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CHAPTER V
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.
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).
Fig. 9. – Interference Bands.
If we take a horizontal line across the spectrum, we shall see what particular colours are missing from the reflected light which falls on the part of the slit corresponding to that line. The colours of some objects, such as of the opal, and the lovely colouring of some feathers are due to interference of light. The partial scattering of different rays by small particles will also cause light to be coloured, as we shall see in the experiments we shall make to imitate the colour of sunlight at various altitudes of the sun. We may, however, take it as a rule that the colour of objects is produced by the greater or less absorption of some rays, and the reflection in the case of opaque bodies, or the transmission, in the case of transparent bodies, of the remainder.
CHAPTER VI
Scattered Light – Sunset Colours – Law of the Scattering by Fine Particles – Sunset Clouds – Luminosities of Sunlight at different Altitudes of the Sun.
It is probable that we should be able to ascertain approximately the true colour of sunlight (if we may talk of the colour of white light) if we could collect all the light from a cloudless sky, and condense it on a patch of sunlight thrown on a screen. For skylight is, after all, only a portion of the light of the sun, scattered from small particles in the atmosphere, part of the light being scattered into space, and part to our earth. The small particles of water and dust – and when we say small we mean small when measured on the same scale as we measure the lengths of waves of light – differentiate between waves of different lengths, and scatter the blue rays more than the green, and the green than the red; consequently what the sun lacks in blue and green is to be found in the light of the sky. The effect that small water particles have upon light passing through them can be very well seen in the streets of London at night, when the atmosphere is at all foggy. Gaslights at the far end of a street appear to become ruby red and dim, and half-way down only orange, but brighter, whilst close to they are of the ordinary yellow colour, and of normal brightness. When no fog is present the gas-lights in the distance and close to are of the same colour and brightness, showing that their change in appearance is simply due to the misty atmosphere intervening between them and the observer. We can imitate the light from the sun, after its passage through various thicknesses of atmosphere, in a very perfect manner in the lecture-room, using the electric light as a source. A condensing lens is put in front of the lamp, and in front of that a circular aperture in a plate. Beyond that again is a lens which throws an enlarged image of the aperture on the screen, which we may call our mock sun. If we place a trough of glass, in which is a dilute solution of hyposulphite of soda, carefully filtered from motes as far as possible, in front of the aperture, we have an image of the aperture unaffected by the insertion of the solution. The white disc on the screen will, as we have said before, be a close approximation to sunlight on a May-day about noon, when the sky is clear. By dropping into the trough a little dilute hydrochloric acid, a change will be found to come over the light of the mock sun; a pale yellow colour will spread over its surface, and this will give way to an orange tint, and at the same time its brightness will diminish. Gradually the orange will give place to red, the luminosity will be very small, being of the same hue as that seen in the sun when viewed through a London fog. Finally the last trace of red will so mingle with the scattered white light that the image will disappear, and then the experiment is over.
If we track the cause of this change of colour in our artificial sun, we shall find that it is due to minute particles of sulphur separating out from the solution of hyposulphite, and the longer the time that elapses the more turbid the dilute solution will become. This experiment exemplifies the action of small particles on light. Examining the trough it will be found that whilst the light which passes through the solution principally loses blue rays, the light which is scattered from the sides is almost cerulean in blue, and can well be compared with the light from the sky. We can analyze the transmitted light very readily by focusing the beam from the positive pole of the electric light on to the slit of our colour apparatus, and placing the lens L₆ (Fig. 6) in position to form the large spectrum on the screen. We can also show the colour of the light which goes to form the spectrum, by sending the patch of light reflected from the first surface of the first prism just above it. We thus have the spectrum and the light forming the spectrum to compare with one another. Using this apparatus and inserting the trough of dilute hyposulphite in the beam, the spectrum is of the character usually seen with the electric light; but on dropping the dilute hydrochloric acid into the solution the same hues fall on the slit of the spectroscope which fell upon the screen to form the mock sun, and the spectrum is seen to change as the light changes from white to yellow, and from yellow to red. First the violet will disappear, the blue and the green being dimmed, the former most however; then the blue will vanish to the eye, the green becoming still less luminous, and the yellow also fading; the green and yellow will successively disappear, leaving finally on the screen a red band alone, which will be a near match to the colour of the unanalyzed light, as may be seen by comparing it with the adjacent patch formed from the reflected beam.
We have here a proof that the succession of phenomena is caused by a scattering of the shorter wave-lengths of light, and that the shorter the waves are the more they are scattered. It has been found theoretically by Lord Rayleigh that the scattering takes place in inverse proportion to the fourth power of the wave-length; thus, if two wave-lengths, which may be waves in the green and violet, are in the proportion of three to four, the former will be scattered as 1/3⁴ to 1/4⁴, or as 256 to 81, which is approximately as three to one. Consequently if the green in passing through a certain thickness of a turbid medium loses one-half the violet in passing through the same thickness will lose five-sixths of its luminosity. The inverse fourth powers of the following wave-lengths, which are within the limits of the whole visible spectrum, are shown below.
Supposing λ7000 by the scattering of small particles loses one-tenth of its luminosity, then λ6000 would have ·454 of its original brightness; λ5000, ·234; and λ4000, ·095; that is, whilst λ7000 would lose one-tenth only of its luminosity, λ4000 in the violet would retain not quite one-hundredth of its brightness.
During the years 1885, 1886, and 1887, the writer measured the luminosity of the solar spectrum at different times of the year, and at different hours of the day (see Phil. Trans. 1887: "Transmission of Sunlight through the Earth's Atmosphere"), and from the results he found that the smallest coefficient of scattering for one atmosphere at sea-level for each wave-length was ·0013, when λ⁻⁴ was for convenience sake multiplied by 10¹⁷ (thus λ6000⁻⁴ on this scale was 77·2), and that the mean was ·0017.
The following table shows the loss of light for the rays denoted by the principal lines given at page 26, using this last coefficient for different air thicknesses. This is equivalent to giving the intensity of the rays of sunlight when the sun is at different altitudes.
The sun traverses the following thicknesses of atmosphere when it is at the angles shown above the horizon.
Fig. 10. – Absorption of Rays by the Atmosphere.
It traverses thirty-two atmospheres when it is very nearly setting. Bougier and Forbes have calculated that the extreme thickness of the atmosphere, traversed by its light when the sun is on the horizon, is approximately 35½ atmospheres. The absorption shown by 32 atmospheres will therefore be very close to that which would be observed at sunset on an ordinary day, and it will be seen that practically all rays have been scattered from the light, except the red, and a little bit of the orange.
As to the luminosity of the sun at these different altitudes, we can easily find it by reducing the luminosity curve of the sun at some known altitude by the factors in the table just given, for as many wave-lengths as we please, and thus construct another curve. The area of the figure thus obtained would be a measure of the total luminosity on the same scale as the area of the luminosity curve from which it was derived.
The following are the approximate luminosities of the sun when the light shines
It will thus be seen that the sun is 420 times less bright just at sunset than it is if it were to shine directly overhead, and about 350 times brighter than it is for a winter sun in a cloudless and mistless sky at twelve o'clock, for the altitude of the sun in our latitude is about 30° at that time, and corresponds with a thickness of two atmospheres, through which the sun has to shine. We all know that to look at the sun at any time near noon in a cloudless sky dazzles the eyes, but that near sunset it may be looked at with impunity. The reduction in luminosity explains this fact.
The distribution of the scattering particles in the atmosphere is very far from regular. As we ascend, the particles get more sparse, as is shown by the less scattering that takes place of the blue rays compared with the red. Thus at an altitude of some 8000 feet the mean coefficient of scattering is about ·0003, instead of ·0017, which it is at sea-level. It must be recollected that there is only about three-fourths of the air above us at 8000 feet, and it is less dense. There will therefore be a diminution of particles not only because there is less air, but because the air itself is less capable of keeping them in suspension. Up to 3000 or 4000 feet there is no very great marked difference in the scattering of light, as observations carried on during five years have shown; but above that the scattering rapidly diminishes, and at 20,000 feet it must be very small indeed, if the diminution increases as rapidly as has been found it does at the altitude of 8000 feet.
We must repeat once more that the blue of the sky is principally if not entirely due to the presence of these particles, the rays scattered by them, which are principally the blue rays, being reflected back from them, giving the sensation of blue which we know as sky-blue. The greater the number of these fine particles that are encountered by sunlight, the greater the scattering will be, and the bluer the sky. It is more than probable that the blue sky of Italy, so proverbial for being beautiful, is due to this cause, since from its geographical position the small particles of water must be very abundant there.
Carrying this argument further, we should expect that as we mount higher the blue would become more fully mixed with the darkness of space, and this Alpine travellers will tell you is the case. At heights of 12,000 feet or more, on a clear day, the sky seems almost black, and it is no uncommon thing to see this admirably rendered in photographs of Alpine scenery when taken at a height. Many of the late Mr. Donkin's photographs show this in great perfection, as also Signor Sella's.
Before quitting this subject we may call attention not only to the colour of the sun itself at sunset, but also to the colouring of the sky which accompanies the sun as it sinks. This colouring is often different to the colour that the sun itself assumes; but we can easily show that the effects so wonderfully beautiful are entirely dependent on this scattering of light by these small intervening particles in the air. We often see a ruddy sun, and perhaps nearly in the zenith, or even further away from the sun, clouds of a beautiful crimson hue, lying on a sky which appears almost pea-green, whilst nearer to the sun the sky is a brilliant orange, which artists imitate with cadmium yellow. Let us fix our attention first on the crimson cloud. The clouds of which the colouring is so gorgeous are often not 1000 feet above us, and were we to be at that altitude we should see the sun not quite so ruddy as we see it from the earth, and the cloud would consequently be illuminated by the sun with a more orange tint; but the light reflected from the cloud to our eyes has to pass through, say 1000 feet of dense atmosphere, and thus the total atmosphere that the light traverses in the latter case is always greater than the air thickness through which the direct light from the sun has to pass; hence more orange is cut off, and the light reflected from the cloud is redder. This red, however, will not account for the brilliant crimson and purples which we so often see. It has to be remembered that not sunlight alone illumines the cloud, but also the blue light of the sky. The feebler the intensity of the red, the more will the blue of the sky be felt in the mixture of light which reaches our eyes, and consequently we may have any tint ranging from crimson to purple, since red and blue make these hues, according to the proportions in which they are mixed.
Now let us see how we get the brilliant orange of the sky itself. When the evening is perfectly clear and free from mist and cloud, the orange in the sky is very feeble, showing that the intensity depends upon their presence. Now a look at the table will show that the sun is very close to the horizon when it becomes ruddy under normal conditions; but that when the light traverses a thickness of eight atmospheres, the blue and violet, and most of the green, are absent, leaving a light of yellowish colour. To traverse eight atmospheres the light has only to come from a point some eight degrees above the horizon. When the sun is near the horizon, it sends its rays not only to us and over us, but in every direction; and an eye placed some few thousand feet above the earth would see the sun almost of its midday colour, for sunset colours of the gorgeous character that we see at sea-level are almost absent at high altitudes. If a cloud or mist were at such an altitude the sunlight would strike it, and whilst only a small portion would be selectively scattered, owing to the general grossness of the particles, the major part would be reflected back to our eyes, and come from an altitude of over eight to ten degrees, and would therefore, after traversing the intervening atmosphere, reach us as the orange-coloured light of which we have just spoken. The clouds which are orange when near the sun, are usually higher than those which are simultaneously red or purple. The pea-green colour of the sky is often due to contrast, for the contrast colour to red is green, and this would make the blue of the sky appear decidedly greener. Sometimes, however, it is due to an absolute mixture of the blue of the sky and the orange light which illuminates the same haze. In the high Alps it is no uncommon occurrence for the snow-clad mountains to be tipped with the same crimson we have described as colouring the clouds, and this is usually just after sunset, when the sun has sunk so low beneath the horizon that the light has to traverse a greater thickness of dense air, and consequently to pass through a larger number of small particles than it has when just above the horizon. In this case the red of the sunlight mixes with blue light of the sky, and gives us the crimson tints. The deeper and richer tints of the clouds just after sunset are also due to the same cause, the thickness of air traversed being greater.
It is worth while to pause a moment and think what extraordinary sensual pleasure the presence of the small scattering particles floating in the air causes us; that without them the colouring which impresses itself upon us so strongly would have been a blank, and that artists would have to rely upon form principally to convey their feelings of art. Indeed without these particles there would probably be no sky, and objects would appear of the same hard definition as do the mountains in the atmosphereless moon. They would be only directly illuminated by sunlight, and their shadows by the light reflected from the surrounding bright surfaces.
