Colour Measurement and Mixture Part 3

+-------------+---------------+ | Colours | Observed | | Measured. | Luminosity. | +-------------+---------------+ | R | 2030 | | G | 385 | | V | 85 | | (R + G) | 242 | | (G + V) | 45 | | (R + V) | 214 | | (R + G + V) | 250 | +-------------+---------------+

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.

R + G + V = 2500 (R + G) + V = 2505 (R + V) + G = 2525 (G + V) + R = 2480 (R + G + V) = 2500

The mean of the first four is 25025, 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 445 and 3 respectively. This should give the green as having a luminosity of 525. The green was measured and found to be 53, whilst a measurement of the red and green together gave a luminosity of 965 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, subst.i.tuting 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=9625, D=89, E=799, F=715, G=535.

VERMILION.

+-----------------------------------------------+ | White Sectors. | | +-----------------------------------|Reading of | | Original |White Cor-|Corrected| Spectrum | | Setting. |rected For| White | Scale. | |--------------+ Black. | 100. | | | White.|Black.| | | | +-------+------+----------+---------+-----------+ | 10 | 350 | 275 | 765 | 71-1/2 | | 20 | 340 | 370 | 1015 | 84 | | 30 | 330 | 465 | 1295 | 862 | | 50 | 310 | 655 | 1810 | 880 | | 70 | 290 | 845 | 2350 | 887 | | 90 | 270 | 1035 | 297 | 895 | | 120 | 240 | 1320 | 372 | 903 | | 150 | 210 | 1605 | 450 | 91 | | 180 | 180 | 1890 | 525 | 916 | | 210 | 150 | 2175 | 602 | 925 | | 220 | 140 | 2270 | 632 | 935 | | 230 | 130 | 2365 | 662 | 945 | | 240 | 120 | 2460 | 685 | 96 | | 230 | 130 | 2365 | 662 | 977 | | 210 | 150 | 2175 | 602 |1000 | +-------+------+----------+---------+-----------+

EMERALD GREEN.

+---------------------------------------+------------+ | White Sectors | | +------------------+--------------------+ Reading of | | Original Setting.|White Cor-|Corrected| Spectrum | +--------+---------|rected For| White | Scale. | | White. | Black. | Black. | 100. | | +--------+---------+----------+---------+------------+ | 10 | 350 | 275 | 765 | 50 | | 20 | 340 | 370 | 1015 | 54 | | 30 | 330 | 465 | 1295 | 55 | | 50 | 310 | 655 | 1810 | 575 | | 70 | 290 | 845 | 235 | 600 | | 90 | 270 | 1035 | 297 | 635 | | 110 | 250 | 1225 | 347 | 655 | | 130 | 230 | 1415 | 395 | 675 | | 150 | 210 | 1605 | 450 | 685 | | 170 | 190 | 1795 | 500 | 71 | | 190 | 170 | 1955 | 547 | 735 | | 210 | 150 | 2175 | 602 | 750 | | 220 | 140 | 227 | 632 | 76 | | 220 | 140 | 227 | 632 | 78 | | 210 | 150 | 2175 | 602 | 80 | | 190 | 170 | 1985 | 547 | 82 | | 170 | 190 | 1795 | 500 | 83 | | 150 | 210 | 1605 | 450 | 84 | | 130 | 230 | 1415 | 395 | 85 | | 110 | 250 | 1225 | 347 | 865 | | 90 | 270 | 1035 | 297 | 875 | | 70 | 290 | 845 | 235 | 885 | | 50 | 310 | 655 | 1810 | 900 | | 30 | 330 | 465 | 1295 | 92 | | 20 | 340 | 370 | 1015 | 94 | | 10 | 350 | 275 | 765 | 98 | +--------+---------+----------+---------+------------+

FRENCH ULTRAMARINE BLUE.

+-----------------------------------------+------------+ | White Sectors. | | +-----------------+-----------+-----------+ Reading of | |Original Setting.| White | Corrected | Spectrum | +--------+--------+ corrected | White | Scale. | | White. | Black. | for black.| 100. | | +--------+--------+-----------+-----------+------------+ | 0 | 360 | 180 | 50 | 84 | | 10 | 350 | 275 | 765 | 80 | | 20 | 340 | 370 | 1015 | 77 | | 30 | 330 | 465 | 1295 | 75 | | 40 | 320 | 560 | 156 | 74 | | 60 | 300 | 750 | 207 | 725 | | 80 | 280 | 940 | 255 | 705 | | 100 | 260 | 1130 | 325 | 68 | | 120 | 240 | 1320 | 372 | 665 | | 140 | 220 | 1510 | 423 | 625 | | 160 | 200 | 1700 | 474 | 595 | | 170 | 190 | 1795 | 500 | 55 | | 160 | 200 | 1700 | 474 | 51 | | 140 | 220 | 1510 | 423 | 46 | | 0 | 360 | 180 | 50 | 95 | | 10 | 350 | 275 | 765 | 98 | | 20 | 340 | 370 | 1015 | 99 | | 30 | 330 | 465 | 1295 | 110 | +--------+--------+-----------+-----------+------------+

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 pa.s.ses 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 pa.s.ses. 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 pa.s.ses 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 s.p.a.ce, 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 pa.s.ses through the same slit, is decomposed by the same prisms, and as the beams diverge in a plane pa.s.sing 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 pa.s.s 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 225 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 gla.s.ses, 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 gla.s.s only allowed 4/100 or 1/25 of the ray to pa.s.s, whilst the green gla.s.s allowed 10/100 or 1/10 to pa.s.s. So at scale No. 4 in the orange, through the blue only 2% was transmitted, through the green gla.s.s 4%, and through the red 20%.

Fig. 17.--Absorption by Red, Blue, and Green Gla.s.ses.

Fig. 18.--Light reflected from Metallic Surfaces.

Fig. 19.--1. Vermilion 2. Carmine. 3. Mercuric Iodide. 4. Indian Red.

From such curves as these we can readily derive the luminosity curves of the spectrum, after the white light has pa.s.sed 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 pa.s.sing through the object. It will be seen that when the luminosity curve of the spectrum of _any_ source is known, this method holds good.

Fig. 20.--1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow. 4. Yellow Ochre.

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 subst.i.tuted, 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 bra.s.s reflects 77% of the light, and the luminosity of the white is 80.

The luminosity of the light from the bra.s.s is therefore 77/100 of 80, or 61. This shows the method which is adopted, of deducing luminosities from intensities.

Fig. 21.--1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte.

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.

Fig. 22.--1. Indigo. 2. Antwerp Blue. 3. Cobalt. 4. French Ultramarine.

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 ident.i.ty 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 s.p.a.ce 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 pa.s.ses through the pigment. The above figure (Fig. 26) shows the truth of this a.s.sertion. 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.