We can go further than Newton, his followers, or Goethe (for that matter) and explain not only how Lucas came to observe the reversal of spectral colours in certain experiments, but also what colours appear, where, and (most importantly) why. In order to accomplish that feat we’ll start with a simpler example—one that is, in principle, identical to Lucas’ first experiment. This experiment, as I was saying earlier, is the subjective version of the basic (objective) prismatic experiment. A white circle (in effect, a beam of light coming from a circular aperture) is viewed through a prism (the eye of the observer being, thus, the screen). The experiment is depicted in the figure below.
If you look through a triangular prism (oriented with the vertex up, from a distance of about 0.5m) at the white circle you will see the following colours: violet, blue, and cyan will be arching the upper half of the circle; red and yellow, the bottom half. This is in violation of the colours observed in the objective experiment (if conducted with a prism in the same orientation), where the colours on the screen will be reversed: red at the top, violet at the bottom. In effect, when you look through a prism you will see an upside-down spectrum. Why? No one seems to know why and no one seems to care (unless they’re willing to go along, in silence, with Lucas’ ‘explanation’). I will show why later, but, for our purpose, at this point I’ll direct your attention to another important observation. If you rotate the prism (with the vertex pointing to your left, then down, then to your right) you will notice that the order of colours relative to the orientation of your prism will stay the same. In fact, the orientation of the spectral colours in all subjective experiments will be VBGYOR (violet, blue, green, yellow, orange, red) relative to your prism (from the vertex to base). (A note of attention: Green and orange are missing in the experiment above, but the principle is unaltered. I will show later why certain colours are absent in certain circumstances.) So, one thing to keep in mind when conducting a subjective experiment is the colour distribution VBGYOR, which will always be observed to occur on the plane of refraction from the vertex down. Just like in the photo below.
As for the colours one observes in any particular subjective experiment, it depends on the size of the source of light and the distance from which it is observed. If you look through a prism at the white circle in the figure below from a distance of 1m, say, you will see five colours (violet, blue, cyan, yellow, red). (A note of caution: Cyan is really part of the spectral blue, but since it overlaps with the white of the circle itself it appears as a ‘diluted’ blue. This is an issue of some importance, and I will talk about it later. In essence, however, cyan is really just blue.) If you look from a distance of about 3m, however, you will see the full spectrum.
Another situation where you will see only part of the spectrum is one that has remained a kind of unnecessary mystery for three centuries. To explain what I mean I will make use again of the earlier figure with a large white circle on a black background. To save you going back to it I’ll display it below.
Keeping in mind what we talked about thus far, look at the circle above through a prism oriented with the vertex up. The familiar spectrum (minus green and orange) will appear. Now lower your prism until you can see only the bottom half of the circle. The only colours you’ll see are red and yellow. Surprised? Of course not. Raise now your prism, until you’ll only have in sight the upper half of the circle, and observe the colours. At this stage you might rightfully wonder what reason could there be for this, rather pointless, exercise. Well, I can tell you that by not considering this pointless exercise all physicists, since Newton, have failed to put subjective prismatic experiments in their rightful place, and consequently failed to understand why the subjective versions of prismatic experiments display the colours they do. And I am not exaggerating one bit. In my next chapter, in which I’ll discuss Goethe and the opposition he encountered to his theory of colours, we’ll see how this innocuous observation will easily explain all subjective experiments, and how they should have been incorporated into Newton’s theory.
For now, what is important to remember is that in subjective experiments the spectrum generated by a source of light has the colour composition VBGYOR (instead of the ROYGBV seen in objective prismatic experiments), and that the spectrum’s colour composition is always concurrent with a prism from the vertex (refractive angle) to the base. Furthermore, regardless of how many colours will be produced by any source, the colours seen in any particular subjective experiment are integral part of the spectrum generated by the source. What does that mean? Suppose you look at a particularly complex figure and you see somewhere only a band of red and yellow. The first thing you should be absolutely certain of is that you are seeing only part of the spectrum generated by that particular source of light, and that the rest of the colours of that spectrum are either outside your field of vision (because the source is larger than your prism), or that the other colours are faint and not immediately obvious, or both. To explain this (very important) point I’ll make use of the simple figure below.
Now, if you look through a prism (vertex up) at the above figure from a distance of less than 0.5m you will only be able to see (at the same time) two sets of colours. One set will comprise of red and yellow, which will extend along the top edge of the figure; the other set will be formed by the violet-blue (and cyan) combination, which is running along the bottom edge side of the black rectangle. Let’s pay attention first to this violet-blue combination. According to what we’ve discussed earlier you can be absolutely sure that these colours are only part of the spectrum generated by the source of light in the figure—the white rectangle. Also, you can be just as certain that the rest of the spectrum will be somewhere below the violet-blue combination, due to the orientation of your prism. And, indeed, if you lower your prism you will see the rest of the spectrum, in the form of the red-yellow combination along the bottom side of the white rectangle. This red-yellow combination is not as conspicuous as the violet-blue one because of the relatively low contrast between the colour of the rectangle (white) and the colour of the page itself (light grey). Basically, the greater the contrast between the luminosity of the source and its surroundings is, the more vibrant are the spectral colours observed. This fact is evident in the case of the violet-blue combination, where the contrast between the white rectangle and the black one is the greatest possible. This fact can also be evidenced if you now take a book, a ruler, or use your palm, to slide it in front of your monitor (in such a manner as to form the base of the figure) while looking through your prism. Try it, and you’ll see what I mean.
Let’s pay attention now to another set of colours which can be seen in a prismatic observation of the figure above. When you look through a prism (with the same orientation as before) at the black rectangle, apart from the violet-blue combination you will also see a red-yellow combination running along the top side of the figure. If you have understood what we have discussed thus far you should be able to explain the provenience of those colours. However, even if you understood the principle of the colours seen in subjective experiments, you may still find it difficult—in this particular example—to locate the rest of the spectrum to which the red-yellow combination belongs. If that is the case look through the prism at the top rim of your monitor. See it? Or, remember that you can determine where the borders of the source of light (which, in this case, is the area of the page above the black rectangle) are by sliding a ruler (book, etc.) in front of your monitor, which will also show you the rest of the spectrum.
Subjective prismatic experiments where the spectral colours bordering black areas have been studied have proved to remain just as mysterious for Goethe and his followers as for Newton’s defenders. In the next chapter I will show a couple of contemporary examples which prove that that is a fair comment. Indeed, because of the general misunderstanding—in both camps—of the reasons for the colours seen in subjective experiments, there is an incorrect consensus that there are two types of spectra. But all this a little later. I will now conclude this chapter by showing one last subjective experiment, in which the principle we have discussed will coherently explain what appears to be a rather bizarre spectral display. We will observe through a prism (vertex up) the figure below, but before doing that I will ask you to look at the figure without a prism and to try to predict what colours will be revealed by the prism.
Now, can you predict what colours will border the grey circle in an observation through a prism oriented with the refractive angle (vertex) pointing upwards? When you reach a conclusion look through your prism and see if your prediction is correct. Was your prediction correct? If it was not, let’s see where you went wrong. The reason for the grey circle being surrounded only by the violet-blue combination is this: the violet-blue combination from the upper half of the circle was generated by the circle itself (because the grey circle is more ‘luminous’ than the black surrounding it; the violet-blue combination of the lower half of the circle, on the other hand, was generated by the white rectangle (white being more luminous than grey). In effect, the red-yellow combination (which should have bordered the bottom semicircle) was ‘overshadowed’ by the violet-blue one. In fact you can also see that the violet-blue combination of the lower semicircle is the product of the white rectangle from the colours’ orientation—which points to where the rest of the spectrum is. You know what I mean? Finally, try to predict what colours will be seen around the grey circle through a prism oriented with the vertex pointing down.
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