterly inexplicable
`
`summarized and extendedall the empirical knowledge
`within the framework of their longitudinal wave pic-
`on the subject in a single set of mathematical equations.
`ture—this was a dark hour indeed. For several years
`
`Beginning with this remarkably succinct and beautifully
`Young, Arago, and Fresnel wrestled with the problem
`until finally Young suggested that the aethereal vibra-
`symmetrical synthesis, he was able to show, purely
`theoretically,
`that
`the electromagnetic field could
`tion might be transverse as is a wave onastring. The
`
`propagate as
`a
`transverse wave
`in the
`luminif-
`two-sidednessoflight was then simply a manifestation
`erous aether. Solving for the speed of the wave, he
`of the two orthogonal vibrations of the aether, trans-
`
`verse to the ray direction. Fresnel went on to evolve a
`arrived at an expression in terms of eleciric and
`mechanistic description of aetheroscillations, which led
`magnetic properties of
`the medium (c= 1/Vep#o).
`
`Upon substituting known empirically determined
`to his now famousformulasfor the amplitudeof reflec-
`
`values for these quantities, he obtained a numerical
`rather strange properties. 1c had to be so tenuousas to
`ted and transmitted light. By 1825 the emission (or
`
`
`allow an apparendy unimpeded motion of celestial
`result equal to the measured speed of light! The con-
`corpuscular) theory had only a few tenacious advocates.
`
`bodies. At the same timeit could support the exceed-
`clusion was inescapable—light was “an electromagnetic
`The first terrestrial determination of the speed of
`
`
`disturbance in the form of waves” propagated through the
`
`
`ingly high-frequency (~10'° Hz) oscillations of light
`light was performed by ArmandHippolyte Louis Fizeau
`traveling at 186,000 miles/s. That implied remarkably
`aether. Maxwell died at the age of 48, eight years too
`(1819-1896) in 1849. His apparatus, consisting of a
`strong restoring forces within the aethereal substance.
`soonto see the experimental confirmationofhis insights
`rotating toothed wheel and a distant mirror (8633 m),
`
`
`was set up in the suburbs of Paris from Suresnes to
`Thespeed at which a wave advances through a medium
`and far too soon for physics. Heinrich Rudolf Hertz
`
`
`is dependent uponthe characteristics of the disturbed
`(1857-1894) verified the existence of long electromag-
`Montmartre. A pulse oflight leaving an opening in the
`
`
`substratum and not upon any motion of the source.
`netic waves by generating and detecting them in an
`wheel struck the mirror and returned. By adjusting the
`extensive series of experiments published in 1888.
`This is in contrast to the behaviorofa streamofparticles
`knownrotational speed of the wheel, the returning
`
`
`whose speed with respect to the source is the essential
`The acceptance of the wavetheory oflight seemed
`pulse could be made either to pass through an opening
`
`
`
`parameter.
`to necessitate an equal acceptance of the existence of
`and be seen or to be obstructed by a tooth. Fizeau
`Certain aspects of the nature of aether intrude when
`an all-pervading substratum, the luminiferousaether.
`arrived at a value of
`the speed of light equal
`to
`
`
`If there were waves,it seemed obvious that there must
`studying the optics of moving objects, and it was this
`315,300km/s. His
`colleague Jean Bernard Léon
`
`
`Foucault (1819-1868) was also involved in research on
`area of researc