Colour Measurement and Mixture

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.

CHAPTER VII

Luminosity of the Spectrum to Normal-eyed and Colour-blind Persons – Method of determining the Luminosity of Pigments – Addition of one Luminosity to another.

The determination of the luminosity of a coloured object, as compared with a colourless surface illuminated by the same light, is the determination of the second colour constant. We will first take the pure spectrum colours, and show how their luminosity or relative brightness can be determined. Viewing a spectrum on the screen, there is not much doubt that in the yellow there is the greatest brightness, and that the brightness diminishes both towards the violet and red. Towards the latter the luminosity gradient is evidently more rapid than towards the former. This being the case, it is evident that, except at the brightest part there are always two rays, one on each side of the yellow, which must be equally luminous. If the spectrum be recombined to form a white patch upon the screen, and the slide with the slit be passed through it, patches of equal area of the different colours will successively appear; but the yellow patch will be the brightest patch. If the patch formed by the reflected beam be superposed over the colour patch, and the rod be interposed, we get a coloured stripe alongside a white stripe, and by placing our rotating sectors in the path of the reflected beam, the brightness of the latter can be diminished at pleasure. Suppose the sectors be set at 45°, which will diminish the reflected beam to one-quarter of its normal intensity, we shall find some place in the spectrum, between the yellow and the red, where the white stripe is evidently less bright than the coloured stripe, and by a slight shift towards the yellow, another place will be found where it is more bright. Between these two points there must be some place where the brightness to the eye is the same. This can be very readily found by moving the slit rapidly backwards and forwards between these two places of "too dark" and "too light," and by making the path the slit has to travel less and less, a spot is finally arrived at which gives equal luminosities. The position that the slit occupies is noted on the scale behind the slide, as is also the opening of the sectors, in this case 45°. As there is another position in the spectrum between the yellow and the violet, which is of the same intensity, this must be found in the same manner, and be similarly noted. In the same way the luminosities of colours in the spectrum, equivalent to the white light passing through other apertures of sectors, can be found, and the results may then be plotted in the form of a curve. This is done by making the scale of the spectrum the base of the curve, and setting up at each position the measure of the angular aperture of the sector which was used to give the equal luminosity or brightness to the white. By joining the ends of these ordinates by lines a curve is formed, which represents graphically the luminosity of the spectrum to the observer. In Fig. 11 the maximum luminosity was taken as 100, and the other ordinates reduced to that scale. The outside curve of the figure was plotted from observations made by the writer, who has colour vision which may be considered to be normal, as it coincides with observations made by the majority of persons. The inner curve requires a little explanation, though it will be better understood when the theory of colour vision has been touched upon.