`

`Modern
`Optical Engineering
`
` Ex. 1015
`
`HP,
`
`

`

`Other McGraw-Hill Titles of Interest
`
`FISCHER • Optical System Design
`HECHT • Laser Guidebook, Second Edition
`MILLER • Photonics Rules of Thumb
`MOUROULIS • Visual Instrumentation Handbook
`OSA • Handbook of Optics, Volumes I to IV
`OSA • Handbook of Optics on CD-ROM
`SMITH • Practical Optical System Layout
`SMITH • Modern Lens Design
`WAYNANT • Electro-Optics Handbook, Second Edition
`
` Ex. 1015
`
`HP,
`
`

`

`Modern
`Optical Engineering
`
`The Design of Optical Systems
`
`Warren J. Smith
`Chief Scientist, Kaiser Electro-Optics Inc.
`Carisbad, California
`and Consultant in Optics and Design
`
`Third Edition
`
`McGraw-Hill
`New York San Francisco Washington, D.C. Auckland Bogotá
`Caracas Lisbon London Madrid Mexico City Milan
`Montreal New Delhi San Juan Singapore
`Sydney Tokyo Toronto
`
` Ex. 1015
`
`HP,
`
`

`

`Library of Congress Cataloging-in-Publication Data
`
`Smith, Warren J.
`Modern optical engineering / Warren J. Smith—3rd ed.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 0-07-136360-2
`1. Optical instruments—Design and construction.
`
`I. Title.
`
`TS513.S55 2000
`621.36—dc21
`
`00-032907
`
`McGraw-Hill
`A Division of The McGraw-Hill Companies
`
`'iZ
`
`Copyright © 2000, 1990, 1966 by The McGraw-Hill Companies, Inc.
`Printed in the United States of America. Except as permitted under the
`United States Copyright Act of 1976, no part of this publication may be
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`the publisher.
`
`1 2 3 4 5 6 7 8 9 0 DOC/DOC 0 5 4 3 2 1 0
`
`P/N 0-07-136379-3
`PART OF
`ISBN 0-07-136360-2
`
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`was Sherri Souffrance. It was set in New Century Schoolbook by
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`
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`
` Ex. 1015
`
` HP,
`
`

`

`Prisms and Mirrors
`
`93
`
`WHITE LIGHT
`
`Figure 4.2 The dispersion of white light into its component
`wavelengths by a refracting prism (highly exaggerated).
`
`almost at normal incidence to the prism faces. Under these conditions,
`we can write
`
`i′
`
`1
`
`⫽
`
`i1ᎏ
`n
`
`⫽ A ⫺ i′
`
`i2
`i′
`
`⫽ ni2
`
`2
`
`⫽ A ⫺
`
`1
`
`i1ᎏ
`n
`⫽ nA ⫺ i1
`
`D ⫽ i1
`
`⫹ i′
`
`⫺ A ⫽ i1
`
`⫹ nA ⫺ i1
`
`2
`
`⫺ A
`
`and finally
`
`D ⫽ A (n ⫺ 1)
`
`(4.8a)
`
`If the prism angle A is small but the angle of incidence I is not small,
`we get the following approximate expression for D (which neglects
`powers of I larger than 3).
`
`D ⫽ A (n ⫺ 1) 冤1 ⫹
`
`I2 (n ⫹ 1)ᎏᎏ
`2n
`
`⫹ . . .冥
`
`(4.8b)
`
`These expressions are of great utility in evaluating the effects of a
`small prismatic error in the construction of an optical system since it
`allows the resultant deviation of the light beam to be determined quite
`readily.
`The dispersion of a “thin” prism is obtained by differentiating Eq.
`4.8a with respect to n, which gives dD ⫽ Adn. If we substitute A from
`Eq. 4.8a, we get
`
`dnᎏ
`(n ⫺ 1)
`Now the fraction (n ⫺ 1)/⌬n is one of the basic numbers used to char-
`acterize optical materials. It is called the reciprocal relative dispersion,
`
`dD ⫽ D
`
`(4.9)
`
` Ex. 1015
`
` HP,
`
`

`

`94
`
`Chapter Four
`
`Abbe V number, or V-value. Ordinarily n is taken as the index for the
`helium d line (0.5876 ␮m) and ⌬n is the index difference between the
`hydrogen F(0.4861 ␮m) and C(0.6563 ␮m) lines, and the V-value is giv-
`en by
`
`nd ⫺ 1ᎏ
`nF
`⫺ nC
`Making the substitution of 1/V for dn/(n ⫺ 1) in Eq. 4.9, we get
`Dᎏ
`V
`which allows us to immediately evaluate the chromatic dispersion pro-
`duced by a thin prism.
`
`(4.10)
`
`(4.11)
`
`V ⫽
`
`dD ⫽
`
`4.4 Minimum Deviation
`The deviation of a prism is a function of the initial angle of incidence
`I1. It can be shown that the deviation is at a minimum when the ray
`passes symmetrically through the prism. In this case I1 ⫽ I′2 ⫽ 1⁄2(A ⫹
`D) and I′1 ⫽ I2 ⫽ A/2, so that if we know the prism angle A and the
`minimum deviation angle D0 it is a simple matter to compute the index
`of the prism from
`
`n ⫽
`
`⫽
`
`sin 1⁄2 (A + D0)ᎏᎏ
`sin I1ᎏ
`sin I′1
`sin 1⁄2 A
`This is a widely used method for the precise measurement of index,
`since the minimum deviation position is readily determined on a spec-
`trometer. This position for the prism is also approximated in most
`spectral instruments because it allows the largest diameter beam to
`pass through a given prism and also produces the smallest amount of
`loss due to surface reflections.
`
`(4.12)
`
`4.5 The Achromatic Prism and the Direct
`Vision Prism
`It is occasionally useful to produce an angular deviation of a light
`beam without introducing any chromatic dispersion. This can be done
`by combining two prisms, one of high-dispersion glass and the other of
`low-dispersion glass. We desire the sum of their deviations to equal
`D1,2 and the sum of their dispersions to equal zero. Using the equations
`for “thin” prisms (Eqs. 4.8 and 4.11), we can express these require-
`ments as follows:
`
`Deviation D1,2
`
`⫽ D1
`
`⫹ D2
`
`⫽ A1 (n1
`
`⫺ 1) ⫹ A2 (n2
`
`⫺ 1)
`
` Ex. 1015
`
`HP,
`
`