Colour Measurement and Mixture

by Sir William de Wiveleslie Abney

Absorption of the Spectrum—Analysis of Colour—Vibrations of Rays—Absorption by Pigments—Phosphorescence—Interference.

We must now briefly consider what is the origin, or at all events the cause, of the colour which we see in objects. It is not proposed to enter into this by any means minutely, but only sufficiently to enable us to understand the subject which is to be brought before you. What for instance is the cause of the colour of this green solution of chlorophyll, which is an extract of cabbage leaves? If we place it in the front of the spectrum apparatus and throw the spectrum on the screen, we find that while there is a certain amount of blue transmitted, the green is strong, and there are red bands left, but a good deal of the spectrum is totally absorbed. Forming a colour patch of this absorption spectrum on the screen, we see that it is the same colour as the chlorophyll solution, and of this we can judge more accurately by using the reflected beam, and placing the rod in position to cast shadows. (The light of the reflected beam is that of the light entering the slit.) The colour then of the chlorophyll is due to the absence of certain colours from the spectrum of white light. When white light passes through it, the material absorbs, or filters out, some of the coloured rays, and allows others to pass more or less unaffected, and it is the re-combination of these last which makes up the colour of the chlorophyll. We have a green dye which to the eye is very similar in colour to chlorophyll, but putting a solution of it in front of the spectrum, we see that it cuts off different rays to the latter. It would be quite possible to mistake one green for the other, but directly we analyze the white light which has filtered through each by means of the spectrum, we at once see that they differ. Hence the spectrum enables the eye to discriminate by analysis what it would otherwise be unable to do. Any coloured solution or transparent body may be analyzed in the same way, and, as we shall see subsequently, the intensity of every ray after passing through it can be accurately compared with the original incident light. There are some cases, indeed the majority of cases, in which the colour transmitted through a small thickness of the material is different to that transmitted through a greater thickness. For instance, a weak solution of litmus in water is blue when a thin layer is examined, and red when it is a thicker or more concentrated layer. Bichromate of potash is more ruddy as the thickness increases. This can be readily understood by a reference to the law of absorption. Suppose we have a thin layer of a liquid which gives a purple colour when two simple colours, red and blue, pass through it, and that this thin layer cuts off one-quarter of the red and one-half of the blue incident on it, another layer of equal thickness will cut off another quarter of the three-quarters of red passing through the first layer, and half of the one-half left of the blue; we shall thus have nine-sixteenths of the red passing and only a quarter of the blue. With a third layer we shall have twenty-seven sixty-fourths of red and only one-eighth of blue left, showing that as the thickness of the liquid is increased the blue rapidly disappears, leaving the red the dominant colour. Now what is true of two simple colours is equally true of any number of them, where the rates of absorption differ from one another, and what is true for a solution is true for a transparent solid. In some opaque bodies, such as rocks, the reflected colour often differs slightly from that of the same when they are cut into thin and polished slices, through which the light can pass. The reason is that when opaque, light penetrates to a very small distance through the surface, and is reflected back, whilst in these layers the colour has to struggle through more coloured matter, and emerges of a different hue.

The question why substances transmit some rays and quench others, brings us into the domain of molecular physics. Of all branches of physical science this is perhaps the most fascinating and the most speculative, yet it is one which is being built up on the solid foundations of experiment and mathematics, till it has attained an importance which the questions depending on it fully warrants. We have to picture to ourselves, in the case in point, molecules, and the atoms composing them, of a size which no microscope can bring to view, vibrating in certain definite periods which are similar to the periods of oscillation of the waves of light. At page 26 we have given the lengths of some of the waves which give the sensation of coloured light. Now as light, of whatever colour it may be, is practically transmitted with the same velocity through air which has the same density throughout, it follows that the number of vibrations per second of each ray can be obtained by dividing the velocity of light in any medium by the wave-length. The following table gives roughly the number of vibrations per second of the ether giving rise to the colours fixed by the dark solar lines.

Name of Line.	Millions of Millions of; Vibrations per Second.
A in the Red	395
B " "	437
C " "	458
D " Orange	510
E " Green	570
F " Blue	618
G " Violet	697
H " Ultra-Violet	757

If we endeavour to gauge what this rate of oscillation means we shall scarcely be able to realize it, even by a comparison with some physically measurable rate of vibration. A tuning-fork, for instance, giving the middle C, vibrates 528 times per second. Compare this with the number of vibrations of the waves of light, and we still are as far as ever from realizing it, yet the velocity of light, and the lengths of the different waves have been accurately determined; the latter, although the much smaller quantity, with even greater accuracy than the first. These rates of vibration must therefore be—cannot help being—at all events approximately true. This being so, we know that some of the atoms of the molecules at least, and perhaps in some cases the molecules themselves, are vibrating at the same rate as those waves of light, which they refuse to allow to pass. If we have a child's swing beginning to oscillate, we know that it is only by well-timed blows that the extent of the swing is permanently increased, and the energy exerted by the person who gives the well-timed blow is expended on producing the increased amplitude. In the same way if the rate of vibration of a wave of light is in accord with that of a molecule or atom, the amplitude or swing of the atom or molecule is increased, and the energy of the wave and therefore its amplitude is totally or partially destroyed; and as the amplitude is a function of the intensity of the light, the ray fails to be seen at all, or else is diminished in brightness.

In what way the atoms vibrate where more than one ray is absorbed is still a matter of speculation, but no doubt as experimental methods are more fully developed, and mathematicians investigate the results of such experiments, we shall be able to form a picture of the vibrations themselves. At page 137 a speculation as to the reason why solids or liquids can absorb more waves of light than one which are adjacent to each other is put forward, but it does not deal with the absorptions which occupy various parts of the spectrum. Again, too, we have the fact that the energy absorbed by these atoms and molecules from the waves of light, must show itself as work done on them—it may be as heat or as chemical action. We shall see by and by that in some cases, no doubt, at least a part is expended in the latter form of work.

Perhaps this mode of looking at the question of colour in objects may make the subject more interesting to the reader than it at first appears to be deserving. The whole subject is one which enlarges the faculty of making mental pictures, and this is one of the most useful forms of scientific education.

But how can we distinguish between pigments which to the eye are apparently the same? If we dye paper with the green dye referred to, we can place it in the spectrum, and we shall see that the dye reflects differently to the white paper. In fact we shall find that it refuses to reflect in those parts of the spectrum which the transparent solution refused to transmit. So long as the light passes through the dye-stuff, it is indifferent, as regards the colour produced, whether the colouring matter be at a distance from the paper or whether the latter be dyed with it, as we can see at once. If we place the solution of the dye in the reflected beam of the apparatus and form a patch on the screen, and alongside throw the patch of white light from the integrated or recombined spectrum upon the dyed paper, it will be found that the two colours are alike; that is, the green-coloured light on the white paper, or the white light on the green paper are the same. Similarly we may experiment on other dyes, such as magenta, log-wood, &c., and we shall see that like results are obtained. It should be said, however, that when the paper is dyed with the colouring matter a small quantity of white light will be reflected from the surface of the paper itself. We may now say that the general colour is given to a body by its refusal to transmit or reflect, more or less completely, certain rays of the spectrum. Should the solvent form a compound with the dye, perhaps this would not be absolutely true, but in the large majority of cases the statement is correct. When we have bodies which are also fluorescent, this statement would also have to be modified, but we need not consider these for the present.

Another source of colour in objects, though very rarely met with, and which for our object we need not stay to explain in detail, is the interference of light. Such is seen in soap-bubbles. Briefly it may be said that the colours are due to rays of light reflected from the inner surface of the film, which quench other rays of light of the same wave-length reflected from the outer surface. If two series of waves of the same wave-length are going in the same direction and from the same source, each of which has the same intensity as the other, that is, having the same amplitude, and it happens that the one series is exactly half a wave-length behind the other, then the crest of one wave in the first series will fill up the trough of the other in the second series, and no motion would result, and this lack of motion means darkness, since it is the wave motion which gives the sensation of light. If then we have white light falling on two reflecting surfaces, such as the front and back of a soap-film, part of the light will be reflected from each, and if the film be of such a thickness that the latter reflects light exactly ½ wave-length, 3/2 or 5/2 wave-length, &c., of some colour behind the former, the colour due to that particular wave-length will be absent from the reflected white light, and instead of white light we shall have coloured light, due to the combination of all the colours less this colour, which is quenched.

A very pretty experiment to make is to throw the image of a soap film on the screen, and to watch the change in the colours of the film. Their brilliancy increases as the film becomes thinner, and the bands, which first appear close to each other, separate, and then we see a large expanse of changing colour. A soap solution should be made according to almost any of the published formulæ, and a piece of flat card be dipped in it, and be drawn across a ring of wire some inch in diameter, or—what the writer prefers best—the stop of a photographic lens. A film will form and fill the aperture. The ring or stop may be placed vertically in a clamp, and a beam of light caused to fall at an angle of about 45 degrees on to the film. If a lens be placed in the path of the reflected beam to form an image of the aperture, the colours which the film shows can be exhibited to an audience, if the diameter of the image be made four or five feet. Instead of this large image, a small image may be thrown on the slit of the spectroscope, by using a lens of a greater focal length, and if the beam be so directed that it falls on the axis of the collimator, a very fairly bright spectrum may be also thrown on the screen. The appearance of the spectrum is somewhat like that shown in the above diagram (Fig. 9).