In regard to your apparent puzzlement with the inverted image of the two merging reflexes close to the first rainbow angle, either completely study the phenomenon in question and read, for instance, the articles by J. D. Walker (I have included also his publications efforts in more educational literature), or simply take your favourite textbook on optics and analyse the sequence of rays around the Cartesian ray (ray of least angular deviation, ray “f” in the ray-racing calculation(!) below): You will see that g-f stay in order, while f-e are inverted opon leaving the drop. The image does NOT show the two possible paths (
http://rainbowstudy.blogspot.de/2010_07_01_archive.html) leading to an equal angular deviation which make up the images of a light source. I will agree that the SKETCH (see below, likely not a raytracing) in https://www.itp.uni-hannover.de/~zawischa/ITP/refraction.html is wrong in the unimportant detail of the point at which the back-side reflection takes place (it won’t be the same point). However, the inversion of the parallel light rays seen in the raytracing and calculations (again, cf. Walker) is the ultimate reason for the image inversion that you parade as a blow to the conventional rainbow theory…
Below is another pearl of the conventional piddling piffle, coming from the fairy tales of the cantankerous mob of physics' freeloaders that have been wasting with sickening impunity the world's hard work and blind generosity. Listen carefully at this other conventional monologue, recited by another Dr. of a spectacular similarity to the perversely supercilious Selmke Markus. Enjoy.
A water-filled spherical vase serves as a model for a falling raindrop (following Antonius de Dominis, Descartes and Goethe). Instead of the sun, a small lamp shines on the drop, its mirror image on the front surface is seen as a white point to the right of the centre. Light which enters the drop is reflected at the back surface and leaves the drop to finally reach the eye of the observer. This can happen along two different paths, and correspondingly two reflexes are seen on the left side of the drop.
The left image shows a drop well inside of the rainbow, where the sky is brighter than outside. Increasing the angle of observation (measured from the point opposite to the sun), the two reflections approach each other (middle image), join while becoming very bright – and eventually vanish. As the shortest waves are refracted most, first the "blue" rays join and get bright while green and red are still separated. Then green becomes bright and vanishes, and finally red (right image). What we see as a rainbow are the tiny, but (in the light of the sun) very bright reflections in the innumerable falling drops.
Over the years I have made so many videos that show to any observer without a vested interest in the reigning academic powers (which, btw, form the modern aristocracy of our times and are driven by the same set of egotistic urges and traits as those who used to strut their over inflated egos in the feudal times of humanity's even darker days) that the conventional fairy tale of rainbows is just a moronic concoction that will only serve as a confutative parody for those that will come tomorrow. For those of us who live alongside these gargantuan narcissists, however, the current story of rainbows is just a real tragedy of human stupidity and ineptness. Alas, for the time being there is not much we can do, for the simple and blatant reason that most of these aristocratic miscreants have totally monopolized the major intellectual avenues that could otherwise be used to persuade those with political clout to begin asking the questions that are needed to overhaul the rotting parasitic establishment that has freely festered in its many years of absolutely authoritarian ruling. (Isn't it blindly obvious that the so-called scientific establishment is unilaterally a party without any opposition in this supposedly democratic world of ours? Think about it.)
Below there are just four of my videos showing the grotesque fallacy of the conventional view of how rainbows emerge from raindrops. Please watch them and judge for yourself whether what I've been saying (with a massive increase of saturated intensity and contempt for the pharisees that are preaching in the current temple of physics) is right or wrong.
There are two things I know about God. One, that he is supremely parsimonious. Two, that he is inherently dichotomous. Knowing these two things about God has served me well over the years. For instance, I know that deep down everything about Universe is marvellously simple. So, if something appears to be too complicated, I know that it most likely is. The more complicated something appears to be, the most likely that it has a human origin and history.
I know that I can account for all chromatic phenomena by using only three spectral colours: Blue, Green and Red. And when I say all chromatic phenomena, I'm including those that involve Yellow, Magenta and Cyan.
I know that I can account for all subjective prismatic observations. To all intents and purposes, I have already done it.
I know that I can account for all objective prismatic experiments by offering a coherent line of reasoning that will ultimately explain both the refractive and the diffractive prismatic phenomena.
The only spectral colours that are needed in order to account for all conceivable hues of light are B, G and R. When these colours are observed subjectively in a prismatic observation, if they are displayed on a dark background, they will be deflected (refracted) by the prism in the following manner: B will be deflected towards the apex of the prism; G will not be deflected at all; R will be deflected towards the base of the prism. Also, quantitatively B will be deflected by an amount about 1.6 times greater than R.
At the same time, if the complementary colours Y, M and C, are subjectively observed through a prism, when they are displayed against a light background they will be deflected in a perfectly symmetrical fashion to their counterparts. Thus, Y will be deflected in a direction towards the apex of the prism; M will not be deflected at all; C will be deflected in a direction towards the base of the prism. Moreover, the amount by which each colour will be affected, will be exactly matched to their respective counterpart's.
If you conduct a subjective prismatic observation on Figure 1 (from a distance of about 0.5 metres, with the prism oriented with the apex pointing to the left), you will be seeing an image similar to that in Figure 1A.
It can be easily observed that the three narrow Y, M and C bars have been generated by the white areas on the sides of the black bars. (The observer can see the creation of the YMC bars by placing his prism next to the monitor over one of the black bars, and then by slowly bringing the prism closer and closer to his eye.)
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This is basically the entire body of knowledge that is required to understand the theory of colours. The rest is details.
As you can see, one can explain the provenance of the complementary colours as being the results of overlapping primary colours. In effect, then, one can get to YMC from BGR. One, however, cannot get the other way around, from YMC to BGR. In other words, one can use the primary colours to create the secondary (complementary) colours, but one cannot create the primary colours from the complementary (secondary) ones.
There is an interesting way of learning more about the nature of the spectral colours, by replicating a kind of objective prismatic experiment developed by Torger Holtsmark and Pehr Sallstrom.
This experiment uses a large prism, with one of the faces acting as a slit, or an aperture. Along the two lengths of the beam emerging from the prism, one can see the two border spectra: R and Y, toward the apex of the prism; B and C, toward the base.
A shadow-casting pole placed halfway in front of the prism, will create two more edge spectra along the borders of the shadow that ensues.
It immediately becomes apparent that the two spectra at the centre of the beam are heading in opposite directions--toward each other. Soon, the B and R overlap and form a band of M, which is flanked on each side by a Y and a C band, respectively.
Placing a screen with a slit on the M band, will cause the two colours (R and B) that formed it to split from each other again, and to continue travelling in opposite directions.
It must be said that it brings a great deal of satisfaction to see that R and B are refracting in opposite directions in objective prismatic experiments, just as they were in the subjective ones. Then, even more beautiful is the fact that the symmetry that exists between the two cases is inversely related. Whereas in the subjective observations B was deflected towards the apex of the prism and R towards its base, in objective experiments the situation is reversed. Beautiful.
(Some may argue that what is seen in this experiment is not a process of refraction at work, but instead that there is one of diffraction that affects the behaviour of R and B. In any event, even if that were indeed the case--which it is not--the problems it would create for the conventional theory would be very similar to those we have already exposed. That's, of course, because diffraction in opposite directions is as much an anathema for Newtonians as refraction in opposite directions is.)
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There are other ways to show that R and B do indeed refract in opposite directions in objective prismatic experiments. One could use, for example, a setup like that in the picture below.
It is manifestly obvious that, with distance, new colours are continuing to appear between the R band and the edge of the black shadow, as well as between the B band and its own border with the shadow. Were the Newtonian theory correct, that is not what the observer should see. Instead, the observer should see be a gradual reduction between the R band and the black shadow--since all colours are supposed to bend in the same direction, towards the base of the prism.
Let us return to one of the earlier pictures above, in order to examine more ways that reveal the B and R refracting in opposite directions.
On this picture I have drawn two black lines, which delimitate the boundaries between the beam of light and the darkness that surrounds it. We have established exactly where those boundaries are in our investigation on the subjective prismatic experiments. We therefore know that the B and R bands in the image above are extending over the dark areas of the image. A natural question thus begs to be asked: How did those two colours came into being in the places where they are at the moment? Can Newton answer satisfactorily that question?
It becomes immediately obvious that there is no way a Newtonian answer could give a plausible account for the locations of R and B. In fact, the disturbing reality is that a Newtonian answer wouldn't be able to offer any kind of account to that question. To see why that is the truth, let's take the conventional explanation for the dispersion of white light in prisms, which is illustrated in the pictures below...
...and compare it with a real image of an objective spectrum.
In the end it is all an exercise in futility. Sure, one can easily imagine the conventional physicist explaining that we should understand that there is a significant difference between illustrative depictions of reality and the reality itself. That the differences between the angles of refraction are tiny, that in certain situations colours are hard to discern, that although there may exist some anomalies in some cases that doesn't mean that the whole theory is necessarily wrong, that even if sometimes we may not directly see some theoretical effects at work their existence may become evident in other ways, etc., etc.
The reality is never a matter of compromise. The conventional physicist may invoke all of the above and more, but the truth is that he will never be able to justify, for example, why in all his illustrations there is abundantly depicted the refraction of colours taking place inside the prism. In my 30 years of research in this field I have conducted hundreds of prismatic experiments, and yet have never seen even the tiniest evidence of colour being dispersed inside the prism.
The conventional physicist would surely invoke at this point one of those many shadowy arguments I mentioned earlier, but the reality is that if there were any colours dispersed inside the prism, however tenuously, they would become visible as soon they would interact with the face of the prism through which they would exit, or with any other face they might come in contact and be reflected by. See the photo below, as a concrete example.
Why this elaborate ruse, then, which the world has been subjected to for 350 years? To give credence to Newton's theory? Why does nobody ever talk about this issue?
Another topic of a similar kind has been pedalled for just as long, and with the same result. It is concerned with the refraction of light in a rectangular slab of glass. The question to be asked is why we cannot observe unequal refractions of differently coloured lights when they are passing through a rectangular slab of glass, or of any similar object in which we should see different amounts of refractions. Searching for a definitive answer online is a complete nightmare, with some of the arguments invoked being as silly as "the distance between the entry face of the slab and the exit one is too short". I, nevertheless, did conduct a number of experiments of that kind. In my experiments, however, I substituted the slab of glass for a fish tank. See the photo below for the setup I used.
Since there is no need of me to say anything at all about the entire setup, I will only mention the results of the experiment: I did not observe any difference between the unrefracted beams of laser at the point of origin, and the twice-refracted beams that landed on the intercepting screen. The only nightmare that this experiment brought was the impossibility of finding straight answers to such straightforward questions like "What is the index of refraction in water of a beam of light with a wavelength of 650 nm".
But we have digressed, and there is still one most important topic I want to discuss today.
The experimental proof that refraction in opposite directions happens in objective experiments too
When it comes to objective prismatic experiments, it turns out that Goethe was much closer to the truth than Newton. A simple examination of Plate IV from his Theory of colours clearly demonstrates that reality.
There are two outstanding features in Goethe's Plate IV (and a handful of erroneous ones, it must be said), which Newton had never managed to learn. The first of those is the pattern that the spectral colours assume after they exit the prism. The second is the fact that at some point, after exiting the prism, the entire Newtonian gamut of colours is reduced to only three hues: B, G and R. (See the last vertical display, on the far left of the picture. In Goethe's view the violet band stands for B.)
On the other hand, Goethe's erroneous features are concerned with the widths of the spectral bands, which in reality are very precisely correlated. (The widths of B and Y are identical, and about 1.6 times greater than those of R and C, at all given points--until Y and C vanish from the emergent beam, leaving only the primary colours on display.)
There is also another thing that escaped Goethe's attention. That is that at even greater distances from the prism, B diverges further and further away from the other two colours, reducing thus the entire spectrum to just two colours: G and R. (There is still one more event that eventually materialises, which is of great importance in the bigger picture. B deflects so much from its counterparts that at some point overlaps the R from another refracted beam, blending into M. So, in the end the spectrum is reduced to M and G. M and G are the colours of the supernumeraries in rainbows, in the kitchen, in the soap bubbles. But, most importantly, M and G are heavily represented in diffraction. Food for thought? You bet.)
Every day I am another
Yesterday I was just about to begin discussing two important issues--one Goethean, the other Newtonian--when I suddenly got sidetracked by a completely different topic, which kept me in a tight leash until this morning, when I finally resolved it. The topic was Newton's rings. A topic that I had half-resolved about ten years ago, when I published the video below on YouTube.
This was a forbidden subject at the best of times. To generate those so-called Newton's rings by simply passing a laser pointer through some crappy planoconvex lenses I found in some of the many flashlights I had acquired over the years was blasphemous. I mean, what was there to do with Newton's apparently flawless maths he used to explain/justify the pattern of the rings that were to carry his name ever since? And that wasn't all. On top of that, to matter not one iota whether the plano or the convex sides were facing the incident light I'm pretty sure that it ruffled many a feather.
A few short months later, however, I was back on YouTube with another, even more outrageous claim. That I could make Newton's rings by using just a spherical glass ball.
That story brings us to yesterday, when--fancy that-- I realised that I could make Newton's rings by using a white LED flashlight (and a crappy planoconvex lens).
If I were you, a Newtonian epigone, I'd be really pissed by now. I mean, let's say that whatever rings you project on a screen are somehow Newtonian. What kind of explanation can you offer, to have even the slightest chance of convincing me?
Really? Is that what you're asking me, after hovering around for so many years that these days I don't even notice you, most times.
What I have is strong, direct experimental evidence. Let's think about it. What is a prism? An equilateral prism. What kind of object is it? An equilateral prism is one half of a double convex lens. A wedge is one half of a planoconvex lens. Of course, the situation is conversely true, isn't it? Lenses are prisms, and as such they are able to refract colours like prisms do--albeit, to some lesser degree, for obvious reasons. Spherical glass balls are also lenses, and by extension prisms.
Now, we know that, at least in subjective observations (at this point), prisms deflect the spectral R and B in opposite directions, and the G (+ C and Y) not at all. We also know that in subjective prismatic experiments the B is deflected in the direction of the apex, and the R towards the base. We cannot overestimate the importance of these facts, for we are all conducting subjective prismatic observations all the time. Think about that on your own, for I don't want to elaborate myself.
Nonetheless, there is a way to summarise pretty much everything that's important in that subject by conducting--for the last time--two subjective prismatic observations of all the six colours of light (B, G, R, Y, M, C). In the first, we'll look through a prism at the figure below from a distance of about 0.5 m. (All the rules of observation being the same that I have repeated so many times in the past that I just cannot do it again. Ever...)
And here are the results of the observation (with the prism oriented with the apex towards the left).
The second observation will involve the same colours, cast on a white background.
And below are the results.
What do all these things mean? Why are they important?
Because every kind of observation that involves prisms, or lenses, is inherently governed by the laws of refraction that I have, empirically, brought forward. Newton may take you on a mathematical trip whose final goal is to give a foundational explanation to the prismatic observations we see, and if you believe what he says, it's fine. Nonetheless, if that is the case, as indeed it has been for 350 years now, then he must also bring into his picture my observations--for they are real, and directly verifiable.
Ultimately, the reality is that without my story, Newton's remains a fairytale. On the other hand, my story remains manifestly real even without Newton's. Think about that, people. Think. That's what you're supposed to do. Isn't it?
It is truly staggering how deep the ignorance of the subject of light and colours runs in today's world, 350 years after Newton's own foray into the matter. I mean, let's take only a very brief look at what is supposedly the very core of the prismatic phenomena: the subject of refraction.
Refraction is perhaps the topic in which the conventional physicist speaks with the most authority and creed.
...the eminent French physicist Edme Mariotte pointed out that in performing the experimentum crucis he had found that the images produced by the refraction of the second prism were decidedly not circular, which they ought to be if that light is truly homogeneous, and that rather than being uniform in hue the images displayed several colors — that is, they had greater or lesser fringes of color different in hue from the presumed color of the light admitted through the hole in the second board, a fact that the Newton of the unpublished Lectiones opticae knew {LO, 164-65; Shap., 452-55). These fringes may be inconspicuous enough to be overlooked on a cursory glance; yet, although there are various methods for reducing them, it is not possible with the apparatus of the experimentum crucis to eliminate them completely. A Newtonian would dismiss these fringes by saying that the light had not been perfectly separated and might advise his opponent to learn better experimental technique.
Yet this answer is scarcely satisfactory. Once again the experimental difficulties cannot prove Newton wrong; nevertheless, if a perfect demonstration of the theory is not possible, and if the geometric-physical interpretation can never be verified directly, how can anyone claim that the theory is proved directly from experiments as a fact beyond doubt? One must admit that the theory is indirectly inferred from the phenomena by speculating about what happens at the limit of the visible and with the assistance of various hypotheses and abstractions; it is not derivable from the phenomena alone, nor can the propositions about light and color be accepted as perfectly unproblematic.
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