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OPTICKS:

OR, A

TREATISE

OF THE

_Reflections_, _Refractions_,
_Inflections_ and _Colours_

OF

LIGHT.

_The_ FOURTH EDITION, _corrected_.

By Sir _ISAAC NEWTON_, Knt.

LONDON:

Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX.

TITLE PAGE OF THE 1730 EDITION




SIR ISAAC NEWTON'S ADVERTISEMENTS




Advertisement I


_Part of the ensuing Discourse about Light was written at the Desire of
some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent
to their Secretary, and read at their Meetings, and the rest was added
about twelve Years after to complete the Theory; except the third Book,
and the last Proposition of the Second, which were since put together
out of scatter'd Papers. To avoid being engaged in Disputes about these
Matters, I have hitherto delayed the printing, and should still have
delayed it, had not the Importunity of Friends prevailed upon me. If any
other Papers writ on this Subject are got out of my Hands they are
imperfect, and were perhaps written before I had tried all the
Experiments here set down, and fully satisfied my self about the Laws of
Refractions and Composition of Colours. I have here publish'd what I
think proper to come abroad, wishing that it may not be translated into
another Language without my Consent._

_The Crowns of Colours, which sometimes appear about the Sun and Moon, I
have endeavoured to give an Account of; but for want of sufficient
Observations leave that Matter to be farther examined. The Subject of
the Third Book I have also left imperfect, not having tried all the
Experiments which I intended when I was about these Matters, nor
repeated some of those which I did try, until I had satisfied my self
about all their Circumstances. To communicate what I have tried, and
leave the rest to others for farther Enquiry, is all my Design in
publishing these Papers._

_In a Letter written to Mr._ Leibnitz _in the year 1679, and published
by Dr._ Wallis, _I mention'd a Method by which I had found some general
Theorems about squaring Curvilinear Figures, or comparing them with the
Conic Sections, or other the simplest Figures with which they may be
compared. And some Years ago I lent out a Manuscript containing such
Theorems, and having since met with some Things copied out of it, I have
on this Occasion made it publick, prefixing to it an_ Introduction, _and
subjoining a_ Scholium _concerning that Method. And I have joined with
it another small Tract concerning the Curvilinear Figures of the Second
Kind, which was also written many Years ago, and made known to some
Friends, who have solicited the making it publick._

                                        _I. N._

April 1, 1704.


Advertisement II

_In this Second Edition of these Opticks I have omitted the Mathematical
Tracts publish'd at the End of the former Edition, as not belonging to
the Subject. And at the End of the Third Book I have added some
Questions. And to shew that I do not take Gravity for an essential
Property of Bodies, I have added one Question concerning its Cause,
chusing to propose it by way of a Question, because I am not yet
satisfied about it for want of Experiments._

                                        _I. N._

July 16, 1717.


Advertisement to this Fourth Edition

_This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed
from the Third Edition, as it was corrected by the Author's own Hand,
and left before his Death with the Bookseller. Since Sir_ Isaac's
Lectiones Opticæ, _which he publickly read in the University of_
Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has
been thought proper to make at the bottom of the Pages several Citations
from thence, where may be found the Demonstrations, which the Author
omitted in these_ Opticks.

       *       *       *       *       *

Transcriber's Note: There are several greek letters used in the
descriptions of the illustrations. They are signified by [Greek:
letter]. Square roots are noted by the letters sqrt before the equation.

       *       *       *       *       *

THE FIRST BOOK OF OPTICKS




_PART I._


My Design in this Book is not to explain the Properties of Light by
Hypotheses, but to propose and prove them by Reason and Experiments: In
order to which I shall premise the following Definitions and Axioms.




_DEFINITIONS_


DEFIN. I.

_By the Rays of Light I understand its least Parts, and those as well
Successive in the same Lines, as Contemporary in several Lines._ For it
is manifest that Light consists of Parts, both Successive and
Contemporary; because in the same place you may stop that which comes
one moment, and let pass that which comes presently after; and in the
same time you may stop it in any one place, and let it pass in any
other. For that part of Light which is stopp'd cannot be the same with
that which is let pass. The least Light or part of Light, which may be
stopp'd alone without the rest of the Light, or propagated alone, or do
or suffer any thing alone, which the rest of the Light doth not or
suffers not, I call a Ray of Light.


DEFIN. II.

_Refrangibility of the Rays of Light, is their Disposition to be
refracted or turned out of their Way in passing out of one transparent
Body or Medium into another. And a greater or less Refrangibility of
Rays, is their Disposition to be turned more or less out of their Way in
like Incidences on the same Medium._ Mathematicians usually consider the
Rays of Light to be Lines reaching from the luminous Body to the Body
illuminated, and the refraction of those Rays to be the bending or
breaking of those lines in their passing out of one Medium into another.
And thus may Rays and Refractions be considered, if Light be propagated
in an instant. But by an Argument taken from the Æquations of the times
of the Eclipses of _Jupiter's Satellites_, it seems that Light is
propagated in time, spending in its passage from the Sun to us about
seven Minutes of time: And therefore I have chosen to define Rays and
Refractions in such general terms as may agree to Light in both cases.


DEFIN. III.

_Reflexibility of Rays, is their Disposition to be reflected or turned
back into the same Medium from any other Medium upon whose Surface they
fall. And Rays are more or less reflexible, which are turned back more
or less easily._ As if Light pass out of a Glass into Air, and by being
inclined more and more to the common Surface of the Glass and Air,
begins at length to be totally reflected by that Surface; those sorts of
Rays which at like Incidences are reflected most copiously, or by
inclining the Rays begin soonest to be totally reflected, are most
reflexible.


DEFIN. IV.

_The Angle of Incidence is that Angle, which the Line described by the
incident Ray contains with the Perpendicular to the reflecting or
refracting Surface at the Point of Incidence._


DEFIN. V.

_The Angle of Reflexion or Refraction, is the Angle which the line
described by the reflected or refracted Ray containeth with the
Perpendicular to the reflecting or refracting Surface at the Point of
Incidence._


DEFIN. VI.

_The Sines of Incidence, Reflexion, and Refraction, are the Sines of the
Angles of Incidence, Reflexion, and Refraction._


DEFIN. VII

_The Light whose Rays are all alike Refrangible, I call Simple,
Homogeneal and Similar; and that whose Rays are some more Refrangible
than others, I call Compound, Heterogeneal and Dissimilar._ The former
Light I call Homogeneal, not because I would affirm it so in all
respects, but because the Rays which agree in Refrangibility, agree at
least in all those their other Properties which I consider in the
following Discourse.


DEFIN. VIII.

_The Colours of Homogeneal Lights, I call Primary, Homogeneal and
Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._
For these are always compounded of the colours of Homogeneal Lights; as
will appear in the following Discourse.




_AXIOMS._


AX. I.

_The Angles of Reflexion and Refraction, lie in one and the same Plane
with the Angle of Incidence._


AX. II.

_The Angle of Reflexion is equal to the Angle of Incidence._


AX. III.

_If the refracted Ray be returned directly back to the Point of
Incidence, it shall be refracted into the Line before described by the
incident Ray._


AX. IV.

_Refraction out of the rarer Medium into the denser, is made towards the
Perpendicular; that is, so that the Angle of Refraction be less than the
Angle of Incidence._


AX. V.

_The Sine of Incidence is either accurately or very nearly in a given
Ratio to the Sine of Refraction._

Whence if that Proportion be known in any one Inclination of the
incident Ray, 'tis known in all the Inclinations, and thereby the
Refraction in all cases of Incidence on the same refracting Body may be
determined. Thus if the Refraction be made out of Air into Water, the
Sine of Incidence of the red Light is to the Sine of its Refraction as 4
to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of
other Colours the Sines have other Proportions: but the difference is so
little that it need seldom be considered.

[Illustration: FIG. 1]

Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of
stagnating Water, and that C is the point of Incidence in which any Ray
coming in the Air from A in the Line AC is reflected or refracted, and I
would know whither this Ray shall go after Reflexion or Refraction: I
erect upon the Surface of the Water from the point of Incidence the
Perpendicular CP and produce it downwards to Q, and conclude by the
first Axiom, that the Ray after Reflexion and Refraction, shall be
found somewhere in the Plane of the Angle of Incidence ACP produced. I
let fall therefore upon the Perpendicular CP the Sine of Incidence AD;
and if the reflected Ray be desired, I produce AD to B so that DB be
equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
Sine of Incidence, as they ought to be by the second Axiom, But if the
refracted Ray be desired, I produce AD to H, so that DH may be to AD as
the Sine of Refraction to the Sine of Incidence, that is, (if the Light
be red) as 3 to 4; and about the Center C and in the Plane ACP with the
Radius CA describing a Circle ABE, I draw a parallel to the
Perpendicular CPQ, the Line HE cutting the Circumference in E, and
joining CE, this Line CE shall be the Line of the refracted Ray. For if
EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
this Sine EF is equal to DH, and consequently in Proportion to the Sine
of Incidence AD as 3 to 4.

In like manner, if there be a Prism of Glass (that is, a Glass bounded
with two Equal and Parallel Triangular ends, and three plain and well
polished Sides, which meet in three Parallel Lines running from the
three Angles of one end to the three Angles of the other end) and if the
Refraction of the Light in passing cross this Prism be desired: Let ACB
[in _Fig._ 2.] represent a Plane cutting this Prism transversly to its
three Parallel lines or edges there where the Light passeth through it,
and let DE be the Ray incident upon the first side of the Prism AC where
the Light goes into the Glass; and by putting the Proportion of the Sine
of Incidence to the Sine of Refraction as 17 to 11 find EF the first
refracted Ray. Then taking this Ray for the Incident Ray upon the second
side of the Glass BC where the Light goes out, find the next refracted
Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
Refraction as 11 to 17. For if the Sine of Incidence out of Air into
Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
out of Glass into Air must on the contrary be to the Sine of Refraction
as 11 to 17, by the third Axiom.

[Illustration: FIG. 2.]

Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
spherically convex on both sides (usually called a _Lens_, such as is a
Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
and it be required to know how Light falling upon it from any lucid
point Q shall be refracted, let QM represent a Ray falling upon any
point M of its first spherical Surface ACB, and by erecting a
Perpendicular to the Glass at the point M, find the first refracted Ray
MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of
the Glass be incident upon N, and then find the second refracted Ray
N_q_ by the Proportion of the Sines 11 to 17. And after the same manner
may the Refraction be found when the Lens is convex on one side and
plane or concave on the other, or concave on both sides.

[Illustration: FIG. 3.]


AX. VI.

_Homogeneal Rays which flow from several Points of any Object, and fall
perpendicularly or almost perpendicularly on any reflecting or
refracting Plane or spherical Surface, shall afterwards diverge from so
many other Points, or be parallel to so many other Lines, or converge to
so many other Points, either accurately or without any sensible Error.
And the same thing will happen, if the Rays be reflected or refracted
successively by two or three or more Plane or Spherical Surfaces._

The Point from which Rays diverge or to which they converge may be
called their _Focus_. And the Focus of the incident Rays being given,
that of the reflected or refracted ones may be found by finding the
Refraction of any two Rays, as above; or more readily thus.

_Cas._ 1. Let ACB [in _Fig._ 4.] be a reflecting or refracting Plane,
and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that
Plane. And if this Perpendicular be produced to _q_, so that _q_C be
equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or
if _q_C be taken on the same side of the Plane with QC, and in
proportion to QC as the Sine of Incidence to the Sine of Refraction, the
Point _q_ shall be the Focus of the refracted Rays.

[Illustration: FIG. 4.]

_Cas._ 2. Let ACB [in _Fig._ 5.] be the reflecting Surface of any Sphere
whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if
in that Radius on the same side the Point T you take the Points Q and
_q_, so that TQ, TE, and T_q_, be continual Proportionals, and the Point
Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of
the reflected ones.

[Illustration: FIG. 5.]

_Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere
whose Centre is E. In any Radius thereof EC produced both ways take ET
and C_t_ equal to one another and severally in such Proportion to that
Radius as the lesser of the Sines of Incidence and Refraction hath to
the difference of those Sines. And then if in the same Line you find any
two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_
the contrary way from _t_ which TQ lieth from T, and if the Point Q be
the Focus of any incident Rays, the Point _q_ shall be the Focus of the
refracted ones.

[Illustration: FIG. 6.]

And by the same means the Focus of the Rays after two or more Reflexions
or Refractions may be found.

[Illustration: FIG. 7.]

_Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically
Convex or Concave or Plane on either side, and let CD be its Axis (that
is, the Line which cuts both its Surfaces perpendicularly, and passes
through the Centres of the Spheres,) and in this Axis produced let F and
_f_ be the Foci of the refracted Rays found as above, when the incident
Rays on both sides the Lens are parallel to the same Axis; and upon the
Diameter F_f_ bisected in E, describe a Circle. Suppose now that any
Point Q be the Focus of any incident Rays. Draw QE cutting the said
Circle in T and _t_, and therein take _tq_ in such proportion to _t_E as
_t_E or TE hath to TQ. Let _tq_ lie the contrary way from _t_ which TQ
doth from T, and _q_ shall be the Focus of the refracted Rays without
any sensible Error, provided the Point Q be not so remote from the Axis,
nor the Lens so broad as to make any of the Rays fall too obliquely on
the refracting Surfaces.[A]

And by the like Operations may the reflecting or refracting Surfaces be
found when the two Foci are given, and thereby a Lens be formed, which
shall make the Rays flow towards or from what Place you please.[B]