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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.
Fig. 11. – Luminosity Curve of the Spectrum of the Positive Pole of the Electric Light.
The observer in this case was colour-blind to the red, that is, he had no perception of red objects as red, but only distinguished them by the other colours which were mixed with the red. This being premised, we should naturally expect that his perception of the spectrum would be shortened, and this the observations fully prove. If it happened that his perceptions of all other colours were equally acute with a normal-eyed person, then his illumination value of the part of the spectrum occupied by the violet and green ought to be the same as that of the latter. The diagram shows that it is so, and the amount of red present in each colour to the normal-eyed observer is shown by the deficiency curve, which was obtained by subtracting the ordinates of colour-blind curve from those of the normal curve. There are other persons who are defective in the perception of green, and they again give a different luminosity curve for the spectrum. These variations in the perception of the luminosity of the different colours are very interesting from a physiological point of view, and this mode of measuring is a very good test as to defective colour vision. We shall allude to the subject of colour-blindness in a subsequent chapter.
The following are the luminosities for the colours fixed by the principal lines of the solar spectrum, and for the red and blue lines of lithium, to which reference has already been made.
The failure of the red colour-blind person to perceive red is very well shown from this table. It will for instance be noticed that he perceives about one-tenth of the light at C which the normal-eyed person perceives.
A modification of this plan can be employed for measuring the luminosity of the spectrum, and it is excessively useful, because we can adapt it to the measurement of colours other than these simple ones. In the plan already explained it was the colour in the patch that was altered, to get an equal luminosity with a certain luminosity of white light. In the modified plan the luminosity of the white light is altered, for the luminosity of the shadow illuminated by the reflected beam can be altered rapidly at will by opening or closing the apertures of the sectors whilst it is rotating. The slit in the slide is placed in the spectrum at any desired point, and the aperture of the sectors altered till equal luminosities are secured. The readings by this plan are very accurate, and give the same results as obtained by the previous method employed.
It must be remembered that we have so far dealt with colours which are spectrum colours, and which are intense because they are colours produced by the spectrum of an intensely bright source of light. By an artifice we can deduce from this curve the luminosity curve of the spectrum of any other source of light. If by any means we can compare, inter se, the intensity of the same rays in two different sources of light, one being the electric light, we can evidently from the above figure deduce the luminosity curve of the spectrum of the other source of light (see p. 109).
We can now show how we can adapt the last method to the measurement of the luminosity of the light reflected from pigments.
Fig. 12. – Rectangles of White and Vermilion.
Fig. 13. – Arrangement for measuring the Luminosities of Pigments.
Suppose the luminosity of a vermilion-coloured surface had to be compared with a white surface when both were illuminated, say by gaslight, the following procedure is adopted. A rectangular space is cut out of black paper (Fig. 12) of a size such that its side is rather less than twice the breadth of the rod used to cast a shadow: a convenient size is about one inch broad by three-quarters of an inch in height. One-half of the aperture is filled with a white surface, and the other half with the vermilion-coloured surface. The light L (Fig. 13) illuminates the whole, and the rod R, a little over half an inch in breadth, is placed in such a position that it casts a shadow on the white surface, the edge of the shadow being placed accurately at the junction of the vermilion and white surface. A flat silvered mirror M is placed at such a distance and at such an angle that the light it reflects casts a second shadow on the vermilion surface. Between R and L are placed the rotating sectors A. The white strip is caused to be evidently too dark and then too light by altering the aperture of the sectors, and an oscillation of diminishing extent is rapidly made till the two shadows appear equally luminous. A white screen is next substituted for the vermilion and again a comparison made. The mean of the two sets of readings of angular apertures gives the relative value of the two luminosities. It must be stated, however, that any diffused light which might be in the room would relatively illuminate the white surface more than the coloured one. To obviate this the receiving screen is placed in a box, in the front of which a narrow aperture is cut just wide enough to allow the two beams to reach the screen. An aperture is also cut at the front angle of the box, through which the observer can see the screen. When this apparatus is adopted, its efficiency is seen from the fact that when the apertures of the rotating sectors are closed the shadow on the white surface appears quite black, which it would not have done had there been diffused light in any measurable quantity present within the box. The box, it may be stated, is blackened inside, and is used in a darkened room. The mirror arrangement is useful, as any variation in the direct light also shows itself in the reflected light. Instead of gaslight, reflected skylight or sunlight can be employed by very obvious artifices, in some cases a gaslight taking the place of the reflected beam. When we wish to measure luminosities in our standard light, viz. the light emitted from the crater of the positive pole of the arc-light, all we have to do is to place the pigment in the white patch of the recombined spectrum, and illuminate the white surface by the reflected beam, using of course the rod to cast shadows, as just described. The rotating sectors must be placed in either one beam or the other, according to the luminosity of the pigment.
The luminosities of the following colours were taken by the above method, and subsequently we shall have to use their values.
Suppose we have two or more colours of the spectrum whose luminosities have been found, the question immediately arises, as to whether, when these two colours are combined, the luminosity of the compound colour is the sum of the luminosities of each separately. Thus suppose we have a slide with two slits placed in the spectrum, and form a colour patch of the mixture of the two colours and measure its luminosity, and then measure the luminosity of the patch first when one slit is covered up, and then the other. Will the sum of the two latter luminosities be equal to the measure of the luminosity of the compounded colour patch? One would naturally assume that it would, but the physicist is bound not to make any assumptions which are not capable of proof; and the truth or otherwise is perfectly easy to ascertain, by employing the method of measurement last indicated. Let us get our answer from such an experiment.
Three apertures were employed, one in the red, another in the green, and the third in the violet, and the luminosity was taken of each separately, next two together, and then all three combined, with the results given above.
The accuracy of the measurements will perhaps be best shown by adding the single colours together, the pairs and the single colours, and comparing these values with that obtained when the three colours were combined. When the pairs are shown they will be placed in brackets; thus (R + G) means that the luminosity of the compound colour made by red and green are being considered.
The mean of the first four is 250·25, which is only 1/10 % different from the value of 250 obtained from the measurement of (R + G + V) combined. Other measures fully bore out the fact that the luminosity of the mixed light is equal to the sum of the luminosities of its components. It is true that we have here only been dealing with spectrum colours, but we shall see when we come to deal with the mixture of colours reflected from pigments that the same law is universally true.
It will be proved by and by that a mixture of three colours, and sometimes of only two colours, be they of the spectrum or of pigments, can produce the impression of white light. If then we measure all the components but one, and also the white light produced by all, then the luminosity of the remaining component can be obtained by deducting the first measures from the last. For instance, red, green and violet were mixed to form white light. The luminosity of the white being taken as 100, the red and violet were measured and found to have a luminosity of 44·5 and 3 respectively. This should give the green as having a luminosity of 52·5. The green was measured and found to be 53, whilst a measurement of the red and green together gave a luminosity of 96·5 instead of 97.
CHAPTER VIII
Methods of Measuring the Intensity of the Different Colours of the Spectrum, reflected from Pigmented Surfaces – Templates for the Spectrum.
Fig. 14. – Measurement of the Intensity of Rays reflected from white and coloured surfaces.
We will now proceed to demonstrate how we can measure the amount of spectral light reflected by different pigments. Let us take a strip of card painted with a paste of vermilion, leaving half the breadth white; and similarly one with emerald green. If we place the first in the spectrum so that half its breadth falls on the red, and the other half on the white card, we shall see that apparently the red and orange rays are undiminished in intensity by reflection from the vermilion, but that in the green and beyond but very little of the spectrum is reflected. With the emerald green placed similarly in the spectrum, the red rays will be found to be absorbed, but in the green rays the full intensity of colour is found, fading off in the blue. What we now have to do is to find a method of comparing the intensities of the different rays reflected from the pigments, with those from the white surface. We will commence with the second of the two methods which the writer devised with this object, and then describe the first, which is more complex. Suppose we have, say a card disc three inches in diameter, painted with the pigment whose reflective power has to be measured, and place it on a rotating apparatus with black and white sectors of say five inches diameter, and capable of overlapping so as to show different proportions of black to white (see Fig. 42). If we throw a colour patch (shown in Fig. 14 as the area inside the dotted square) on the combination of black and white, and at the same time on the pigmented disc, it is probable that either one or other will be the brighter. By moving the slit along the spectrum it is evident, however, that a colour can be found which is equally reflected from them both whilst rotating. Take as an example the sectors as set at two parts white, to one part black, the centre disc being vermilion, the slit is moved along the spectrum until such a point is reached that the colour reflected from the ring and the disc appears of the same brightness, for it must be recollected that they cannot differ in hue, as the light is monochromatic. It will be found that the place where they match in brightness is in the red, the exact position being fixed by the scale at the back of the slide. Taking the proportion of black to white as three to one, the match will be found to take place in the orange. Increasing the proportion of black more and more, a point will be reached where the reflection takes place uniformly along the blue end of the spectrum, this will be from the green to the end of the violet. By sufficiently increasing the number of matches made, a curve of reflection can be made showing the exact proportion of each ray of the spectrum that is reflected. The uniform reflection along the blue end of the spectrum shows that a certain amount of white light is reflected from the pigment.
Next taking the emerald green disc, if we adopt the same procedure it will be found that for some shades of the ring there are two places in the spectrum from which the colours reflected give the same brightness. By plotting curves in exactly the same way as that shown for the curve of luminosity at page 78, substituting for the open aperture of the sector the angular value of the white used, we can show graphically the correct reflection for each part of the spectrum. Sometimes three places in the spectrum will be read, as giving equal reflections from the coloured disc and the grey ring.
The accompanying figures show the results obtained for reflection from vermilion, emerald green, and French blue, after having made a correction for the white by adding the amount which the black reflects.
The scale is that of the prismatic spectrum employed. On page 46 we stated that a white surface could be made to appear darker than a black surface, by illuminating the latter and cutting off the light from the former. By placing the black surface in place of one of the coloured ones, as shown in page 82, the luminosity of the black surface can be ascertained. In this case it was found that almost exactly 5 % of the white light from the crater of the positive pole was reflected.In the table the original measures are shown, and also the corrected measures, and for convenience sake the intensity of every ray throughout the length of the spectrum reflected from white, has been taken as 100. The position of the reference lines on the scale (Fig. 15) are as follows —
Fig. 15. – Intensity of Rays reflected from Vermilion, Emerald Green, and French Ultramarine.
B=101, C=96·25, D=89, E=79·9, F=71·5, G=53·5.
VERMILION.
EMERALD GREEN.
FRENCH ULTRAMARINE BLUE.
These three measurements have been given in full, since they will be useful for reference when other experiments are described.
Fig. 16. – Method of obtaining two Patches of identical Colour.
When we have to measure the colour transmitted through coloured bodies, we have to adopt a slightly different plan, which is extremely accurate. The first thing necessary is to make some arrangement whereby two beams of identical colour – that is, of the same wave-length – reach the screen, one of which passes through the transparent body to be measured, and the other unabsorbed. If we in addition have some means of equalizing the intensity of the two beams, we can then tell the amount cut off by the body through which one beam passes. The method that would be first thought of would be to use two spectra, from two sources of light; but should we adopt that plan there would be no guarantee that the spectra would not vary in intensity from time to time. The point then that had to be aimed at was to form two spectra from the same source of light, and with the same beam that passes through the slit of the collimator. Here we are helped by the property of Iceland spar, which is able to split up a ray into two divergent rays. By placing what is called a double-image prism of Iceland spar at the end of the collimator, we get two divergent beams of light falling on the prisms, and by turning the double-image prism we are able to obtain two spectra on the screen of the camera one above the other, and if the slit of the slide be sufficiently long two beams would issue through it of identical colour, and separated from one another by a dark space, the breadth of which depends on the length of the slit of the collimator. It is to be observed that by this arrangement we have exactly what we require: a light from one source passes through the same slit, is decomposed by the same prisms, and as the beams diverge in a plane passing through the slit of the collimator, the length of spectrum is the same. The problem to solve is how to utilize these two spectra now we have got them. We can make the light from the top spectrum pass through the coloured body by the following artifice. Let us place a right-angled prism in front of the top slit, reflecting say the beam to the right, and after it has travelled a certain distance, catch it by another right-angled prism, and thus reflect it on to the screen. Already in the path of the ray, issuing through the slit from the bottom spectrum, the lens L₄ is placed, forming a square patch on the screen. By placing a similar lens in the path of the other ray after reflection from the second right-angled prism, we can superpose a second patch of the same colour over the first patch, and by putting a rod in the path of the two beams we can have as before two shadows side by side, but this time each illuminated by the same colour. One shadow will be more strongly illuminated than the other, owing to the different intensities of beams into which the double-image prism splits up the primary ray. The two, however, can be equalized by placing a rotating apparatus in the path of one of the beams. When equalized the sector is read off, and tells us how much brighter one spectrum is than the other. Thus suppose in the direct beam the sectors had to be closed to an angle of 80°, to effect this, the bottom spectrum would be 180/80, or 2·25 times brighter than the bottom spectrum. It should be noted that as the two spectra are formed by the identical quality of light, this same ratio will hold good throughout their length. If it does not, it shows that the double-image prism is not in adjustment, and that the same rays are not coming through the slit in the slide, and it must be rotated till the readings throughout are the same. One of the most sensitive tests for adjustment is to form a patch with orange light, when the slightest deviation from adjustment will be seen by the two patches differing in hue.
We can now place the coloured transparent object in the path of the beam which is most convenient, and by again equalizing the shadows, measure the amount it cuts off; this we can do for any ray we choose. As both right-angled prisms can be attached to the card or slide which moves across the spectrum, nothing besides the card need be moved. In the following diagram we have the proportion of rays transmitted by the three different glasses, red, green, and blue, in terms of the unabsorbed spectrum. Take for instance on the scale of the spectrum the number 11. The curve shows that at that particular part of the spectrum which lies in the blue, the blue glass only allowed 4/100 or 1/25 of the ray to pass, whilst the green glass allowed 10/100 or 1/10 to pass. So at scale No. 4 in the orange, through the blue only 2 % was transmitted, through the green glass 4 %, and through the red 20 %.
Fig. 17. – Absorption by Red, Blue, and Green Glasses.
Fig. 18. – Light reflected from Metallic Surfaces.
1. Vermilion 2. Carmine. 3. Mercuric Iodide. 4. Indian Red.
Fig. 19.
From such curves as these we can readily derive the luminosity curves of the spectrum, after the white light has passed through the coloured object. All we have to do is to alter the ordinates of the luminosity curve of white light in the proportion to the intensities of the rays before and after passing through the object. It will be seen that when the luminosity curve of the spectrum of any source is known, this method holds good.
1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow. 4. Yellow Ochre.
Fig. 20.
The intensity of the different rays of the spectrum reflected from metallic surfaces can also be measured, if for the first or second right-angled prism a small piece of the metal is substituted, using it as a reflecting surface, as can also the rays reflected from any surface which is bright and polished. In Fig. 18 the dotted curves show the luminosity of the spectrum reflected from the different metals, curve V being that of white light. These curves are derived by reducing the ordinates of curve V proportionately to the intensity curves. Thus at 49 brass reflects 77 % of the light, and the luminosity of the white is 80. The luminosity of the light from the brass is therefore 77/100 of 80, or 61. This shows the method which is adopted, of deducing luminosities from intensities.
1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte. Fig. 21.
The light reflected from pigments can also be measured by the same plan. The procedure adopted is that carried out when measuring their luminosities, viz. to cause the ray from one spectrum to fall on a strip of a white surface, and that from the other on a strip of the coloured surface (see page 82). This is a more convenient method than that just described, when the coloured surface is small. The annexed figures (Figs. 19, 20, 21, 22) show the results obtained from various pigments.
1. Indigo. 2. Antwerp Blue. 3. Cobalt. 4. French Ultramarine. Fig. 22.
Fig. 23. – Method of obtaining a Colour Template.
From curves such as these we are able to produce the colour of the pigment on the screen from the spectrum itself. This is a useful proof of the truth of the measurements made. To do this we must mark off on a card (Fig. 23) the absolute scale of the spectrum along the radius of a circle, and draw circles at the various points of the scale from its centre. From the same centre we must draw lines at angles to the fixed radius corresponding to the various apertures of the sectors required at the various points of the scale to measure the light reflected from a pigment. Where each radial line cuts the circle drawn through the particular point of the scale to which its angle has reference, gives us points which joined give a curved figure. Such a figure, when cut out and rotated in front of the spectrum in the proper position (as for instance by making the D sodium line correspond with that on the scale), will cut off exactly the same proportion of each colour that the pigment absorbs. The spectrum, when recombined, should give a patch of the exact colour of that measured. The spectrum must be made narrow, as the template is only theoretically correct for a spectrum of the width of a line, as can be readily seen.
Templates like these will always enable any colour to be reproduced on the screen, and if the light be used for the spectrum in which the colour has to be viewed, be it sunlight, gaslight, starlight – whatever light it is – the colour obtained will be that which the pigment would reflect if it were viewed in that light.
The identity of the colour produced on the screen by this plan with that measured, can be readily seen by placing the latter in the reflected beam of white light alongside the coloured patch formed on the white surface.
Fig. 24. – Template of Carmine.
In Fig. 24 we have a mask or template of carmine, which was used for determining if the measurements were right. The black fingerlike-looking space on the right was the amount of red reflected light, and the other that of the blue and violet; scarcely any light at all was reflected from the green part of the spectrum.
Fig. 26. – Absorption of transmitted and reflected Light by Prussian Blue and Carmine.
On page 108 we have given the diagram of the luminosity of the spectrum in reference to a standard white light. It will bring this luminosity more home if, in a similar manner to that described above, we make a template of this curve (Fig. 25). We can place a narrow slit horizontally in front of the condensing lens of the optical lantern, and throw an image of it on to the screen. If in close contact with this slit we rotate the template, we shall have on the screen a graduated strip of white light, giving in black and white the apparent luminosity of the spectrum as seen by the eye.
Fig. 25. – Template of Luminosity of White Light.
It has been stated in chapter V., that it is generally immaterial whether a pigment is in contact with the paper or away from it, so long as the light passes through the pigment. The above figure (Fig. 26) shows the truth of this assertion. I. and II. are the curves taken of the light transmitted by Prussian blue and carmine respectively, and III. and IV., from the light reflected from these colours on paper.
Fig. 27. – Collimator for comparing the intensity of two sources of Light.
To measure the difference in the intensities of the rays of different sources of light we can use a spectroscopic arrangement with two slits (S) (Fig. 27) placed in a line at right angles to the axis of the collimator. One slit is a little below the other, the rays being reflected to the collimating lens L, by means of two right-angled prisms P, and two spectra are formed, one above the other. By placing the rotating sectors in front of one of the sources, the intensities of the different parts of the spectrum can be equalized and measured.
Fig. 28. – Spectrum Intensities of Sunlight, Gaslight, and Blue Sky.
The curves for the annexed figure (Fig. 28) were derived from measures taken in this manner. If the rays of a May-day sun are taken at 100, it will be seen what a rapid diminution there is in the green and the blue rays in gaslight. Gaslight only possesses about 20 % of the green rays, whilst of the violet hardly 5 %. On the other hand the light which comes to us from the sky shows a very marked falling off in the yellow and red rays. A very easy experiment will convince us of the difference in colour between skylight and gaslight. If we let a beam of daylight fall on a sheet of paper at the end of a blackened box, and cast a shadow with a rod by such a beam, and then bring a lighted candle or gas-flame so that it casts another shadow of the rod alongside, one shadow will be illuminated by the artificial light, and the other by the daylight. The difference in colour will be most marked: the blue of the latter light and the yellow of the former being intensified by the contrast (see page 198).
Fig. 29. – Comparison of Sun and Sky Lights.
By a little trouble the blue light from the sky may be compared with sunlight. A beam of light B (Fig. 29) is reflected by a silvered glass mirror from the blue sky into the box HH, at the end of which is a screen E. Another mirror A, which is preferably of plain glass, reflects light from the sun on to a second unsilvered mirror G (shown in the figure as a prism), which again reflects it on to the screen, and each of these lights casts a shadow from the rod D; K are rotating sectors to diminish the sunlight, and we can make two equally bright shadows alongside one another. The bluer colour of the sky will be very evident.
