BOYLE appears to have been the first that observed the colours of
scratches on polished surfaces. NEWTON has not noticed them. MAZEAS and
Mr. BROUGHAM have made some experiments on the subject, yet without
deriving any satisfactory conclusion. But all the varieties of these
colours are very easily deduced from this proposition.
Let there be in a given plane two reflecting points very near each
other, and let the plane be so situated that the reflected image of
a luminous object seen in it may appear to coincide with the points;
then it is obvious that the length of the incident and reflected ray,
taken together, is equal with respect to both points, considering them
as capable of reflecting in all directions. Let one of the points
be now depressed below the given plane; then the whole path of the
light reflected from it, will be lengthened by a line which is to the
depression of the point as twice the cosine of incidence to the radius.
Fig. 2.
If, therefore, equal undulations of given dimensions be reflected
from two points, situated near enough to appear to the eye but as one,
wherever this line is equal to half the breadth of a whole undulation,
the reflection from the depressed point will so interfere with the
reflection from the fixed point, that the progressive motion of the one
will coincide with the retrograde motion of the other, and they will
both be destroyed; but, when this line is equal to the whole breadth
of an undulation, the effect will be doubled; and when to a breadth
and a half, again destroyed; and thus for a considerable number of
alternations; and, if the reflected undulations be of different kinds,
they will be variously affected, according to their proportions to the
various length of the line which is the difference between the lengths
of their two paths, and which may be denominated the interval of
retardation.
In order that the effect may be the more perceptible, a number of pairs
of points must be united into two parallel lines; and, if several such
pairs of lines be placed near each other, they will facilitate the
observation. If one of the lines be made to revolve round the other as
an axis, the depression below the given plane will be as the sine of
the inclination; and, while the eye and luminous object remain fixed,
the difference of the length of the paths will vary as this sine.
The best subjects for the experiment are Mr. COVENTRY’s exquisite
micrometers; such of them as consist of parallel lines drawn on
glass, at the distance of one five hundredth of an inch, are the most
convenient. Each of these lines appears under a microscope to consist
of two or more finer lines, exactly parallel, and at the distance of
somewhat more than a twentieth, of that of the adjacent lines. I placed
one of these so as to reflect the sun’s light at an angle of 45°, and
fixed it in such a manner, that while it revolved round one of the
lines as an axis, I could measure its angular motion; and I found, that
the brightest red colour occurred at the inclinations 10-1/4°, 20-1/4°,
32°, and 45°; of which the sines are as the numbers 1, 2, 3, and 4.
At all other angles also, when the sun’s light was reflected from the
surface, the colour vanished with the inclination, and was equal at
equal inclinations on either side.
This experiment affords a very strong confirmation of the theory.
It is impossible to deduce any explanation of it from any hypothesis
hitherto advanced; and I believe it would be difficult to invent any
other that would account for it. There is a striking analogy between
this separation of colours, and the production of a musical note by
successive echoes from equidistant iron palisades; which I have found
to correspond pretty accurately with the known velocity of sound, and
the distances of the surfaces.
It is not improbable that the colours of the integuments of some
insects, and of some other natural bodies, exhibiting in different
lights the most beautiful versatility, may be found to be of this
description, and not to be derived from thin plates. In some cases, a
single scratch or furrow may produce similar effects, by the reflection
of its opposite edges.
COROLLARY II. _Of the Colours of thin Plates_.
When a beam of light falls on two parallel refracting surfaces, the
partial reflections coincide perfectly in direction; and, in this case,
the interval of retardation, taken between the surfaces, is to their
distance as twice the cosine of the angle of refraction to the radius.
For, in Fig. 3, drawing AB and CD perpendicular to the rays, the times
of passing through BC and AD will be equal, and DE will be half the
interval of retardation; but DE is to CE as the sine of DCE to the
radius. Hence, that DE may be constant, or that the same colour may be
reflected, the thickness CE must vary as the secant of the angle of
refraction CED: which agrees exactly with NEWTON’s experiments; for the
correction is perfectly inconsiderable.
Let the medium between the surfaces be rarer than the surrounding
mediums; then the impulse reflected at the second surface, meeting a
subsequent undulation at the first, will render the particles of the
rarer medium capable of wholly stopping the motion of the denser, and
destroying the reflection, (PROP. IV.) while they themselves will
be more strongly propelled than if they had been at rest; and the
transmitted light will be increased. So that the colours by reflection
will be destroyed, and those by transmission rendered more vivid, when
the double thicknesses, or intervals of retardation, are any multiples
of the whole breadths of the undulations; and, at intermediate
thicknesses the effects will be reversed; according to the NEWTONIAN
observations.
If the same proportions be found to hold good with respect to thin
plates of a denser medium, which is indeed not improbable, it will be
necessary to adopt the corrected demonstration of PROP. IV. but, at
any rate, if a thin plate be interposed between a rarer and a denser
medium, the colours by reflection and transmission may be expected to
change places.
From NEWTON’s measures of the thicknesses reflecting the different
colours, the breadth and duration of their respective undulations
may be very accurately determined; although it is not improbable,
that when the glasses approach very near, the atmosphere of ether may
produce some little irregularity. The whole visible spectrum appears
to be comprised within the ratio of three to five, or a major sixth in
music; and the undulations of red, yellow, and blue, to be related in
magnitude as the numbers 8, 7, and 6; so that the interval from red
to blue is a fourth. The absolute frequency expressed in numbers is
too great to be distinctly conceived, but it may be better imagined by
a comparison with sound. If a chord sounding the tenor ̅/c, could be
continually bisected 40 times, and should then vibrate, it would afford
a yellow green light: this being denoted by 41/c, the extreme red would
be 40/a, and the blue 41/d. The absolute length and frequency of each
vibration is expressed in the table; supposing light to travel in 8-1/8
minutes 500,000,000000 feet.
+---------------+--------------+-----------+-------------------------+
| | Length of an | Number of | |
| Colours. | Undulation |Undulations| Number of Undulations |
| |in parts of an|in an Inch.| in a second. |
| | Inch, in Air.| | |
+---------------+--------------+-----------+-------------------------+
| Extreme - | .0000266 | 37640 |463 millions of millions |
|Red - - | .0000256 | 39180 |482 |
| Intermediate | .0000246 | 40720 |501 |
|Orange - | .0000240 | 41610 |512 |
| Intermediate | .0000235 | 42510 |523 |
|Yellow - | .0000227 | 44000 |542 |
| Intermediate | .0000219 | 45600 |561 (= 2^{48} nearly) |
|Green - - | .0000211 | 47460 |584 |
| Intermediate | .0000203 | 49320 |607 |
|Blue - - | .0000196 | 51110 |629 |
| Intermediate | .0000189 | 52910 |652 |
|Indigo - | .0000185 | 54070 |665 |
| Intermediate | .0000181 | 55240 |680 |
|Violet - | .0000174 | 57490 |707 |
| Extreme - | .0000167 | 59750 |735 |
+---------------+--------------+-----------+-------------------------+
_Scholium_. It was not till I had satisfied myself respecting all
these phenomena, that I found in HOOKE’s Micrographia, a passage which
might have led me earlier to a similar conclusion. “It is most evident
that the reflection from the under or further side of the body, is the
principal cause of the production of these colours....Let the ray fall
obliquely on the thin plate, part therefore is reflected back by the
first superficies,...part refracted to the second surface,...whence it
is reflected and refracted again.... So that, after two refractions and
one reflection, there is propagated a kind of fainter ray,...and, by
reason of the time spent in passing and repassing,...this fainter pulse
comes behind the former reflected pulse; so that hereby, (the surfaces
being so near together that the eye cannot discriminate them from one,)
this confused or duplicated pulse, whose strongest part precedes, and
whose weakest follows, does produce on the retina,...the sensation of
a yellow.... If these surfaces are further removed asunder, the weaker
pulse may become coincident with the reflection of the second, or next
following pulse, from the first surface, and lagg behind that also,
and be coincident with the third, fourth, fifth, sixth, seventh, or
eighth; so that, if there be a thin transparent body, that from the
greatest thinness requisite to produce colours, does by degrees grow
to the greatest thickness,...the colours shall be so often repeated,
as the weaker pulse does lose paces with its primary or first pulse,
and is coincident with a subsequent pulse.... And this, as it is
coincident, or follows from the first hypothesis I took of colours, so
upon experiment have I found it in multitudes of instances that seem
to prove it.” (P. 65—67.) This was printed about seven years before
any of NEWTON’s experiments were made. We are informed by Newton, that
Hooke was afterwards disposed to adopt his “suggestion” of the nature
of colours; and yet it does not appear that HOOKE ever applied that
improvement to his explanation of these phenomena, or inquired into
the necessary consequence of a change of obliquity, upon his original
supposition, otherwise he could not but have discovered a striking
coincidence with the measures laid down by Newton from experiment. All
former attempts to explain the colours of thin plates, have either
proceeded on suppositions which, like NEWTON’s, would lead us to expect
the greatest irregularities in the direction of the refracted rays;
or, like Mr. MICHELL’s, would require such effects from the change of
the angle of incidence, as are contrary to the effects observed; or
they are equally deficient with respect to both these circumstances,
and are inconsistent with the most moderate attention to the principal
phenomena.