_Colours of thin Plates first studied by Boyle and Hooke—Newton
determines the Law of their Production—His Theory of Fits of Easy
Reflection and Transmission—Colours of thick Plates._
In examining the nature and origin of colours as the component parts
of white light, the attention of Newton was directed to the curious
subject of the colours of thin plates, and to its application to
explain the colours of natural bodies. His earliest researches on this
subject were communicated, in his Discourse on Light and Colours,
to the Royal Society, on the 9th December, 1675, and were read at
subsequent meetings of that body. This discourse contained fuller
details respecting the composition and decomposition of light than
he had given in his letter to Oldenburg, and was concluded with nine
propositions, showing how the colours of thin transparent plates stand
related to those of all natural bodies.
The colours of thin plates seem to have been first observed by Mr.
Boyle. Dr. Hooke afterward studied them with some care, and gave a
correct account of the leading phenomena, as exhibited in the coloured
rings upon soap-bubbles, and between plates of glass pressed together.
He recognised that the colour depended upon some certain thickness of
the transparent plate, but he acknowledges that he had attempted in
vain to discover the relation between the thickness of the plate and
the colour which it produced.
Dr. Hooke succeeded in splitting a mineral substance, called mica,
into films of such extreme thinness as to give brilliant colours. One
plate, for example, gave a yellow colour, another a blue colour, and
the two together a deep purple; but, as plates which produced those
colours were always less than the 12,000th part of an inch thick,
it was quite impracticable, by any contrivance yet discovered, to
measure their thickness, and determine the law according to which the
colour varied with the thickness of the film. Newton surmounted this
difficulty by laying a double convex lens, the radius of curvature
of each side of which was fifty feet, upon the flat surface of a
plano-convex object-glass, and in this way he obtained a plate of air
or of space varying from the thinnest possible edge at the centre of
the object-glass where it touched the plane surface, to a considerable
thickness at the circumference of the lens. When light was allowed to
fall upon the object-glass, every different thickness of the plate
of air between the object-glass gave different colours, so that the
point where the two object-glasses touched one another was the centre
of a number of concentric coloured rings. Now, as the curvature of
the object-glass was known, it was easy to calculate the thickness of
the plate of air at which any particular colour appeared, and thus to
determine the law of the phenomena.
In order to understand how he proceeded, let CED be the convex surface
of the one object-glass, and AEB the flat surface of the other. Let
them touch at the point E, and let homogeneous _red_ rays fall upon
them, as shown in the figure. At the point of contact E, where the
plate of air is inconceivably thin, not a single ray of the pencil RE
is reflected. The light is wholly transmitted, and, consequently, to
an eye above E, there will appear at E a black spot. At _a_, where
the plate of air is thicker, the red light _ra_ is reflected in the
direction _aa′_, and as the air has the same thickness in a circle
round the point E, the eye above E, at _a_, will see next the black
spot E a ring of red light. At _m_, where the thickness of the air is
a little greater than at _a_, the light _r′m_ is all transmitted as at
E, and not a single ray suffers reflection, so that to an eye above E
at _m′_ there will be seen without the red ring _a_ a dark ring _m_.
In like manner, at greater thicknesses of the plate of air, there is a
succession of _red_ and dark rings, diminishing in breadth as shown in
the diagram.
[Illustration: _Fig. 8._]
When the same experiment was repeated in _orange_, _yellow_, _green_,
_blue_, _indigo_, and _violet_ light, the very same phenomenon was
observed; with this difference only, that the rings were _largest_ in
_red_ light, and _smallest_ in _violet_ light, and had intermediate
magnitudes in the intermediate colours.
If the observer now places his eye below E, so as to see the
transmitted rays, he will observe a set of rings as before, but they
will have a bright spot in their centre at E, and the luminous rings
will now correspond with those which were dark when seen by reflection,
as will be readily understood from inspecting the preceding diagram.
When the object-glasses are illuminated by _white_ light, the _seven_
systems of rings, formed by all the _seven_ colours which compose white
light, will now be seen at once. Had the rings in each colour been all
of the same diameter they would all have formed brilliant white rings,
separated by dark intervals; but, as they have all different diameters,
they will overlap one another, producing rings of various colours by
their mixture. These colours, reckoning from the centre E, are as
follows:—
1st Order. Black, blue, white, yellow, orange, red.
2d Order. Violet, blue, green, yellow, orange, red.
3d Order. Purple, blue, green, yellow, red, bluish-red.
4th Order. Bluish-green, green, yellowish-green, red.
5th Order. Greenish-blue, red.
6th Order. Greenish-blue, red.
By accurate measurements, Sir Isaac found that the thicknesses of _air_
at which the most luminous parts of the first rings were produced, were
in parts of an inch 1/178000, 3/178000, 5/178000, 7/178000, 9/178000,
11/178000. If the medium or the substance of the thin plate is water,
as in the case of the soap-bubble, which produces beautiful colours
according to its different degrees of thinness, the thicknesses at
which the most luminous parts of the rings appear are produced at
1/1·336 of the thickness at which they are produced in air, and in the
case of glass or mica at 1/1·525 of that thickness; the numbers 1.336,
1.525 expressing the ratio of the sines of the angles of incidence and
refraction in the substances which produce the colours.
From the phenomena thus briefly described, Sir Isaac Newton deduces
that ingenious, though hypothetical, property of light, called its
_fits of easy reflection and transmission_. This property consists in
supposing that every particle of light from its first discharge from
a luminous body possesses, at equally distant intervals, dispositions
to be reflected from, and transmitted through, the surfaces of bodies
upon which it is incident. Hence, if a particle of light reaches a
reflecting surface of glass when it is in its _fit of reflection_,
or in its disposition to be reflected, it will yield more readily
to the reflecting force of the surface; and, on the contrary, if it
reaches the same surface while in a _fit of easy transmission_, or in
a disposition to be transmitted, it will yield with more difficulty to
the reflecting force. Sir Isaac has not ventured to inquire into the
cause of this property; but we may form a very intelligible idea of
it by supposing, that the particles of light have two attractive and
two repulsive poles at the extremities of two axes at right angles to
each other, and that the particles revolve round their axes, and at
equidistant intervals bring one or other of these axes into the line
of the direction in which the particle is moving. If the attractive
axis is in the line of the direction in which the particle moves when
it reaches the refracting surface, the particle will yield to the
attractive force of the medium, and be refracted and transmitted; but
if the repulsive axis is in the direction of the particle’s motion when
it reaches the surface, it will yield to the repulsive force of the
medium, and be reflected from it.
The application of the theory of alternate fits of reflection and
transmission to explain the colours of thin plates is very simple.
When the light falls upon the first surface AB, Fig. 8 of the plate of
air between AB and CED, the rays that are in a fit of reflection are
reflected, and those that are in a fit of transmission are transmitted.
Let us call F the length of a fit, or the distance through which the
particle of light moves while it passes from the state of being in
a fit of reflection to the state of being in a fit of transmission.
Now, as all the particles of light transmitted through AB were in a
state of easy transmission when they entered AB, it is obvious, that,
if the plate of air at E is so thin as to be less than one-half of
F, the particles of light will still be in their disposition to be
transmitted, and consequently the light will be all transmitted, and
none reflected at the curve surface at E. When the plate becomes
thicker towards _a_, so that its thickness exceeds half of F, the
light will not reach the surface CE till it has come under its fit of
reflection, and consequently at _a_ the light will be all reflected,
and none transmitted. As the thickness increases towards _m_, the
light will have come under its fit of transmission, and so on, the
light being reflected at _a_, _l_, and transmitted at E, _m_. This
will perhaps be still more easily understood from _fig. 9_, where we
may suppose AEC to be a thin wedge of glass or any other transparent
body. When light is incident on the first surface AE, all the particles
of it that are in a fit of easy reflection will be reflected, and all
those in a fit of easy transmission will be transmitted. As the fits of
transmission all commence at AE, let the first fit of transmission end
when the particles of light have reached _ab_, and the second when they
have reached _ef_; and let the fits of reflection commence at _cd_ and
_gh_. Then, as the fit of transmission continues from AE to _ab_, all
the light that falls upon the portion _m_E of the second surface will
be transmitted and none reflected, so that to an eye above E the space
_m_E will appear black. As the fit of reflection commences at _ab_,
and continues to _cd_, all the light which falls upon the portion _nm_
will be reflected, and none transmitted; and so on, the light being
transmitted at _m_E and _pn_, and reflected at _nm_ and _qp_. Hence to
an eye above E the wedge-shaped film of which AEC is a section will
be covered with parallel bands or fringes of light separated by dark
fringes of the same breadth, and they will be all parallel to the thin
edge of the plate, a dark fringe corresponding to the thinnest edge.
To an eye placed below CE, similar fringes will be seen, but the one
corresponding to the thinnest edge _m_E will be luminous.
[Illustration: _Fig. 9._]
If the thickness of the plate does not vary according to a regular law
as in _fig. 9_, but if, like a film of blown glass, it has numerous
inequalities, then the alternate fringes of light and darkness will
vary with the thickness of the film, and throughout the whole length of
each fringe the thickness of the film will be the same.
We have supposed in the preceding illustration that the light employed
is homogeneous. If it is white, then the differently coloured fringes
will form by their superposition a system of fringes analogous to those
seen between two object-glasses, as already explained.
The same periodical colours which we have now described as exhibited
by thin plates were discovered by Newton in thick plates, and he has
explained them by means of the theory of fits; but it would lead
us beyond the limits of a popular work like this to enter into any
details of his observations, or to give an account of the numerous and
important additions which this branch of optics has received from the
discoveries of succeeding authors.