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2Paolucci and the Online Distributed Proofreading Team at
3http://www.pgdp.net.
4
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8
9
10OPTICKS:
11
12OR, A
13
14TREATISE
15
16OF THE
17
18_Reflections_, _Refractions_,
19_Inflections_ and _Colours_
20
21OF
22
23LIGHT.
24
25_The_ FOURTH EDITION, _corrected_.
26
27By Sir _ISAAC NEWTON_, Knt.
28
29LONDON:
30
31Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX.
32
33TITLE PAGE OF THE 1730 EDITION
34
35
36
37
38SIR ISAAC NEWTON'S ADVERTISEMENTS
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40
41
42
43Advertisement I
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45
46_Part of the ensuing Discourse about Light was written at the Desire of
47some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent
48to their Secretary, and read at their Meetings, and the rest was added
49about twelve Years after to complete the Theory; except the third Book,
50and the last Proposition of the Second, which were since put together
51out of scatter'd Papers. To avoid being engaged in Disputes about these
52Matters, I have hitherto delayed the printing, and should still have
53delayed it, had not the Importunity of Friends prevailed upon me. If any
54other Papers writ on this Subject are got out of my Hands they are
55imperfect, and were perhaps written before I had tried all the
56Experiments here set down, and fully satisfied my self about the Laws of
57Refractions and Composition of Colours. I have here publish'd what I
58think proper to come abroad, wishing that it may not be translated into
59another Language without my Consent._
60
61_The Crowns of Colours, which sometimes appear about the Sun and Moon, I
62have endeavoured to give an Account of; but for want of sufficient
63Observations leave that Matter to be farther examined. The Subject of
64the Third Book I have also left imperfect, not having tried all the
65Experiments which I intended when I was about these Matters, nor
66repeated some of those which I did try, until I had satisfied my self
67about all their Circumstances. To communicate what I have tried, and
68leave the rest to others for farther Enquiry, is all my Design in
69publishing these Papers._
70
71_In a Letter written to Mr._ Leibnitz _in the year 1679, and published
72by Dr._ Wallis, _I mention'd a Method by which I had found some general
73Theorems about squaring Curvilinear Figures, or comparing them with the
74Conic Sections, or other the simplest Figures with which they may be
75compared. And some Years ago I lent out a Manuscript containing such
76Theorems, and having since met with some Things copied out of it, I have
77on this Occasion made it publick, prefixing to it an_ Introduction, _and
78subjoining a_ Scholium _concerning that Method. And I have joined with
79it another small Tract concerning the Curvilinear Figures of the Second
80Kind, which was also written many Years ago, and made known to some
81Friends, who have solicited the making it publick._
82
83 _I. N._
84
85April 1, 1704.
86
87
88Advertisement II
89
90_In this Second Edition of these Opticks I have omitted the Mathematical
91Tracts publish'd at the End of the former Edition, as not belonging to
92the Subject. And at the End of the Third Book I have added some
93Questions. And to shew that I do not take Gravity for an essential
94Property of Bodies, I have added one Question concerning its Cause,
95chusing to propose it by way of a Question, because I am not yet
96satisfied about it for want of Experiments._
97
98 _I. N._
99
100July 16, 1717.
101
102
103Advertisement to this Fourth Edition
104
105_This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed
106from the Third Edition, as it was corrected by the Author's own Hand,
107and left before his Death with the Bookseller. Since Sir_ Isaac's
108Lectiones Opticæ, _which he publickly read in the University of_
109Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has
110been thought proper to make at the bottom of the Pages several Citations
111from thence, where may be found the Demonstrations, which the Author
112omitted in these_ Opticks.
113
114 * * * * *
115
116Transcriber's Note: There are several greek letters used in the
117descriptions of the illustrations. They are signified by [Greek:
118letter]. Square roots are noted by the letters sqrt before the equation.
119
120 * * * * *
121
122THE FIRST BOOK OF OPTICKS
123
124
125
126
127_PART I._
128
129
130My Design in this Book is not to explain the Properties of Light by
131Hypotheses, but to propose and prove them by Reason and Experiments: In
132order to which I shall premise the following Definitions and Axioms.
133
134
135
136
137_DEFINITIONS_
138
139
140DEFIN. I.
141
142_By the Rays of Light I understand its least Parts, and those as well
143Successive in the same Lines, as Contemporary in several Lines._ For it
144is manifest that Light consists of Parts, both Successive and
145Contemporary; because in the same place you may stop that which comes
146one moment, and let pass that which comes presently after; and in the
147same time you may stop it in any one place, and let it pass in any
148other. For that part of Light which is stopp'd cannot be the same with
149that which is let pass. The least Light or part of Light, which may be
150stopp'd alone without the rest of the Light, or propagated alone, or do
151or suffer any thing alone, which the rest of the Light doth not or
152suffers not, I call a Ray of Light.
153
154
155DEFIN. II.
156
157_Refrangibility of the Rays of Light, is their Disposition to be
158refracted or turned out of their Way in passing out of one transparent
159Body or Medium into another. And a greater or less Refrangibility of
160Rays, is their Disposition to be turned more or less out of their Way in
161like Incidences on the same Medium._ Mathematicians usually consider the
162Rays of Light to be Lines reaching from the luminous Body to the Body
163illuminated, and the refraction of those Rays to be the bending or
164breaking of those lines in their passing out of one Medium into another.
165And thus may Rays and Refractions be considered, if Light be propagated
166in an instant. But by an Argument taken from the Æquations of the times
167of the Eclipses of _Jupiter's Satellites_, it seems that Light is
168propagated in time, spending in its passage from the Sun to us about
169seven Minutes of time: And therefore I have chosen to define Rays and
170Refractions in such general terms as may agree to Light in both cases.
171
172
173DEFIN. III.
174
175_Reflexibility of Rays, is their Disposition to be reflected or turned
176back into the same Medium from any other Medium upon whose Surface they
177fall. And Rays are more or less reflexible, which are turned back more
178or less easily._ As if Light pass out of a Glass into Air, and by being
179inclined more and more to the common Surface of the Glass and Air,
180begins at length to be totally reflected by that Surface; those sorts of
181Rays which at like Incidences are reflected most copiously, or by
182inclining the Rays begin soonest to be totally reflected, are most
183reflexible.
184
185
186DEFIN. IV.
187
188_The Angle of Incidence is that Angle, which the Line described by the
189incident Ray contains with the Perpendicular to the reflecting or
190refracting Surface at the Point of Incidence._
191
192
193DEFIN. V.
194
195_The Angle of Reflexion or Refraction, is the Angle which the line
196described by the reflected or refracted Ray containeth with the
197Perpendicular to the reflecting or refracting Surface at the Point of
198Incidence._
199
200
201DEFIN. VI.
202
203_The Sines of Incidence, Reflexion, and Refraction, are the Sines of the
204Angles of Incidence, Reflexion, and Refraction._
205
206
207DEFIN. VII
208
209_The Light whose Rays are all alike Refrangible, I call Simple,
210Homogeneal and Similar; and that whose Rays are some more Refrangible
211than others, I call Compound, Heterogeneal and Dissimilar._ The former
212Light I call Homogeneal, not because I would affirm it so in all
213respects, but because the Rays which agree in Refrangibility, agree at
214least in all those their other Properties which I consider in the
215following Discourse.
216
217
218DEFIN. VIII.
219
220_The Colours of Homogeneal Lights, I call Primary, Homogeneal and
221Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._
222For these are always compounded of the colours of Homogeneal Lights; as
223will appear in the following Discourse.
224
225
226
227
228_AXIOMS._
229
230
231AX. I.
232
233_The Angles of Reflexion and Refraction, lie in one and the same Plane
234with the Angle of Incidence._
235
236
237AX. II.
238
239_The Angle of Reflexion is equal to the Angle of Incidence._
240
241
242AX. III.
243
244_If the refracted Ray be returned directly back to the Point of
245Incidence, it shall be refracted into the Line before described by the
246incident Ray._
247
248
249AX. IV.
250
251_Refraction out of the rarer Medium into the denser, is made towards the
252Perpendicular; that is, so that the Angle of Refraction be less than the
253Angle of Incidence._
254
255
256AX. V.
257
258_The Sine of Incidence is either accurately or very nearly in a given
259Ratio to the Sine of Refraction._
260
261Whence if that Proportion be known in any one Inclination of the
262incident Ray, 'tis known in all the Inclinations, and thereby the
263Refraction in all cases of Incidence on the same refracting Body may be
264determined. Thus if the Refraction be made out of Air into Water, the
265Sine of Incidence of the red Light is to the Sine of its Refraction as 4
266to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of
267other Colours the Sines have other Proportions: but the difference is so
268little that it need seldom be considered.
269
270[Illustration: FIG. 1]
271
272Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of
273stagnating Water, and that C is the point of Incidence in which any Ray
274coming in the Air from A in the Line AC is reflected or refracted, and I
275would know whither this Ray shall go after Reflexion or Refraction: I
276erect upon the Surface of the Water from the point of Incidence the
277Perpendicular CP and produce it downwards to Q, and conclude by the
278first Axiom, that the Ray after Reflexion and Refraction, shall be
279found somewhere in the Plane of the Angle of Incidence ACP produced. I
280let fall therefore upon the Perpendicular CP the Sine of Incidence AD;
281and if the reflected Ray be desired, I produce AD to B so that DB be
282equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
283the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
284Sine of Incidence, as they ought to be by the second Axiom, But if the
285refracted Ray be desired, I produce AD to H, so that DH may be to AD as
286the Sine of Refraction to the Sine of Incidence, that is, (if the Light
287be red) as 3 to 4; and about the Center C and in the Plane ACP with the
288Radius CA describing a Circle ABE, I draw a parallel to the
289Perpendicular CPQ, the Line HE cutting the Circumference in E, and
290joining CE, this Line CE shall be the Line of the refracted Ray. For if
291EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
292Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
293this Sine EF is equal to DH, and consequently in Proportion to the Sine
294of Incidence AD as 3 to 4.
295
296In like manner, if there be a Prism of Glass (that is, a Glass bounded
297with two Equal and Parallel Triangular ends, and three plain and well
298polished Sides, which meet in three Parallel Lines running from the
299three Angles of one end to the three Angles of the other end) and if the
300Refraction of the Light in passing cross this Prism be desired: Let ACB
301[in _Fig._ 2.] represent a Plane cutting this Prism transversly to its
302three Parallel lines or edges there where the Light passeth through it,
303and let DE be the Ray incident upon the first side of the Prism AC where
304the Light goes into the Glass; and by putting the Proportion of the Sine
305of Incidence to the Sine of Refraction as 17 to 11 find EF the first
306refracted Ray. Then taking this Ray for the Incident Ray upon the second
307side of the Glass BC where the Light goes out, find the next refracted
308Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
309Refraction as 11 to 17. For if the Sine of Incidence out of Air into
310Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
311out of Glass into Air must on the contrary be to the Sine of Refraction
312as 11 to 17, by the third Axiom.
313
314[Illustration: FIG. 2.]
315
316Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
317spherically convex on both sides (usually called a _Lens_, such as is a
318Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
319and it be required to know how Light falling upon it from any lucid
320point Q shall be refracted, let QM represent a Ray falling upon any
321point M of its first spherical Surface ACB, and by erecting a
322Perpendicular to the Glass at the point M, find the first refracted Ray
323MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of
324the Glass be incident upon N, and then find the second refracted Ray
325N_q_ by the Proportion of the Sines 11 to 17. And after the same manner
326may the Refraction be found when the Lens is convex on one side and
327plane or concave on the other, or concave on both sides.
328
329[Illustration: FIG. 3.]
330
331
332AX. VI.
333
334_Homogeneal Rays which flow from several Points of any Object, and fall
335perpendicularly or almost perpendicularly on any reflecting or
336refracting Plane or spherical Surface, shall afterwards diverge from so
337many other Points, or be parallel to so many other Lines, or converge to
338so many other Points, either accurately or without any sensible Error.
339And the same thing will happen, if the Rays be reflected or refracted
340successively by two or three or more Plane or Spherical Surfaces._
341
342The Point from which Rays diverge or to which they converge may be
343called their _Focus_. And the Focus of the incident Rays being given,
344that of the reflected or refracted ones may be found by finding the
345Refraction of any two Rays, as above; or more readily thus.
346
347_Cas._ 1. Let ACB [in _Fig._ 4.] be a reflecting or refracting Plane,
348and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that
349Plane. And if this Perpendicular be produced to _q_, so that _q_C be
350equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or
351if _q_C be taken on the same side of the Plane with QC, and in
352proportion to QC as the Sine of Incidence to the Sine of Refraction, the
353Point _q_ shall be the Focus of the refracted Rays.
354
355[Illustration: FIG. 4.]
356
357_Cas._ 2. Let ACB [in _Fig._ 5.] be the reflecting Surface of any Sphere
358whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if
359in that Radius on the same side the Point T you take the Points Q and
360_q_, so that TQ, TE, and T_q_, be continual Proportionals, and the Point
361Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of
362the reflected ones.
363
364[Illustration: FIG. 5.]
365
366_Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere
367whose Centre is E. In any Radius thereof EC produced both ways take ET
368and C_t_ equal to one another and severally in such Proportion to that
369Radius as the lesser of the Sines of Incidence and Refraction hath to
370the difference of those Sines. And then if in the same Line you find any
371two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_
372the contrary way from _t_ which TQ lieth from T, and if the Point Q be
373the Focus of any incident Rays, the Point _q_ shall be the Focus of the
374refracted ones.
375
376[Illustration: FIG. 6.]
377
378And by the same means the Focus of the Rays after two or more Reflexions
379or Refractions may be found.
380
381[Illustration: FIG. 7.]
382
383_Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically
384Convex or Concave or Plane on either side, and let CD be its Axis (that
385is, the Line which cuts both its Surfaces perpendicularly, and passes
386through the Centres of the Spheres,) and in this Axis produced let F and
387_f_ be the Foci of the refracted Rays found as above, when the incident
388Rays on both sides the Lens are parallel to the same Axis; and upon the
389Diameter F_f_ bisected in E, describe a Circle. Suppose now that any
390Point Q be the Focus of any incident Rays. Draw QE cutting the said
391Circle in T and _t_, and therein take _tq_ in such proportion to _t_E as
392_t_E or TE hath to TQ. Let _tq_ lie the contrary way from _t_ which TQ
393doth from T, and _q_ shall be the Focus of the refracted Rays without
394any sensible Error, provided the Point Q be not so remote from the Axis,
395nor the Lens so broad as to make any of the Rays fall too obliquely on
396the refracting Surfaces.[A]
397
398And by the like Operations may the reflecting or refracting Surfaces be
399found when the two Foci are given, and thereby a Lens be formed, which
400shall make the Rays flow towards or from what Place you please.[B]
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