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.DEFINITIONSDEFIN. 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 ofJupiter'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. VIIThe 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.
Fig. 1
Suppose therefore, that RS [inFig.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 [inFig.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.
Fig. 2.
Much after the same manner, if ACBD [inFig.3.] represent a Glass spherically
convex on both sides (usually called aLens, 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
Nqby 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.
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 theirFocus. 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 [inFig.4.] be a reflecting or refracting
Plane, and Q the Focus of the incident Rays, and QqC a Perpendicular to that Plane. And
if this Perpendicular be produced toq, so thatqC be equal to
QC, the Pointqshall be the
Focus of the reflected Rays: Or ifqC 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 Pointqshall be
the Focus of the refracted Rays.
Fig. 4.
Cas.2. Let ACB [inFig.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 andq, so
that TQ, TE, and Tq, be
continual Proportionals, and the Point Q be the Focus of the
incident Rays, the Pointqshall
be the Focus of the reflected ones.
Fig. 5.
Cas.3. Let ACB [inFig.6.] be the refracting Surface of
any Sphere whose Centre is E. In any Radius thereof EC produced
both ways take ET and Ctequal
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 andq, so that
TQ be to ET as Ettotq, takingtqthe contrary way fromtwhich TQ lieth from T, and if the
Point Q be the Focus of any incident Rays, the Pointqshall be the Focus of the refracted
ones.
Fig. 6.
And by the same means the Focus of the Rays after two
or more Reflexions or Refractions may be found.
Fig. 7.
Cas.4. Let ACBD [inFig.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 andfbe 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 Ffbisected 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 andt, and therein
taketqin such proportion
totE astE or TE hath to TQ. Lettqlie the contrary way fromtwhich TQ doth from T, andqshall 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]So then the Meaning of this Axiom is, that if Rays fall upon
any Plane or Spherical Surface or Lens, and before their Incidence
flow from or towards any Point Q, they shall after Reflexion or
Refraction flow from or towards the Pointqfound by the foregoing Rules. And if
the incident Rays flow from or towards several points Q, the
reflected or refracted Rays shall flow from or towards so many
other Pointsqfound by the same
Rules. Whether the reflected and refracted Rays flow from or
towards the Pointqis easily
known by the situation of that Point. For if that Point be on the
same side of the reflecting or refracting Surface or Lens with the
Point Q, and the incident Rays flow from the Point Q, the reflected
flow towards the Pointqand the
refracted from it; and if the incident Rays flow towards Q, the
reflected flow fromq, and the
refracted towards it. And the contrary happens whenqis on the other side of the
Surface.AX. VII.Wherever the Rays which come from all the Points of any
Object meet again in so many Points after they have been made to
converge by Reflection or Refraction, there they will make a
Picture of the Object upon any white Body on which they
fall.So if PR [inFig.3.]
represent any Object without Doors, and AB be a Lens placed at a
hole in the Window-shut of a dark Chamber, whereby the Rays that
come from any Point Q of that Object are made to converge and meet
again in the Pointq; and if a
Sheet of white Paper be held atqfor the Light there to fall upon it, the Picture of that
Object PR will appear upon the Paper in its proper shape and
Colours. For as the Light which comes from the Point Q goes to the
Pointq, so the Light which
comes from other Points P and R of the Object, will go to so many
other correspondent Pointspandr(as is manifest by
the sixth Axiom;) so that every Point of the Object shall
illuminate a correspondent Point of the Picture, and thereby make a
Picture like the Object in Shape and Colour, this only excepted,
that the Picture shall be inverted. And this is the Reason of that
vulgar Experiment of casting the Species of Objects from abroad
upon a Wall or Sheet of white Paper in a dark Room.In like manner, when a Man views any Object PQR, [inFig.8.] the Light which comes from the
several Points of the Object is so refracted by the transparent
skins and humours of the Eye, (that is, by the outward coat EFG,
called theTunica Cornea, and
by the crystalline humour AB which is beyond the Pupilmk) as to converge and meet again in
so many Points in the bottom of the Eye, and there to paint the
Picture of the Object upon that skin (called theTunica Retina) with which the bottom
of the Eye is covered. For Anatomists, when they have taken off
from the bottom of the Eye that outward and most thick Coat called
theDura Mater, can then see
through the thinner Coats, the Pictures of Objects lively painted
thereon. And these Pictures, propagated by Motion along the Fibres
of the Optick Nerves into the Brain, are the cause of Vision. For
accordingly as these Pictures are perfect or imperfect, the Object
is seen perfectly or imperfectly. If the Eye be tinged with any
colour (as in the Disease of theJaundice) so as to tinge the Pictures
in the bottom of the Eye with that Colour, then all Objects appear
tinged with the same Colour. If the Humours of the Eye by old Age
decay, so as by shrinking to make theCorneaand Coat of theCrystalline Humourgrow flatter than
before, the Light will not be refracted enough, and for want of a
sufficient Refraction will not converge to the bottom of the Eye
but to some place beyond it, and by consequence paint in the bottom
of the Eye a confused Picture, and according to the Indistinctness
of this Picture the Object will appear confused. This is the reason
of the decay of sight in old Men, and shews why their Sight is
mended by Spectacles. For those Convex glasses supply the defect of
plumpness in the Eye, and by increasing the Refraction make the
Rays converge sooner, so as to convene distinctly at the bottom of
the Eye if the Glass have a due degree of convexity. And the
contrary happens in short-sighted Men whose Eyes are too plump. For
the Refraction being now too great, the Rays converge and convene
in the Eyes before they come at the bottom; and therefore the
Picture made in the bottom and the Vision caused thereby will not
be distinct, unless the Object be brought so near the Eye as that
the place where the converging Rays convene may be removed to the
bottom, or that the plumpness of the Eye be taken off and the
Refractions diminished by a Concave-glass of a due degree of
Concavity, or lastly that by Age the Eye grow flatter till it come
to a due Figure: For short-sighted Men see remote Objects best in
Old Age, and therefore they are accounted to have the most lasting
Eyes.
Fig. 8.
AX. VIII.An Object seen by Reflexion or Refraction, appears in
that place from whence the Rays after their last Reflexion or
Refraction diverge in falling on the Spectator's
Eye.
Fig. 9.
If the Object A [in Fig. 9.] be seen by Reflexion of a
Looking-glassmn, it shall
appear, not in its proper place A, but behind the Glass ata, from whence any Rays AB, AC, AD,
which flow from one and the same Point of the Object, do after
their Reflexion made in the Points B, C, D, diverge in going from
the Glass to E, F, G, where they are incident on the Spectator's
Eyes. For these Rays do make the same Picture in the bottom of the
Eyes as if they had come from the Object really placed atawithout the Interposition of the
Looking-glass; and all Vision is made according to the place and
shape of that Picture.In like manner the Object D [in Fig. 2.] seen through a
Prism, appears not in its proper place D, but is thence translated
to some other placedsituated
in the last refracted Ray FG drawn backward from F tod.
Fig. 10.
And so the Object Q [in Fig. 10.] seen through the Lens
AB, appears at the placeqfrom
whence the Rays diverge in passing from the Lens to the Eye. Now it
is to be noted, that the Image of the Object atqis so much bigger or lesser than the
Object it self at Q, as the distance of the Image atqfrom the Lens AB is bigger or less
than the distance of the Object at Q from the same Lens. And if the
Object be seen through two or more such Convex or Concave-glasses,
every Glass shall make a new Image, and the Object shall appear in
the place of the bigness of the last Image. Which consideration
unfolds the Theory of Microscopes and Telescopes. For that Theory
consists in almost nothing else than the describing such Glasses as
shall make the last Image of any Object as distinct and large and
luminous as it can conveniently be made.I have now given in Axioms and their Explications the sum of
what hath hitherto been treated of in Opticks. For what hath been
generally agreed on I content my self to assume under the notion of
Principles, in order to what I have farther to write. And this may
suffice for an Introduction to Readers of quick Wit and good
Understanding not yet versed in Opticks: Although those who are
already acquainted with this Science, and have handled Glasses,
will more readily apprehend what followeth.FOOTNOTES:[A]In our Author'sLectiones
Opticæ, Part I. Sect. IV. Prop 29, 30, there is
an elegant Method of determining theseFoci; not only in spherical Surfaces,
but likewise in any other curved Figure whatever: And in Prop. 32,
33, the same thing is done for any Ray lying out of the
Axis.[B]Ibid.Prop.
34.PROPOSITIONS.PROP.I.Theor.I.Lights which differ in Colour, differ also in Degrees of
Refrangibility.The Proof by Experiments.Exper.1. I took a black oblong stiff
Paper terminated by Parallel Sides, and with a Perpendicular right
Line drawn cross from one Side to the other, distinguished it into
two equal Parts. One of these parts I painted with a red colour and
the other with a blue. The Paper was very black, and the Colours
intense and thickly laid on, that the Phænomenon might be more
conspicuous. This Paper I view'd through a Prism of solid Glass,
whose two Sides through which the Light passed to the Eye were
plane and well polished, and contained an Angle of about sixty
degrees; which Angle I call the refracting Angle of the Prism. And
whilst I view'd it, I held it and the Prism before a Window in such
manner that the Sides of the Paper were parallel to the Prism, and
both those Sides and the Prism were parallel to the Horizon, and
the cross Line was also parallel to it: and that the Light which
fell from the Window upon the Paper made an Angle with the Paper,
equal to that Angle which was made with the same Paper by the Light
reflected from it to the Eye. Beyond the Prism was the Wall of the
Chamber under the Window covered over with black Cloth, and the
Cloth was involved in Darkness that no Light might be reflected
from thence, which in passing by the Edges of the Paper to the Eye,
might mingle itself with the Light of the Paper, and obscure the
Phænomenon thereof. These things being thus ordered, I found that
if the refracting Angle of the Prism be turned upwards, so that the
Paper may seem to be lifted upwards by the Refraction, its blue
half will be lifted higher by the Refraction than its red half. But
if the refracting Angle of the Prism be turned downward, so that
the Paper may seem to be carried lower by the Refraction, its blue
half will be carried something lower thereby than its red half.
Wherefore in both Cases the Light which comes from the blue half of
the Paper through the Prism to the Eye, does in like Circumstances
suffer a greater Refraction than the Light which comes from the red
half, and by consequence is more refrangible.Illustration.In the eleventh Figure,
MN represents the Window, and DE the Paper terminated with parallel
Sides DJ and HE, and by the transverse Line FG distinguished into
two halfs, the one DG of an intensely blue Colour, the other FE of
an intensely red. And BACcabrepresents the Prism whose refracting Planes ABbaand ACcameet in the Edge of the refracting
Angle Aa. This Edge Aabeing upward, is parallel both to the
Horizon, and to the Parallel-Edges of the Paper DJ and HE, and the
transverse Line FG is perpendicular to the Plane of the Window.
Andderepresents the Image of
the Paper seen by Refraction upwards in such manner, that the blue
half DG is carried higher todgthan the red half FE is tofe, and therefore suffers a greater Refraction. If the Edge of
the refracting Angle be turned downward, the Image of the Paper
will be refracted downward; suppose to δε, and the blue half will
be refracted lower to δγ than the red half is to πε.
Fig. 11.
Exper.2. About the aforesaid
Paper, whose two halfs were painted over with red and blue, and
which was stiff like thin Pasteboard, I lapped several times a
slender Thred of very black Silk, in such manner that the several
parts of the Thred might appear upon the Colours like so many black
Lines drawn over them, or like long and slender dark Shadows cast
upon them. I might have drawn black Lines with a Pen, but the
Threds were smaller and better defined. This Paper thus coloured
and lined I set against a Wall perpendicularly to the Horizon, so
that one of the Colours might stand to the Right Hand, and the
other to the Left. Close before the Paper, at the Confine of the
Colours below, I placed a Candle to illuminate the Paper strongly:
For the Experiment was tried in the Night. The Flame of the Candle
reached up to the lower edge of the Paper, or a very little higher.
Then at the distance of six Feet, and one or two Inches from the
Paper upon the Floor I erected a Glass Lens four Inches and a
quarter broad, which might collect the Rays coming from the several
Points of the Paper, and make them converge towards so many other
Points at the same distance of six Feet, and one or two Inches on
the other side of the Lens, and so form the Image of the coloured
Paper upon a white Paper placed there, after the same manner that a
Lens at a Hole in a Window casts the Images of Objects abroad upon
a Sheet of white Paper in a dark Room. The aforesaid white Paper,
erected perpendicular to the Horizon, and to the Rays which fell
upon it from the Lens, I moved sometimes towards the Lens,
sometimes from it, to find the Places where the Images of the blue
and red Parts of the coloured Paper appeared most distinct. Those
Places I easily knew by the Images of the black Lines which I had
made by winding the Silk about the Paper. For the Images of those
fine and slender Lines (which by reason of their Blackness were
like Shadows on the Colours) were confused and scarce visible,
unless when the Colours on either side of each Line were terminated
most distinctly, Noting therefore, as diligently as I could, the
Places where the Images of the red and blue halfs of the coloured
Paper appeared most distinct, I found that where the red half of
the Paper appeared distinct, the blue half appeared confused, so
that the black Lines drawn upon it could scarce be seen; and on the
contrary, where the blue half appeared most distinct, the red half
appeared confused, so that the black Lines upon it were scarce
visible. And between the two Places where these Images appeared
distinct there was the distance of an Inch and a half; the distance
of the white Paper from the Lens, when the Image of the red half of
the coloured Paper appeared most distinct, being greater by an Inch
and an half than the distance of the same white Paper from the
Lens, when the Image of the blue half appeared most distinct. In
like Incidences therefore of the blue and red upon the Lens, the
blue was refracted more by the Lens than the red, so as to converge
sooner by an Inch and a half, and therefore is more
refrangible.Illustration.In the twelfth Figure (p.
27), DE signifies the coloured Paper, DG the blue half, FE the red
half, MN the Lens, HJ the white Paper in that Place where the red
half with its black Lines appeared distinct, andhithe same Paper in that Place where
the blue half appeared distinct. The Placehiwas nearer to the Lens MN than the
Place HJ by an Inch and an half.Scholium.The same Things succeed,
notwithstanding that some of the Circumstances be varied; as in the
first Experiment when the Prism and Paper are any ways inclined to
the Horizon, and in both when coloured Lines are drawn upon very
black Paper. But in the Description of these Experiments, I have
set down such Circumstances, by which either the Phænomenon might
be render'd more conspicuous, or a Novice might more easily try
them, or by which I did try them only. The same Thing, I have often
done in the following Experiments: Concerning all which, this one
Admonition may suffice. Now from these Experiments it follows not,
that all the Light of the blue is more refrangible than all the
Light of the red: For both Lights are mixed of Rays differently
refrangible, so that in the red there are some Rays not less
refrangible than those of the blue, and in the blue there are some
Rays not more refrangible than those of the red: But these Rays, in
proportion to the whole Light, are but few, and serve to diminish
the Event of the Experiment, but are not able to destroy it. For,
if the red and blue Colours were more dilute and weak, the distance
of the Images would be less than an Inch and a half; and if they
were more intense and full, that distance would be greater, as will
appear hereafter. These Experiments may suffice for the Colours of
Natural Bodies. For in the Colours made by the Refraction of
Prisms, this Proposition will appear by the Experiments which are
now to follow in the next Proposition.PROP.II.Theor.
II.The Light of the Sun consists of Rays differently
Refrangible.The Proof by Experiments.
Fig. 12.
Fig. 13.
Exper.3.In a very dark Chamber, at a round Hole, about one third Part
of an Inch broad, made in the Shut of a Window, I placed a Glass
Prism, whereby the Beam of the Sun's Light, which came in at that
Hole, might be refracted upwards toward the opposite Wall of the
Chamber, and there form a colour'd Image of the Sun. The Axis of
the Prism (that is, the Line passing through the middle of the
Prism from one end of it to the other end parallel to the edge of
the Refracting Angle) was in this and the following Experiments
perpendicular to the incident Rays. About this Axis I turned the
Prism slowly, and saw the refracted Light on the Wall, or coloured
Image of the Sun, first to descend, and then to ascend. Between the
Descent and Ascent, when the Image seemed Stationary, I stopp'd the
Prism, and fix'd it in that Posture, that it should be moved no
more. For in that Posture the Refractions of the Light at the two
Sides of the refracting Angle, that is, at the Entrance of the Rays
into the Prism, and at their going out of it, were equal to one
another.[C]So also in other
Experiments, as often as I would have the Refractions on both sides
the Prism to be equal to one another, I noted the Place where the
Image of the Sun formed by the refracted Light stood still between
its two contrary Motions, in the common Period of its Progress and
Regress; and when the Image fell upon that Place, I made fast the
Prism. And in this Posture, as the most convenient, it is to be
understood that all the Prisms are placed in the following
Experiments, unless where some other Posture is described. The
Prism therefore being placed in this Posture, I let the refracted
Light fall perpendicularly upon a Sheet of white Paper at the
opposite Wall of the Chamber, and observed the Figure and
Dimensions of the Solar Image formed on the Paper by that Light.
This Image was Oblong and not Oval, but terminated with two
Rectilinear and Parallel Sides, and two Semicircular Ends. On its
Sides it was bounded pretty distinctly, but on its Ends very
confusedly and indistinctly, the Light there decaying and vanishing
by degrees. The Breadth of this Image answered to the Sun's
Diameter, and was about two Inches and the eighth Part of an Inch,
including the Penumbra. For the Image was eighteen Feet and an half
distant from the Prism, and at this distance that Breadth, if
diminished by the Diameter of the Hole in the Window-shut, that is
by a quarter of an Inch, subtended an Angle at the Prism of about
half a Degree, which is the Sun's apparent Diameter. But the Length
of the Image was about ten Inches and a quarter, and the Length of
the Rectilinear Sides about eight Inches; and the refracting Angle
of the Prism, whereby so great a Length was made, was 64 degrees.
With a less Angle the Length of the Image was less, the Breadth
remaining the same. If the Prism was turned about its Axis that way
which made the Rays emerge more obliquely out of the second
refracting Surface of the Prism, the Image soon became an Inch or
two longer, or more; and if the Prism was turned about the contrary
way, so as to make the Rays fall more obliquely on the first
refracting Surface, the Image soon became an Inch or two shorter.
And therefore in trying this Experiment, I was as curious as I
could be in placing the Prism by the above-mention'd Rule exactly
in such a Posture, that the Refractions of the Rays at their
Emergence out of the Prism might be equal to that at their
Incidence on it. This Prism had some Veins running along within the
Glass from one end to the other, which scattered some of the Sun's
Light irregularly, but had no sensible Effect in increasing the
Length of the coloured Spectrum. For I tried the same Experiment
with other Prisms with the same Success. And particularly with a
Prism which seemed free from such Veins, and whose refracting Angle
was 62-1/2 Degrees, I found the Length of the Image 9-3/4 or 10
Inches at the distance of 18-1/2 Feet from the Prism, the Breadth
of the Hole in the Window-shut being 1/4 of an Inch, as before. And
because it is easy to commit a Mistake in placing the Prism in its
due Posture, I repeated the Experiment four or five Times, and
always found the Length of the Image that which is set down above.
With another Prism of clearer Glass and better Polish, which seemed
free from Veins, and whose refracting Angle was 63-1/2 Degrees, the
Length of this Image at the same distance of 18-1/2 Feet was also
about 10 Inches, or 10-1/8. Beyond these Measures for about a 1/4
or 1/3 of an Inch at either end of the Spectrum the Light of the
Clouds seemed to be a little tinged with red and violet, but so
very faintly, that I suspected that Tincture might either wholly,
or in great Measure arise from some Rays of the Spectrum scattered
irregularly by some Inequalities in the Substance and Polish of the
Glass, and therefore I did not include it in these Measures. Now
the different Magnitude of the hole in the Window-shut, and
different thickness of the Prism where the Rays passed through it,
and different inclinations of the Prism to the Horizon, made no
sensible changes in the length of the Image. Neither did the
different matter of the Prisms make any: for in a Vessel made of
polished Plates of Glass cemented together in the shape of a Prism
and filled with Water, there is the like Success of the Experiment
according to the quantity of the Refraction. It is farther to be
observed, that the Rays went on in right Lines from the Prism to
the Image, and therefore at their very going out of the Prism had
all that Inclination to one another from which the length of the
Image proceeded, that is, the Inclination of more than two degrees
and an half. And yet according to the Laws of Opticks vulgarly
received, they could not possibly be so much inclined to one
another.[D]For let EG
[Fig.13. (p. 27)] represent
the Window-shut, F the hole made therein through which a beam of
the Sun's Light was transmitted into the darkened Chamber, and ABC
a Triangular Imaginary Plane whereby the Prism is feigned to be cut
transversely through the middle of the Light. Or if you please, let
ABC represent the Prism it self, looking directly towards the
Spectator's Eye with its nearer end: And let XY be the Sun, MN the
Paper upon which the Solar Image or Spectrum is cast, and PT the
Image it self whose sides towardsvandware Rectilinear and
Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
two Rays, the first of which comes from the lower part of the Sun
to the higher part of the Image, and is refracted in the Prism at K
and H, and the latter comes from the higher part of the Sun to the
lower part of the Image, and is refracted at L and J. Since the
Refractions on both sides the Prism are equal to one another, that
is, the Refraction at K equal to the Refraction at J, and the
Refraction at L equal to the Refraction at H, so that the
Refractions of the incident Rays at K and L taken together, are
equal to the Refractions of the emergent Rays at H and J taken
together: it follows by adding equal things to equal things, that
the Refractions at K and H taken together, are equal to the
Refractions at J and L taken together, and therefore the two Rays
being equally refracted, have the same Inclination to one another
after Refraction which they had before; that is, the Inclination of
half a Degree answering to the Sun's Diameter. For so great was the
inclination of the Rays to one another before Refraction. So then,
the length of the Image PT would by the Rules of Vulgar Opticks
subtend an Angle of half a Degree at the Prism, and by Consequence
be equal to the breadthvw; and
therefore the Image would be round. Thus it would be were the two
Rays XLJT and YKHP, and all the rest which form the Image PwTv, alike refrangible. And therefore seeing by Experience it is
found that the Image is not round, but about five times longer than
broad, the Rays which going to the upper end P of the Image suffer
the greatest Refraction, must be more refrangible than those which
go to the lower end T, unless the Inequality of Refraction be
casual.This Image or Spectrum PT was coloured, being red at its
least refracted end T, and violet at its most refracted end P, and
yellow green and blue in the intermediate Spaces. Which agrees with
the first Proposition, that Lights which differ in Colour, do also
differ in Refrangibility. The length of the Image in the foregoing
Experiments, I measured from the faintest and outmost red at one
end, to the faintest and outmost blue at the other end, excepting
only a little Penumbra, whose breadth scarce exceeded a quarter of
an Inch, as was said above.Exper.4. In the Sun's Beam which was
propagated into the Room through the hole in the Window-shut, at
the distance of some Feet from the hole, I held the Prism in such a
Posture, that its Axis might be perpendicular to that Beam. Then I
looked through the Prism upon the hole, and turning the Prism to
and fro about its Axis, to make the Image of the Hole ascend and
descend, when between its two contrary Motions it seemed
Stationary, I stopp'd the Prism, that the Refractions of both sides
of the refracting Angle might be equal to each other, as in the
former Experiment. In this situation of the Prism viewing through
it the said Hole, I observed the length of its refracted Image to
be many times greater than its breadth, and that the most refracted
part thereof appeared violet, the least refracted red, the middle
parts blue, green and yellow in order. The same thing happen'd when
I removed the Prism out of the Sun's Light, and looked through it
upon the hole shining by the Light of the Clouds beyond it. And yet
if the Refraction were done regularly according to one certain
Proportion of the Sines of Incidence and Refraction as is vulgarly
supposed, the refracted Image ought to have appeared
round.So then, by these two Experiments it appears, that in Equal
Incidences there is a considerable inequality of Refractions. But
whence this inequality arises, whether it be that some of the
incident Rays are refracted more, and others less, constantly, or
by chance, or that one and the same Ray is by Refraction disturbed,
shatter'd, dilated, and as it were split and spread into many
diverging Rays, asGrimaldosupposes, does not yet appear by these Experiments, but will
appear by those that follow.Exper.5. Considering therefore, that
if in the third Experiment the Image of the Sun should be drawn out
into an oblong Form, either by a Dilatation of every Ray, or by any
other casual inequality of the Refractions, the same oblong Image
would by a second Refraction made sideways be drawn out as much in
breadth by the like Dilatation of the Rays, or other casual
inequality of the Refractions sideways, I tried what would be the
Effects of such a second Refraction. For this end I ordered all
things as in the third Experiment, and then placed a second Prism
immediately after the first in a cross Position to it, that it
might again refract the beam of the Sun's Light which came to it
through the first Prism. In the first Prism this beam was refracted
upwards, and in the second sideways. And I found that by the
Refraction of the second Prism, the breadth of the Image was not
increased, but its superior part, which in the first Prism suffered
the greater Refraction, and appeared violet and blue, did again in
the second Prism suffer a greater Refraction than its inferior
part, which appeared red and yellow, and this without any
Dilatation of the Image in breadth.Illustration.Let S [Fig.14, 15.] represent the Sun, F the
hole in the Window, ABC the first Prism, DH the second Prism, Y the
round Image of the Sun made by a direct beam of Light when the
Prisms are taken away, PT the oblong Image of the Sun made by that
beam passing through the first Prism alone, when the second Prism
is taken away, andptthe Image
made by the cross Refractions of both Prisms together. Now if the
Rays which tend towards the several Points of the round Image Y
were dilated and spread by the Refraction of the first Prism, so
that they should not any longer go in single Lines to single
Points, but that every Ray being split, shattered, and changed from
a Linear Ray to a Superficies of Rays diverging from the Point of
Refraction, and lying in the Plane of the Angles of Incidence and
Refraction, they should go in those Planes to so many Lines
reaching almost from one end of the Image PT to the other, and if
that Image should thence become oblong: those Rays and their
several parts tending towards the several Points of the Image PT
ought to be again dilated and spread sideways by the transverse
Refraction of the second Prism, so as to compose a four square
Image, such as is represented at πτ. For the better understanding
of which, let the Image PT be distinguished into five
Fig. 14
equal parts PQK, KQRL, LRSM, MSVN, NVT. And by the same
irregularity that the orbicular Light Y is by the Refraction of the
first Prism dilated and drawn out into a long Image PT, the Light
PQK which takes up a space of the same length and breadth with the
Light Y ought to be by the Refraction of the second Prism dilated
and drawn out into the long Imageπqkp, and the Light KQRL into the long Imagekqrl, and the Lights LRSM, MSVN, NVT,
into so many other long Imageslrsm,msvn,nvtτ; and all these long Images would
compose the four square Imagesπτ. Thus it ought to be were every Ray dilated by Refraction,
and spread into a triangular Superficies of Rays diverging from the
Point of Refraction. For the second Refraction would spread the
Rays one way as much as the first doth another, and so dilate the
Image in breadth as much as the first doth in length. And the same
thing ought to happen, were some rays casually refracted more than
others. But the Event is otherwise. The Image PT was not made
broader by the Refraction of the second Prism, but only became
oblique, as 'tis represented atpt, its upper end P being by the Refraction translated to a
greater distance than its lower end T. So then the Light which went
towards the upper end P of the Image, was (at equal Incidences)
more refracted in the second Prism, than the Light which tended
towards the lower end T, that is the blue and violet, than the red
and yellow; and therefore was more refrangible. The same Light was
by the Refraction of the first Prism translated farther from the
place Y to which it tended before Refraction; and therefore
suffered as well in the first Prism as in the second a greater
Refraction than the rest of the Light, and by consequence was more
refrangible than the rest, even before its incidence on the first
Prism.Sometimes I placed a third Prism after the second, and
sometimes also a fourth after the third, by all which the Image
might be often refracted sideways: but the Rays which were more
refracted than the rest in the first Prism were also more refracted
in all the rest, and that without any Dilatation of the Image
sideways: and therefore those Rays for their constancy of a greater
Refraction are deservedly reputed more refrangible.
Fig. 15
But that the meaning of this Experiment may more
clearly appear, it is to be considered that the Rays which are
equally refrangible do fall upon a Circle answering to the Sun's
Disque. For this was proved in the third Experiment. By a Circle I
understand not here a perfect geometrical Circle, but any orbicular
Figure whose length is equal to its breadth, and which, as to
Sense, may seem circular. Let therefore AG [inFig.15.] represent the Circle which
all the most refrangible Rays propagated from the whole Disque of
the Sun, would illuminate and paint upon the opposite Wall if they
were alone; EL the Circle which all the least refrangible Rays
would in like manner illuminate and paint if they were alone; BH,
CJ, DK, the Circles which so many intermediate sorts of Rays would
successively paint upon the Wall, if they were singly propagated
from the Sun in successive order, the rest being always
intercepted; and conceive that there are other intermediate Circles
without Number, which innumerable other intermediate sorts of Rays
would successively paint upon the Wall if the Sun should
successively emit every sort apart. And seeing the Sun emits all
these sorts at once, they must all together illuminate and paint
innumerable equal Circles, of all which, being according to their
degrees of Refrangibility placed in order in a continual Series,
that oblong Spectrum PT is composed which I described in the third
Experiment. Now if the Sun's circular Image Y [inFig.15.] which is made by an
unrefracted beam of Light was by any Dilation of the single Rays,
or by any other irregularity in the Refraction of the first Prism,
converted into the oblong Spectrum, PT: then ought every Circle AG,
BH, CJ, &c. in that Spectrum, by the cross Refraction of the
second Prism again dilating or otherwise scattering the Rays as
before, to be in like manner drawn out and transformed into an
oblong Figure, and thereby the breadth of the Image PT would be now
as much augmented as the length of the Image Y was before by the
Refraction of the first Prism; and thus by the Refractions of both
Prisms together would be formed a four square Figurepπtτ, as I described above. Wherefore
since the breadth of the Spectrum PT is not increased by the
Refraction sideways, it is certain that the Rays are not split or
dilated, or otherways irregularly scatter'd by that Refraction, but
that every Circle is by a regular and uniform Refraction translated
entire into another Place, as the Circle AG by the greatest
Refraction into the placeag,
the Circle BH by a less Refraction into the placebh, the Circle CJ by a Refraction
still less into the placeci,
and so of the rest; by which means a new Spectrumptinclined to the former PT is in like
manner composed of Circles lying in a right Line; and these Circles
must be of the same bigness with the former, because the breadths
of all the Spectrums Y, PT andptat equal distances from the Prisms are equal.I considered farther, that by the breadth of the hole F
through which the Light enters into the dark Chamber, there is a
Penumbra made in the Circuit of the Spectrum Y, and that Penumbra
remains in the rectilinear Sides of the Spectrums PT andpt. I placed therefore at that hole a
Lens or Object-glass of a Telescope which might cast the Image of
the Sun distinctly on Y without any Penumbra at all, and found that
the Penumbra of the rectilinear Sides of the oblong Spectrums PT
andptwas also thereby taken
away, so that those Sides appeared as distinctly defined as did the
Circumference of the first Image Y. Thus it happens if the Glass of
the Prisms be free from Veins, and their sides be accurately plane
and well polished without those numberless Waves or Curles which
usually arise from Sand-holes a little smoothed in polishing with
Putty. If the Glass be only well polished and free from Veins, and
the Sides not accurately plane, but a little Convex or Concave, as
it frequently happens; yet may the three Spectrums Y, PT andptwant Penumbras, but not in equal
distances from the Prisms. Now from this want of Penumbras, I knew
more certainly that every one of the Circles was refracted
according to some most regular, uniform and constant Law. For if
there were any irregularity in the Refraction, the right Lines AE
and GL, which all the Circles in the Spectrum PT do touch, could
not by that Refraction be translated into the Linesaeandglas distinct and straight as they were before, but there would
arise in those translated Lines some Penumbra or Crookedness or
Undulation, or other sensible Perturbation contrary to what is
found by Experience. Whatsoever Penumbra or Perturbation should be
made in the Circles by the cross Refraction of the second Prism,
all that Penumbra or Perturbation would be conspicuous in the right
Linesaeandglwhich touch those Circles. And
therefore since there is no such Penumbra or Perturbation in those
right Lines, there must be none in the Circles. Since the distance
between those Tangents or breadth of the Spectrum is not increased
by the Refractions, the Diameters of the Circles are not increased
thereby. Since those Tangents continue to be right Lines, every
Circle which in the first Prism is more or less refracted, is
exactly in the same proportion more or less refracted in the
second. And seeing all these things continue to succeed after the
same manner when the Rays are again in a third Prism, and again in
a fourth refracted sideways, it is evident that the Rays of one and
the same Circle, as to their degree of Refrangibility, continue
always uniform and homogeneal to one another, and that those of
several Circles do differ in degree of Refrangibility, and that in
some certain and constant Proportion. Which is the thing I was to
prove.There is yet another Circumstance or two of this Experiment
by which it becomes still more plain and convincing. Let the second
Prism DH [inFig.16.] be placed
not immediately after the first, but at some distance from it;
suppose in the mid-way between it and the Wall on which the oblong
Spectrum PT is cast, so that the Light from the first Prism may
fall upon it in the form of an oblong Spectrum πτ parallel to this
second Prism, and be refracted sideways to form the oblong
Spectrumptupon the Wall. And
you will find as before, that this Spectrumptis inclined to that Spectrum PT,
which the first Prism forms alone without the second; the blue ends
P andpbeing farther distant
from one another than the red ones T andt, and by consequence that the Rays
which go to the blue end π of the Image πτ, and which therefore
suffer the greatest Refraction in the first Prism, are again in the
second Prism more refracted than the rest.
Fig. 16.
Fig. 17.
The same thing I try'd also by letting the Sun's Light
into a dark Room through two little round holes F and φ [inFig.17.] made in the Window, and with
two parallel Prisms ABC and αβγ placed at those holes (one at each)
refracting those two beams of Light to the opposite Wall of the
Chamber, in such manner that the two colour'd Images PT and MN
which they there painted were joined end to end and lay in one
straight Line, the red end T of the one touching the blue end M of
the other. For if these two refracted Beams were again by a third
Prism DH placed cross to the two first, refracted sideways, and the
Spectrums thereby translated to some other part of the Wall of the
Chamber, suppose the Spectrum PT toptand the Spectrum MN tomn, these translated Spectrumsptandmnwould not lie in
one straight Line with their ends contiguous as before, but be
broken off from one another and become parallel, the blue
endmof the Imagemnbeing by a greater Refraction
translated farther from its former place MT, than the red
endtof the other Imageptfrom the same place MT; which puts
the Proposition past Dispute. And this happens whether the third
Prism DH be placed immediately after the two first, or at a great
distance from them, so that the Light refracted in the two first
Prisms be either white and circular, or coloured and oblong when it
falls on the third.Exper.6. In the middle of two thin
Boards I made round holes a third part of an Inch in diameter, and
in the Window-shut a much broader hole being made to let into my
darkned Chamber a large Beam of the Sun's Light; I placed a Prism
behind the Shut in that beam to refract it towards the opposite
Wall, and close behind the Prism I fixed one of the Boards, in such
manner that the middle of the refracted Light might pass through
the hole made in it, and the rest be intercepted by the Board. Then
at the distance of about twelve Feet from the first Board I fixed
the other Board in such manner that the middle of the refracted
Light which came through the hole in the first Board, and fell upon
the opposite Wall, might pass through the hole in this other Board,
and the rest being intercepted by the Board might paint upon it the
coloured Spectrum of the Sun. And close behind this Board I fixed
another Prism to refract the Light which came through the hole.
Then I returned speedily to the first Prism, and by turning it
slowly to and fro about its Axis, I caused the Image which fell
upon the second Board to move up and down upon that Board, that all
its parts might successively pass through the hole in that Board
and fall upon the Prism behind it. And in the mean time, I noted
the places on the opposite Wall to which that Light after its
Refraction in the second Prism did pass; and by the difference of
the places I found that the Light which being most refracted in the
first Prism did go to the blue end of the Image, was again more
refracted in the second Prism than the Light which went to the red
end of that Image, which proves as well the first Proposition as
the second. And this happened whether the Axis of the two Prisms
were parallel, or inclined to one another, and to the Horizon in
any given Angles.Illustration.Let F [inFig.18.] be the wide hole in the
Window-shut, through which the Sun shines upon the first Prism ABC,
and let the refracted Light fall upon the middle of the Board DE,
and the middle part of that Light upon the hole G made in the
middle part of that Board. Let this trajected part of that Light
fall again upon the middle of the second Boardde, and there paint such an oblong
coloured Image of the Sun as was described in the third Experiment.
By turning the Prism ABC slowly to and fro about its Axis, this
Image will be made to move up and down the Boardde, and by this means all its parts
from one end to the other may be made to pass successively through
the holegwhich is made in the
middle of that Board. In the mean while another Prismabcis to be fixed next after that
holeg, to refract the
trajected Light a second time. And these things being thus ordered,
I marked the places M and N of the opposite Wall upon which the
refracted Light fell, and found that whilst the two Boards and
second Prism remained unmoved, those places by turning the first
Prism about its Axis were changed perpetually. For when the lower
part of the Light which fell upon the second Boarddewas cast through the holeg, it went to a lower place M on the
Wall and when the higher part of that Light was cast through the
same holeg, it went to a
higher place N on the Wall, and when any intermediate part of the
Light was cast through that hole, it went to some place on the Wall
between M and N. The unchanged Position of the holes in the Boards,
made the Incidence of the Rays upon the second Prism to be the same
in all cases. And yet in that common Incidence some of the Rays
were more refracted, and others less. And those were more refracted
in this Prism, which by a greater Refraction in the first Prism
were more turned out of the way, and therefore for their Constancy
of being more refracted are deservedly called more
refrangible.
Fig. 18.
Fig. 20.
Exper.