ELECTROMAGNETIC THEORY OF PROPAGATION
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`Sixth Edition
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`INTERFERENCE AND DIFERACTION OF lIGHT
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`IMMERVISION Ex. 2017
`LG v. ImmerVision
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`k Principles of Optics
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`Electromagnetic Theory of Propagation,
`Interference and Difi‘raction of Light
`
`by
`
`MAX BORN
`M.A., Dr.Phil., F.R.S.
`Nobel Laureate
`Former/y Professor at the Universities of Goningen and Edinburgh
`and
`
`EMIL WOLF
`Ph.D., D.Sc.
`Professor of Physics, University of Rochester, N. Y.
`
`with contributions by
`
`A. B. BHATIA, P. C. CLEMMOW, D. GABOR, A. R. STOKES,
`A. M. TAYLOR. P. A. VVAYMAN and W. L. Wmoocx
`
`SIXTH EDITION
`
`@7
`
`PERGAMON PRESS
`
`OXFORD ' NEW YORK ' TORONTO ' SYDNEY ' PARIS ' FRANKFURT
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`UK.
`
`L'iS.Ai
`
`CANADA
`
`AUSTRALIA
`
`FRANCE
`
`FEDERAL REPUBLIC
`OF GERMANY
`
`Pergamon Press Ltd. IIeadington Hill Hall,
`Oxford OX3 OBW, England
`Pergamon Press Inc.. Maxwell House. Fairview Park,
`Elmsford, New York 10523. U.S.A.
`Pcrgamnn of Canada‘ Suite 104, 150 Consumers Road,
`Willowdale. Ontario M2] 1P9, Canada
`Pergamon Press (Aust.) Pty. Ltd, P.O. Box 544,
`Potts Point. N.S,W. 20“, Australia
`Pergamon Press SARL, 24 rue des Ecoles,
`75240 Paris Cedex 05, France
`Pergamon Press GmbH, 6242 Kronbcrg-Taunus,
`Hammerweg 6, Federal Republic of Germany
`
`Copyright © 1980 Max Born and Emil Wolf
`All Rights Reserved No part ofthz‘s publication may be
`reprodured, stored in a retrieval system or transmitted in
`any form 01 by any means: electronic, electrostatic,
`magnetic tape. mechanical, photocopying, recording or
`otherwise. without permission in writing from [he
`copyright holders
`First edition 1959
`
`Second (revised) edition 1964
`Third (revised) edition 1965
`Fourth (revised) edition 1970
`Fifth (revised) edition 1975
`Reprinted 1975, 1977
`Sixth edition 1980
`
`Library of Congress Cataloging in Publication Data
`Born, Max
`Principles of optics. - 6th ed.
`1. Optics - Collected works
`I. Title
`II. \Nolf, Emil
`535
`QC351
`80-4-1470
`ISBN 0-03-026482-4 hardcover
`ISBN 0—08-026481-6 flexicover
`
`Printed in Great Britain by A. Wheaten 8‘ Co. Ltd., Exeter
`
`PREFACE '
`
`THE idea of writing this boc
`of publishing in the English :
`twenty-five years ago A pr
`researches on almost every
`
`years, so that the book no 1»
`field. In consequence it was
`a substantially new book we
`In planning this book it 500
`developments which took pl
`book would become impral
`restrict its scope to a narro
`The optics of moving media.
`full connection between op:
`old book consider the efiec
`subjects can be treated nic-
`relativity, quantum mechar.
`book not only are these subjz
`was the subject—matter of a
`restricted to those optical p
`phenomenological theory.
`'I
`of matter plays no decisiv
`mechanics, and physiology
`The fact that, even after t?
`some indication about the
`classical optics in recent tin
`We have aimed at giving
`plete picture of our present
`such a way that practically .
`MAXWELL’s electromagnetic
`In Chapter I the main prl
`effect of matter on the pro
`formally, in terms of the us
`question of influence of ma
`presence of an external in(
`may be assumed to give rise
`tion of these wavelets leads
`considerable physical signi
`(Chapter XII) "in connectic
`treated in this Way by A. B
`by Prof. BHATIA himself.
`A considerable part of C
`follows from MAXWELL’s v
`addition to discussing the
`
`‘ MAX BORN, Optik (Berlin.
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`3/5
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`GIOEETRICAL
`
`
`:Jinerour a:te:
`
`..e. i: xvi:Ibe ass
`
`optics. The (if:
`Q; and Q: are the
`
`ejections of QZQ
`
`
`
`
`‘5 Mé1ii—1’. of the wavelength
`
`m
`
`27m..._'
`
`
`
`Fig. 4.23. The Iongj:
`
`M ~ 7. "-D and no are the refre
`-A. 5893 A 6.563 A res
`
`3f the glass, and15 calls
`
`
`
`m we ::fractive index of the usL
`an: r: r Fig-1:324. The correspor
`_: 2::ain an image of good qua
`:35 must be small. Usuall
`
`211:2»:— zhe chromatic aberration
`125: ~avelengths Will naturally
`25;: :for example, since the o
`w‘9:311 than1s the human e}e. I
`-:-: ;rs nearer to the blue end of
`
`atization with respect to t
`we .eznoval of the colour error
`3: r-{fZ'IL’ZaTy spectrum.
`Let “=z'nov. examine under ahat
`ztttaaion with respect to their 1
`1' :5 focal length of a combinati
`2:":- by
`
`l f
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`17-1
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`PRINCIPLES OF OPTICS
`
`'
`
`'
`
`. From (145 in
`This relation gives the position of the focus F1 of the refracted rays
`is seen that the focal line through F1 is perpendicular to the yz-plane so that F1 is
`primary focus.
`To find the position of the other focus, consider the rays which proceed from 3—,.
`Then 20 = :6, 6050 = (53/0 = (520 = 0. Since all these rays intersect the focal line f,
`dqo = 61m, = 0. Equations (14) and (16) now give
`
`4’
`no
`
`_ 0,
`
`(14:
`
`1
`r6 — 6
`sec 006
`110- I, M P1
`100)
`(1'5
`691 ~
`and
`(16b) shows that the refracted rays now lie in the :cz- plane. All these rays will 13::
`through the other focus F1(zz] = {1), so that (15) must be satisfied with 21—— I.
`6:51—— 63/1—— 621:0,whate1ver the value of 612,, Hence,
`Z’
`1
`—- sec 015
`73(61’1 " 5P0) = 0-
`"1
`121— .“
`
`L'JI
`
`(1
`
`Since (15b) and (14b) hold simultaneously for any arbitrary value of 6pc, it follows tbs:
`
`n0 cos (9.J
`I
`:0
`
`n1 cos 6]
`I
`C1
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`=
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`no cos 00 —— nl cos 0,
`V
`V
`77 7'
`re:
`
`ll;
`
`This relation gives the position of the secondary focus F;
`It is often convenient to specify the position of the foci by means of their distally:
`from 0 rather than by means of their 2 coordinates. If 0F0 = do‘”, 0F; = (10‘
`0F1 '2 d1”), 0F; = dli” (in Fig. 4.22 do”) < 0, do") < 0, all”) > 0, d1”) > 0), ther.
`
`Co = dom 003 90)
`
`{3 = dam cos 60,
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`:1 = d1”) “05 01’}
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`E; = d1”) cos 61,
`
`and the two relations (18) and (19) become
`
`and
`
`
`n,I 0082 0fJ _ n1 cos2 01 __ no cos 00 — n1 cos 0,
`do”)
`dim
`r1,
`
`
`no _ n1 _ n0 cos 6,, — n1 cos 6,.
`do“)
`‘11") ‘
`T:
`
`(mi
`
`L
`
`(a:
`'
`
`a:
`('-
`
`The corresponding relations for reflection may be obtained by setting n1 2 — no.
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`4.7 CHROMATIC ABERRATION. DISPERSION BY A PRISM
`
`In Chapter II it was shown that the refractive index is not a material constant b:
`depends on colour, i.e. 011 the wavelength of light. We shall now discuss some elemer:
`tary consequences of this result in relation to the performance of lenses and prisms.
`
`4.7.1 Chromatic aberration
`
`If a. ray of polychromatic light is incident upon a refracting surface, it is split into a
`set of rays, each of which is associated with a different wavelength. In traversing 8:
`optical system, light of different wavelengths will therefore, after the first refraction.
`follow slightly different paths.
`In consequence, the image will not be sharp and the
`system is said to suffer from chromatic aberration.
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`
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`[4.7
`
`(14a) it
`F1 is a
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`70m F6.
`line f0,
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`(14b)
`
`(16b)
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`rill pass
`31 = :1:
`
`(15b)
`
`rWS that
`
`(19)
`
`istanoes
`= dam,
`, then
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`(20)
`
`(21)
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`(22)
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`— no.
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`ISM
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`ant but
`elemen-
`)risms.
`
`: into a
`sing an
`-action,
`LDCl the
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`4.7]
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`GEOMETRICAL THEORY or OPTICAL IMAGING
`
`175
`
`We shall again confine our attention to points and rays in the immediate neighbour-
`hood of the axis, i.e. it will be assumed that the imaging in each wavelength obeys the
`laws of Gaussian optics. The chromatic aberration is then said to be of the first order,
`or primary. If 01 and Q, are the images of a point P in two different wavelengths
`(Fig. 4.23), the projections of (1)an in the directions parallel and perpendicular to the
`axis are known as longitudinal and lateral chromatic aberration respectively.
`Consider the change (if in the focal length of a thin lens, due to a change On in the
`refractive index. According to §4.4 (36) the quantity (n. —— ])f will, for a given lens,
`be independent of the wavelength. Hence
`
` M an
`:—
`f + n _ I
`n
`—— n
`A : —F0,
`n D — 1
`
`1
`
`<
`
`)
`
`(2)
`
`The quantity
`
`= 0,
`
`_.
`
`_______
`
`4
`
`[2g_____ Lafera/
`0a
`I
`i. chroma/Io
`T"‘ " ‘ ‘1"""" aberraflon
`i
`l
`L;—
`7‘4
`Longi/udina/ chromafic
`aberrafian
`
`Fig. 4.23. The longitudinal and lateral chromatic aberration.
`
`where 71F, nD and no are the refractive indices for the Fraunhofer F, D and 0 lines
`(1. :7 4861 A, 5893 A, 6563 A respectively) is a rough measure of the dispersive
`properties of the glass, and is called the dispersive power. From (1) it is seen that it is
`approximately equal to the distance between the red and blue image divided by the
`focal length of the lens, when the object is at infinity. The variation with wavelength,
`of the refractive index of the usual types of glass employed in optical systems is
`shown in Fig. 4.21. The corresponding values of A lie between about 1/60 and 1/30.
`To obtain an image of good quality, the monochromatic as well as the chromatic
`aberrations must be small. Usually a compromise has to be made, since in general it
`is impossible to eliminate all the aberrations simultaneously. Often it is sufficient to
`eliminate the chromatic aberration for two selected wavelengths only. The choice of
`these wavelengths will naturally depend on the purpose for which the system is
`designed;
`for example, since the ordinary photographic plate is more sensitive to the
`blue region than is the human eye, photographic objectives are usually “achromatized”
`for colours nearer to the blue end of the spectrum than is the case in visual instruments.
`Achromatization with respect to two wavelengths does, of course, not secure a com-
`plete removal of the colour error. The remaining chromatic aberration is known as
`the secondary spectrum.
`Let us now examine under What conditions two thin lenses will form an achromatic
`combination with respect to their focal lengths. According to §4.4 (39) the reciprocal
`of the focal length of a. combination of two thin lenses separated by a distance I is
`given by
`
`1
`f
`
`1
`1
`l
`1+ng—JE.
`
`(3)
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