My analysis of Newton's theory of light and colours

The first proposition in Newton’s Opticks says that colours are refracted at different angles. For example, blue is refracted at a greater angle than red. Newton had based this proposition on the results of his experimentum crucis and on a number of additional experiments which, he insisted, proved that proposition. One experiment held as a proof of validity for Newton’s proposition is a subjective prismatic experiment where a blue and a red square, on a black background, are viewed through a prism. (See figure below.) 

The consensus about this experiment has always been that it indeed supports Newton’s first proposition. Even Dennis Sepper—who seems to be a defender of Goethe’s theory—says the following about this experiment.

Another demonstration entails reproducing the first experiment of Newton’s Opticks, in which we need only put side by side against a black background two rectangles, one an intensely saturated (dark) blue, the other an intense red, and observe them through a prism. We will see that they are no longer side by side, the blue rectangle being apparently moved further away from the line of sight than the red. Once more we see that light is differently refrangible, and according to color.

To my mind, the conventional consensus is a gigantic mistake. To see why let’s look at the two squares above through a prism oriented with its refracting angle pointing up. If you conduct your observation from a distance of about 0.5m, you will see an image similar to the one below.

Now, ignoring the two half-spectra at the top and bottom of the figure, I have never accepted Newton’s (and others’) claim that the blue square appears displaced because blue suffers a greater refraction than red, for the simple reason that, if that were the case, the blue square should appear displaced lower than the red one! In view of what is proposed and claimed, and in relation to the orientation of the prism, there cannot be any interpretation that could render the proposition correct. As simple and as uncompromising as that.

But there is more—much more than that. Let’s overlook my “uncompromising” argument and consider another line of reasoning. If Newton’s proposition is correct, then we shall observe the displacement of the blue square taking place onto a background of any colour. Let’s see if that is the case with the two squares placed onto a white background.

In this case, of course, there isn’t any displacement at all. We can try most other colours as the background, in fact, but we’ll get the same result. (There is a good reason for my saying most, not all, and I don’t think I have to say anything more on this subject.) This is yet another valid argument that should have created in the Newtonian camp cause for concern, but—as it stands—physicists have never engaged in any genuine debate on this issue. As, indeed, they have never considered another anomaly related to the first proposition in Opticks, an anomaly illustrated in the experiment below. In this experiment I have marked the positions of the two squares, superimposed onto a black background, and then I observed them through a prism with the same orientation as before. In the figure below left you can see the marking points, and in the one on the right I have depicted the image the observer will see from a distance of 0.5m. You can verify that my depiction is correct by looking at the figure on the left through your prism.

Now, in my depiction on the right I have ignored the little spectra generated by the marking points, but you can easily establish that their real positions are quite accurately depicted in the figure on the right. (If you have doubts grab a pencil and place its tip on the marking dots. In fact, even with the generated spectra you can safely establish the true positions of the marking points because you can see where the spectral colours are.) From this observation it becomes evident that the two squares are displaced in opposite directions. If the displacements observed were the result of refraction, then both squares should appear displaced in the same direction. This is yet another argument that cannot be reconciled with Newton’s theory.

But the most interesting fact concerning the arguments I’ve raised is that if we take as valid Goethe’s proposal (which, incidentally, is basically incorporated in my law of colour-display in subjective prismatic experiments) we find that it successfully explains all anomalies I’ve mentioned. Since Goethe’s proposal is incorporated in my law, I will now apply it in order to prove the claim I’ve just made.

Let’s begin by using the law of colour-display to predict what image we’ll get if we looked through a prism (oriented with the refracting angle up) at the two squares on a black background. Below is the relevant picture. 

According to the law, the two squares will generate two individual spectra, because both squares are more luminous than the background. Knowing this fact we can confidently predict two things: First, that each spectrum will be formed by a violet-blue combination, running along the top edge of each square, and a red-yellow combination, which will be running along their bottom; second, that the widths of the spectral colours will be determined by the distance from which the observation is conducted. On the basis of this prediction we might suspect that since the two squares are themselves coloured in spectral colours, we’ll probably find it difficult to separate two of the real spectral colours (red and blue) from the colours of the squares themselves. Keeping these things in mind let’s look once again at the picture above from a distance of about 0.5m. This observation will produce an image similar to the one we had looked at earlier.

The prediction we made, by using the law of colour-display in subjective prismatic experiments, is fully consistent with this image. In the case of the red square the mix of the spectral colours with the red of the square itself makes it quite difficult to see the spectrum it generates. At the top of this square, for instance, the violet-blue spectral combination mixed with the red colour of the square itself makes it almost impossible to distinguish it from the black background. A good prism and a sharp eye would help to prove that the red square generates a spectrum, but for the die-hard sceptic perhaps a better proof would be a prismatic observation of different shades of red in similar experiments—like in the three examples below.

Similarly, at the bottom of the red square (see the figure previous to the three examples above), the mix of the spectral yellow with the red of the square creates a hue that is almost impossible to distinguish from the colour of the square itself. The spectral red, on the other hand, although just as hard to separate from the red of the square, it—nevertheless—shows its existence by the fact that it ‘transforms’ the red square into a red rectangle. A similar situation happens in the case of the blue square. At the top of this square the spectral blue mixes with the blue of the square, which—in effect—elongates the square into a rectangle. The rest of the spectral colours generated by the blue square are easier to distinguish.

The law of colour-display in subjective prismatic experiments does not only account for the results of the experiment we’re discussing, it also eliminates the anomalies that plague a Newtonian analysis of the experiment. To see that this is true let’s examine, for example, the case where the two squares are placed onto a white background. In this case the observer (by looking through a prism with the same orientation as before) will see an image similar to the one below on the right.

The reason for what is seen is that in this case the spectra observed are generated by the more luminous source—which is the white background itself. Thus, at the top of the two squares we get the half-spectra formed by the red-yellow combination. The other half, formed by the violet-blue combination can be seen at the top of the figure. In the same vein, along the bottom of the two squares we get the violet-blue combination, which are the half-spectra of the red-yellow half spectrum at the bottom of the figure. As for the colours observed, they can all be fully explained by the mixing process that takes place between the spectral colours and the colours of the squares. (I urge you to take the time and see for yourselves that what I've just said is absolutely correct, for I am not going to spend time depicting it in words.)


The other apparent anomaly, where a defender of Newton’s theory would have to explain how refractions of different colours could happen in opposite directions (as seen earlier), presents no problem at all for someone who adheres to Goethe’s explanation (or to the law of colour-display). That’s simply because we can offer tangible evidence that the apparent displacements of coloured objects (like the two squares) are not caused by refraction. And the law of colour-display in subjective prismatic experiments goes even further—by bringing additional evidence to that effect through specific predictions. For example, if the apparent displacements are the effect of the mixing process that takes place between the spectral colours and the colours of the objects observed, and if the widths of the spectral colours are determined by the distance from which an observation is made, then a systematic increase in the distance should produce specific differences in the images observed. The specific differences we should see are two-fold: one, the apparent displacements should systematically increase with distance; and two, in cases where we use symmetrical objects (like the squares we have used) an increase in the distance from which the observations are conducted should manifest in an apparent systematic departure from the true symmetry of the objects. In our specific case, the two squares should appear as increasingly elongated rectangles. And this is exactly what we’ll observe, if we increase the distance from which to look at the figure with the two red and blue squares on a black background. Below I have once again placed the now familiar figure of the two squares (to be looked at through a prism with the same orientation), and I have also depicted what images we’ll get from three different distances: 0.5m, 1m, and 2m.

There’s no need of me to say anything more on this subject. Nevertheless, I have conducted many similar experiments and they are all consistent with Goethe’s explanation (his “general law” of elementary fringes) and my law of colour-display in subjective prismatic experiments. In spite of all the evidence against Newton’s first proposition (from Opticks) physicists have never gone further than calling Goethe’s explanation “quite plausible”. They have admitted, however, that the colour aspect of Newton’s theory presents some problems, but that those problems are really “neurological and physiological”—and that, therefore, those problems do not belong to the science of physics! I have no intention of debating this issue, so I’ll leave it at that. But the truth you have seen now, that there is a beautiful way of explaining all subjective prismatic experiments and that that way belongs entirely to physics. Through that way we can clearly see that the authors of the article published in Physics Today incorrectly had asserted that “The colors generated by a simpler checkerboard pattern were periodic and exhibited regular changes as the checkerboard was rotated, but were still too complicated to be expressed in a law”, for we know that there is a law—and a simple one, at that.


In fact, if we look through a prism at a checkerboard pattern we can easily explain the colours observed. Below we have two such patterns—one with black and white squares, the other with interchanging black and white diamonds. Before looking through the prism we can predict what colours will be seen by using the law of colour-display. There are only two factors we need to consider: the orientation of the prism and the distance from which the observation is made. The orientation of the prism tells us how the violet-blue and red-yellow components are displayed relative to each individual ‘source of light’, which—in the cases below—is either a white square or a white diamond. The distance from which we conduct our observation determines how broad the spectral colours will be. This means that in every prismatic experiment of a subjective nature, increasing the distance will eventually lead to a superposition of the spectral colours—which will result in the “mixing-process” that creates the other colours observed, like green or magenta. Qualitatively, this is all we need to know.

An interesting aspect of an observation of patterns like those above occurs if you happen to be wearing glasses, like reading glasses. If that is the case I’m sure you have already noticed that you can see the spectra generated (albeit, as very thin lines) without a prism. That is not an optical illusion, of course; that is explained by the fact that lenses are a kind of special prisms. In the next chapter we’ll see why we need prism-like objects in order to see spectra, and we’ll also explore how prism-like objects help us understand what spectra truly are.

The law of colour-display predicts and explains the spectral colours seen in all possible subjective prismatic experiments. In Goethe contra Newton by Dennis Sepper, I found three paragraphs that caught my attention more than any others. In the first one Sepper asks:

What does someone see by looking through a prism? Even a person fully conversant with Newton’s theory may not be able to say with certainty what the outcome will be. At any rate, the outcome depends on the circumstances...

There is little doubt that no person could predict the outcome of a subjective prismatic experiment by using the conventional understanding (“The boundaries of wider rectangles acted as isolated black-white contrasts, displaying red and yellow fringes when the black was above, blue and violet when it was below...”). This kind of 'understanding' cannot help someone who faces a complex arrangement of different shapes, let alone an arrangement with shapes of different colours. But I have no doubt that anyone who understands the law of colour-display can predict and explain all spectra generated by all possible subjective prismatic experiments. That’s because the principle behind the law is simple and comprehensive, and because the human mind can fully understand it. It is incredible that physicists have failed to adopt it, despite the fact that it is a known physical principle. Indeed Newton had used it in his debates, and Huygens had used it in his wave theory of light.

These edge spectra seem to emerge from the boundaries, so that red, yellow, green, blue, violet, and purple appear in a certain order and harmony, although the exact nature of this orderliness is not immediately evident.

No spectrum in any subjective prismatic experiment is generated by an edge or a boundary. The fact that spectra appear along edges and boundaries is incidental to the issue of where the spectra come from. (It will become evident in the next chapter where the spectra do come from, and also why it is always bordering the source that generates them.) That is where Goethe went astray in his work on colours, and—most interestingly—that’s also the reason for the physicists’ failure to incorporate the nature of colour seamlessly into Newton’s theory. (There was no need for physicists’ throw of the ball in the court of physiologists, for physics can fully account for the existence of colour.) In effect, although Goethe’s work on colours was repudiated by physicists, his obsession with boundaries and edges remained so stuck in physicists’ mind that they too failed to look beyond them! That is truly the reason for the hitherto failure to see “the nature of orderliness” Sepper mentions in the paragraph above. Physicists have failed to see the forest for the trees.

We can state generalizations that conform to our experimental results, for instance that the width of the edge of the spectrum varies according to the mutual orientation of the refracting angle and the boundary. These rules and generalizations are not only summaries of the previous experiences but also leading principles for future research and testing; they have genuine predictive power, perhaps not enough to impress devotees of the Newtonian theory, but nevertheless real.

In this paragraph Sepper reveals his conviction that the last word in the subject of light and colours has not been spoken yet. At least this is the impression I got from it, and—if such is the case—I totally agree with him. But I disagree that “the rules and generalizations” one can extract from Goethe’s work “have genuine predictive power”. That’s simply because Goethe’s work is fundamentally modificationist, and in the next chapter we’ll see that Newton was (fundamentally) correct—colours are connate properties of light and no modificationist theory can account for colour phenomena. That’s why Goethe’s work on colour leads nowhere.


The law of colour-display in subjective prismatic experiments, on the other hand, leads to a comprehensive explanation of where the spectral colours come from. This law is consistent with some of Goethe’s observations, but it does not at all extrapolate from those observational facts that light is modified by media. On the contrary, the law—in its final form—shows that colours are properties of light and that those colours are brought into view in certain circumstances. I will conclude this chapter on Goethean subjective experiments by showing you three examples of how the law of colour-display is applied to predict and explain what is generally observed in subjective prismatic experiments. In the first example, below, an observation conducted with a prism oriented with the refracting angle pointing up will show two sets of violet-blue and red-yellow combinations.

That’s because the shape of the white figure creates two sources of spectra. This fact has to be kept in mind, when predicting the spectral colours in similar experiments, but I’m sure that I don’t need to explain why there are two sources in this example—or, indeed, how certain shapes can create a virtually unlimited number of sources.


In the second example below I have put, in the upper figure, seven squares (six in spectral colours + one white) on a black background, and—in the lower figure—the ‘spectral’ squares + one black onto a white background.

The purpose of this example is to see that the law of colour-display can account perfectly for what is observed, and that Newton’s proposal that different colours are refracted at different angles cannot account for what is observed. The most interesting part of this example is that of the yellow square on white background. This is one way to prove that Huygens was correct when he proposed that white can be formed by mixing only two colours: yellow and blue.

In the final example below, the figure on the left (looked at through a prism with the same orientation as in the previous examples) covers just about every possible spectrum observed in subjective prismatic experiments. Because there are a number of different spectra that will be generated I have numbered each half-spectrum.

The half-spectra numbered 1, 3, 4 and 6 are produced at the boundaries between the figure and the page. Their respective complementary half-spectra are at the next boundaries. The half-spectra 7 are generated by the grey rectangle. The magenta line is formed on top of the black line, and it is the product of the spectral violet and red produced by the white rectangles numbered 2 and 5. Spend a bit of time contemplating the intensity of the colours—it reflects the contrast between the colours of their respective sources.