`
`ELECTROMAGNETIC THEORY OF PROPAGATION
`INTERFERENCE AND DIFFRACTION OF LIGHT
`Sixth Edition
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`IMMERVISION Ex. 2017
`LG v. ImmervVision
`IPR2020-00179
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`Principles of Optics
`
`Electromagnetic Theory of Propagation,
`Interference and Diffraction of Light
`by
`
`MAX BORN
`M.A., Dr.Phil., F.R.S.
`Nobel Laureate
`Formerly Professor at the Universities of Géttingen and Edinburgh
`and
`
`EMIL WOLF
`Ph.D., D.Sc.
`Professor of Physics, University of Rochester, N.Y.
`
`with contributions by
`
`A. B. Buatta, P. C. Curmmow, D. Gazpor, A. R. Stoxss,
`A. M. Taytor, P. A. Wayman and W. L. Witcock
`
`SIXTH EDITION
`
`PERGAMON PRESS
`
`OXFORD - NEW YORK : TORONTO : SYDNEY - PARIS : FRANKFURT
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`U.S.A,
`
`CANADA
`
`AUSTRALIA
`
`FRANCE
`
`FEDERAL REPUBLIC
`OF GERMANY
`
`PergamonPress Ltd., Headington Hill Hall,
`Oxford OX3 OBW, England
`PergamonPress Inc., Maxwell House, Fairview Park,
`Elmsford, New York 10523, U.S.A.
`Pergamon of Canada, Suite 104, 150 Consumers Road,
`Willowdale, Ontario M2J 1P9, Canada
`PergamonPress (Aust.) Pty. Ltd., P.O. Box 544,
`Potts Point, N.S.W. 2011, Australia
`Pergamon Press SARL, 24 rue des Ecoles,
`75240 Paris, Cedex 05, France
`Pergamon Press GmbH, 6242 Kronberg-Taunus,
`Hammerweg6, Federal Republic of Germany
`
`Copyright © 1980 Max Born and Emil Wolf
`All Rights Reserved. No part of this publecation may be
`reproduced, stored ina retrieval systemor transmitted in
`any form or by any means. electronic, electrostatic,
`magnetic tape, mechanical, photocopying, recording or
`otherwise, without permission in writing from the
`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
`IL. Wolf, Emil
`535
`Qc351
`80-41470
`ISBN 0-08-026482-4 hardcover
`ISBN 0-08-026481-6 flexicover
`
`Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
`
`PREFACE °
`
`Tur 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 wa:
`a substantially new book w:
`In planning this book it soo
`developments which took pl
`book would become impra
`restrict its scope to a narro
`The optics of moving media,
`full connection between opt
`old book consider the effec
`subjects can be treated mo
`relativity, quantum mechan
`book not only are these sub}:
`was the subject-matter of <
`restricted to those optical p
`phenomenological theory. 1
`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 waythat practically:
`MaxweEtv’s electromagnetic
`In Chapter I the main pri
`effect of matter on the pro
`formally, in terms of the us
`question of influence of ma
`presence of an external inc
`may be assumedtogive rise
`tion of these wavelets leads
`considerable physical signi
`(Chapter XII) in connectic
`treated in this way by A. B
`by Prof. BuattA himself.
`A considerable part of C
`follows from MaxwWELL’s ¥
`addition to discussing the
`
`* Max Born, Optik (Berlin,
`
`
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`

`

`iv4
`
`PRINCIPLES OF OPTICS
`
`<7
`
`GEOMETRICAL
`
`= 0,
`
`= 9.
`
`lo = dy‘ cos Oo,
`
`£5 = d,") cos 4,
`
`£, = 4,"cos nl
`
`fi = d,©) cos 6,
`
`
`Mo MH _ Mo 608 6) — m, cos Oy
`d,'*)
`d,'*)
`Ts
`
`le aati:
`
`
`
`Fig. 4.28, The longit
`
`;
`158
`
`a
`(+=
`
`(n
`
`5
`
`(23
`“a
`
`The correspondingrelations for reflection may be obtained by setting ny = — 7.
`
`4.7.1 Chromatic aberration
`
`This relation gives the position of the focus F, of the refracted rays. From (14s =
`is seen that the focal line through F, is perpendicular to the yz-plane so that F, i =
`primary focus.
`To find the position of the other focus, consider the rays which proceed from #_
`Then 2 = C), 6% = bY) = 6% = 0. Since all these rays intersect the focal line +,
`dg) = dm, = 0. Equations (14) and (16) now give
`;
`bo
`1
`(142
`= sec O45 — — (6p, — dM)
`No
`zu
`0°Po
`(6p,
`Do)
`(162
`éq, = 0.
`and
`(16b) shows that the refracted rays now lie in the xz-plane. All these rays will pas
`dx, = dy, = dz, = 0, wrhater the value of dp). Hence,
`through the other focus F{(z, = ¢)), so that (15) must be satisfied with z=
`a
`i
`(
`ny
`in
`19°P1
`(Sp,
`Po)
`= sec 0,dp, — — r,(dp, — Spo)
`Since (15b) and (14b) hold simultaneously for any arbitrary value of ds,it follows that
`
`Ny cos,
`mn, cos 6,
`ng cos Oy — 2, cos ty
`,
`,
`: —
`—_
`=
`f
`oy
`Ty
`This relation gives the position of the secondary focus F}.
`It is often convenient to specify the position of the foci by meansoftheir distances
`from O rather than by means of their z coordinates. If OF) = dj’, OF, = d;*
`OF, = d,, OF, = d,®) (in Fig. 4.22 do<0, d,) <0, d," > 0, d,'*) > 0), then
`
`
`
`We ma
`confineoour atter
`i.e. it will be assu
`
`
`optics. The chro
`
`Q. and Q; are the
`
`ojections of 0,0
`
`
`tudinal an
`
`= change 6f in the fc
`
`x. According to §-
`Gieimtiecendent of the wavelength
`
`
`
`
`
`
`
`
`Gers a>. Np and vgarethe refre
`=
`<s61 A. 5893 A, 6563 A res
`
`of the glass, andis calle:
`
`and the two relations (18) and (19) become
`mately equal to the distan
`
`
`h of the lens, whenthe o|
`
`7M, cos® 6,—m, cos? A, 4 cos Oy — n, cos A, (21
`
`
`@ “te refractive index of the ust
`d,
`ad,
`ry
`=
`
`ern in Fig. 4.24. The correspon
`and
`T. obtain an image of good quz
`
`
`ons must be small. Usuall
`
`ies the chromatic aberration
`
`= merclengths will naturally
`
`‘escc<d:
`for example,since the o
`4.7 CHROMATIC ABERRATION. DISPERSION BY A PRISM
`_s= vezion than is the humaneye, ¢
`
`Se ours nearerto the blue endof
`
`In Chapter IT it was shown that the refractive index is not a material constant but
`
`atization with respect to t
`dependson colour, i.e. on the wavelength of light. We shall now discuss some elemen-
`
`ers removal of the colourerror.
`tary consequencesof this result in relation to the performance of lenses and prisms.
`© scondary spectrum.
`
`Le us now examine under what
`
`m=Dination with respectto their !
`~ +2= focal length of a combinati
`grea by
`
`1
`
`If a ray of polychromatic light is incident upon a refracting surface, it is split into
`set of rays, each of which is associated with a different wavelength. In traversing an
`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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`

`4.7]
`
`GEOMETRICAL THEORY OF OPTICAL IMAGING
`
`175
`
`Weshall again confine our attention to points and rays in the immediate neighbour-
`hoodof theaxis, 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 Q, and Q, are the images of a point P in two different wavelengths
`(Fig. 4.23), the projections of Q,Q, in the directions parallel and perpendicular to the
`axis are known as longitudinal and lateral chromatic aberration respectively.
`Consider the change 6f in the focal length of a thin lens, due to a change dn in the
`refractive index. According to §4.4 (36) the quantity (n — 1)f will, for a given lens,
`be independent of the wavelength. Hence
`
` of én
`=
`eo
`lpn
`A=,
`Np —1
`
`The quantity
`
`= 0.
`
`1
`(1)
`
`(2)
`
`Qseae Lateral
`Ger
`r
`| chromatic
`TSSTS aberration
`
`es os es
`
`EE
`
`fo
`—_——
`Longitudinal chromatic
`aberration
`
`Fig. 4.23, The longitudinal and lateral chromatic aberration.
`
`(4.7
`
`(14a)it
`Fy, isa
`
`com Fy.
`line fo,
`
`(14b)
`
`(16b)
`
`vill pass
`= oh
`
`(15b)
`
`ws that
`
`(19)
`
`istances
`= dy,
`, then
`
`(21)
`
`(22)
`
`— N,.
`
`ISM
`
`ant but
`slemen-
`orisms.
`
`
`
`where p, Np and rg are the refractive indices for the Fraunhofer F, D andClines
`(20)
`(A = 4861 A, 5893 A, 6563 A respectively) is a rough measure of the dispersive
`properties of the glass, and is called the despersive 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, whenthe 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. 4.24. 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 generalit
`is impossible to eliminate all the aberrations simultaneously. Often it is sufficient ta
`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 humaneye, photographic objectives are usually‘‘achromatized”’
`for colours nearerto the blue end of the spectrum thanis 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
`t into a
`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 distanceJis
`sing an
`‘action,
`given by
`ind the
`
`1
`1
`1
`i
`FRR ER
`
`(3)
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