# An Elementary Treatise on Optics

OPTICS.
AN
ELEMENTARY TREATISE
ON
OPTICS.
BY THE
Rev. HENRY CODDINGTON, M. A.
FELLOW OF TRINITY COLLEGE.
CAMBRIDGE:
Printed by J. Smith, Printer to the University; FOR J. DEIGHTON & SONS; AND G. & W. B. WHITTAKER, LONDON.
1823
PREFACE.
It has been for some time a subject of complaint that there existed no easy Elementary work on Optics, suited to the present state of Mathematical knowledge. The works of Newton, of Harris, of Smith, contain, it is true, a vast deal of important information, but that information is conveyed in such a shape as hardly to be tangible to modern readers. Perhaps it may be permitted to say that objections of the same kind have been made to Dr. Wood’s elegant little Treatise, which being composed after the model of those mentioned, does not harmonize, if I may be allowed the expression, with the other mathematical works which are at present the object of study in our University.
This consideration induced Mr. Whewell to draw up in the Spring of 1819 a Syllabus of those parts of the Science of Optics that are usually inquired into, and that Syllabus, with the instructions conveyed in his Lectures, which I had then the pleasure of attending, formed the basis of the little Treatise which, at the instigation of himself and others of my friends, I now venture to offer to the public.
​Upon the whole, this Work is to be considered as a compilation rather than an original production, and all the merit I can lay claim to is that of having arranged the materials which I found at hand, and endeavoured, with what success I leave it to the reader to judge, to present facts and reasonings in such language as should be at once concise and clear. I have studiously avoided long and diffuse investigations and demonstrations, leaving many things to be supplied which an intelligent reader can readily supply, in order that the several steps of a process might be seen as it were with one glance.
For a similar reason I have often omitted to notice parts of Figures which did not seem to me to require being mentioned, as my object was not to give detailed descriptions from which Figures might be drawn, but merely to make intelligible those which accompany the work.
The Notation I have used, is in a great measure adopted from M. Biot, to whom I am indebted for an Appendix on the higher parts of the Science, which I have taken the liberty of translating from the "Additions à l'Optique," in his Edition of Fischer's Physique Mécanique, p. 396.
I have occasionally consulted Harris's Optics; of Smith's I could make but little use; Hayes’s Fluxions ​afforded me a good deal of information on the subject of Caustics. Dr. Wood's Treatise I have naturally had almost constantly on my table; but perhaps my greatest obligations are due to Dr. Young, whose Lectures do not need my praise or recommendation to those who wish to study this or almost any other branch of Mathematical Science.
For one very elegant Article I am indebted to my excellent friend John C. S. Lefevre, Esq. M. Cuvier's valuable Work on Comparative Anatomy, has furnished some details on the subject of the Eye, which I hope will not be thought misplaced.
I am afraid it will be said that many of the Figures are too small, or not sufficiently clear: the student may in some measure correct this defect, by copying them for himself on a larger scale, which I hope he will find no difficulty in doing, with the assistance of the descriptions.
Au reste, the reader whom according to the usual courtesy of Authors, I will suppose as benevolent as possible, will be pleased to remember that this is my first public appearance before the world in print, and that it may be his fault if it be the last, so that I pray him to regard my weaknesses with a lenient eye, and if he should find any one passage in the Book, which he may judge praiseworthy, to accept it as an omen ​of future improvement, to be perchance displayed in that desirable consummation, a Second Edition.
The Syndics of the University Press have, from the funds at their disposal contributed liberally to the expence of the Work, and I gladly take this opportunity of acknowledging my obligations to them.
    Trinity College,
    Oct. 20, 1823.
CONTENTS.
Introductory Observations, p. 1
Chap. I.
Reflexion at Plane Surfaces, p. 4.
Chap. II.
Reflexion at Spherical Surfaces, p. 6.
Chap. III.
Aberration in reflexion at Spherical Surfaces, p. 13.
q′=qf/q+f+q$^2$fv/(q+f)$^2$+
Chap. IV.
Reflexion at Curved Surfaces in general, p. 16.
Chap. V.
Caustics produced by Reflexion, p. 17.
1/u+1/v=1/fcosφ, v=du/dlp$^2$/u.
Chap. VI.
Images produced by Reflexion, p. 28.
Chap. VII.
Refraction at Plane Surfaces, p. 42.
∆′=m∆.
∆′=m∆(1+m$^2$−1/2m$^2$tanθ$^2$).
∆″=∆−m−1/mT.
δ=φ+ψ−ι, δ=(m−1)ι, m=δ+1/ι.
Chap. VIII.
Refraction at spherical Surfaces, p. 53.
m=QE·Rq/QR·Eq=QE·Aq/AQ·Eq (ultimately.) 1/∆′=−m−1/mr+1/m∆. 1/q′=−m−1/r+1/q,
1/∆″=(m−1){1/r−1/r′}+1/∆, 1/∆″=1/F+1/∆.
1/q″=−2m−1/mr+1/q
1/F$_n$=1/F+1/F′+1/F″+…+1/F$^{(u)}$
Chap. IX.
Aberration in refraction at spherical Surfaces, p. 70.
α=(∆′−r)$^2$·(m/∆−1/∆′)·v, m/∆−1/∆′=m−1/m(m+1/∆−1/r).
Chap. X.
Refraction at curved Surfaces not spherical, p. 76.
Chap. XI.
Caustics produced by Refraction, p. 80.
v=urcosφ·tanφ/utanφ−(u+rcosφ)tanφ′, 1/v=1/rcosφ′−(u+rcosφ)sinφ′/urcosφ′$^2$·tanφ.
Chap. XII.
Images produced by Refraction, p. 89.
Chap. XIII.
Unequal refrangibility of Light, p. 90.
Chap. XIV.
The Eye, p. 98.
    (1) Change of conformation in the Eye.
    (2) Inclination of the axes of the Eye.
    (3) Length of the ground plane.
    (4) Different appearances of known objects.
    (5) Different degrees of brightness, and change of colour.
Chap. XV.
Optical Instruments, p. 112.
Chap. X.
Optical Phænomena, p. 134.
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
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