About the refraction and dispersion of light in my own universe. Part 1.

Let me begin this post by showing you the first out-of-the-blue email I received from Dr. Markus Selmke on December 5, 2018.

Dear Remus,

I can’t resist. I just read your latest blog post out of a mixture of sheer incredulity and fun.
https://remusporadin.blogspot.com/2018/11/on-rainbows-part-7.html

You make a point about the “claim” of most people who have spent some thoughts on the rainbow phenomenon that the rays hitting a raindrop are almost parallel. Now, you see, any good textbook will have this limitation, i.e. referring to rays which are parallel for all intents and purposes / for all relevant calculations. It is a simplification that is justified by the fact that its incorporation would not alter the result in any meaningful way. As for every problem in physics for which an understanding is sought after, some simplifications are required. A study of the rainbow will not start with the nuclear fusion providing the energy for the light emanating from the sun. 

No person in his right mind would state that the sun’s rays are perfectly parallel. After all, the sun is a light source of finite extent (roughly a spherical surface, the sun’s photosphere). Roughly, seen from a distance, it emits like a point source in all directions. It is the distance of the sun relative to the lateral extent of a raindrop which leads a mathematically-versed person to the conclusion (via basic trigonometry) that the maximum angle subtended by two rays will be about 2*ArcSin((R/2) / d), i.e. 4 x 10^(-13)°, i.e. less than a millionth of a millionth of a degree.

https://www.wolframalpha.com/input/?i=(180%2Fpi)*2*ArcSin(1mm+%2F+(2*(distance+earth+sun)))

I, and most other people, feel comfortable calling that practically parallel. If you should be able to measure the non-parallelism of that order of magnitude please file a patent. The reference to the railroad is indeed inadequate if one tries to explain or compute this (minute) non-parallelism or practical paralelism via an argument based on perspective. But it is appropriate in the typical context, which is to explain the apparent everyday experience of crepuscular rays which seem to radially diverge from the sun despite the small non-parallelism of the actual rays (this time, set R = distance observed at the horizon, i.e. a few tens of kilometers, which is small compared to d=distance sun earth = 1.4*10^8 km).

Also, you seem puzzled for not directly seeing dispersion in a sphere. In fact, if you look close at the pictures you posted, you do see dispersion: the edges of the ray bundles show reddish and bluish colors. They occur because of incomplete addition, while the complete superposition causes the inner of the refracted bundle of rays to be white (=well, whiteish, i.e. the color of the sun). It is a typical phenomenon also observed in lateral dispersion, e.g. es seen for refraction through planar wedges of glass.

BTW: Transparent balls are lenses. Raindrops are lenses. Glass-Spheres are commercially available and used in many applications, https://www.edmundoptics.com/f/N-BK7-Ball-Lenses/12436/. The physics, including the paraxial focal length, is fully compatible with classical rainbow theory. So I’m not sure why you are eager to construct the next conspiracy here? Also, lenses do show refraction and dispersion. Please take a close look at any given picture of a sharp edge taken with a digital camera, best at low f-number (large aperture = far from paraxial).

Please, read a physics book in full. Other people have spent time thinking about nature as well, it is not just you. In fact, as I have pointed out before, the detailled understanding they have developed in a community effort and method called “science” has brought you the very laptop / PC you sit in front of.

Then, an hour or two later I received the message below from the man.


...damn, I should have spent two more minutes on my quick mail… my mistake indeed. But the main point of course remains:

the finite but small non-parallalism is described in both situations by the same geometry, with R=radius of the sun, d=distance sun to earth, max angle 2*ArcSin((R/2) / d). I should have drawn the text-book sketch I had in mind and I would have avoided my blunder. My bad. Back to the point: The parallelism is negligible for the main characteristics of the phenomenon. The fine details do require consideration of the angular diameter of the sun (0.5°) which smears out any parallel-ray bundle computation. Alternatively, Monte-Carlo simulations like those done by MiePlot (vectorial EM wave theory-based), if I remember correctly (http://www.philiplaven.com/mieplot.htm), do allow this details incorporation. But understanding the rainbow does not require non-parallel rays to be considered, parallel ray bundles work just fine to produce the rainbow caustics (i.e. the various orders). In fact, using widened collimated (arbitrarily parallel, again not perfectly, though, since there is nothing like a perfect parallel beam in nature, just like there is no perfect electromagnetic plane wave) laser beam, you could get the caustic as well...

Before anything else let me say that there are a number of very good reasons for which I chose to show you in full the rather long and 'slippery' email above. Additionally, I ought to also mention that all of those reasons will become manifestly apparent by the end of this post (albeit, not in the order that they've been laid down by Dr. Selmke in his email).

Now, let me first direct your attention to the following paragraph from Dr. Selmke's email.

Also, you seem puzzled for not directly seeing dispersion in a sphere. In fact, if you look close at the pictures you posted, you do see dispersion: the edges of the ray bundles show reddish and bluish colors. They occur because of incomplete addition, while the complete superposition causes the inner of the refracted bundle of rays to be white (=well, whiteish, i.e. the color of the sun). It is a typical phenomenon also observed in lateral dispersion, e.g. es seen for refraction through planar wedges of glass.

Starting with the first sentence in the paragraph I would like to confess that I was, and still am, in fact, puzzled indeed. However, not for the reason contained in the sentence. Not at all, let me make that abundantly clear. Instead, the real reasons for which I was/am puzzled are, firstly, the obvious refusal--or perhaps omission--of Dr. Selmke to either see or make any mention at all that the truly crucial matter of fact is the conspicuously evident reality that a beam of light is basically 'sharpened' inside a sphere, not 'blunted' as the conventional understanding undeniably proclaims. (And that is the only thing I addressed in the post mentioned by Dr. Selmke, BTW.) Secondly, what truly puzzled me was the blatant 'spin' that Dr. Selmke chose to use in a premeditated attempt to probably appear unfazed by my conclusions and also, possibly, to somehow show that the conventional belief is still in just as much control as ever in the matter at stake.

For those who'd perhaps want to get a clear and objective picture of what I have thus far discussed above I'd recommend a re-visitation here. For anybody else, and also for the benefit of all, I will display below a couple of pictures that are most relevant to the issues concerned.

In fact, if you look close at the pictures you posted, you do see dispersion: the edges of the ray bundles show reddish and bluish colors. They occur because of incomplete addition, while the complete superposition causes the inner of the refracted bundle of rays to be white (=well, whiteish, i.e. the color of the sun). It is a typical phenomenon also observed in lateral dispersion, e.g. es seen for refraction through planar wedges of glass.

I brought forward the next part of the paragraph we're scrutinising at the moment for your convenience. (There's almost nothing more annoying to me than the manner in which all conventional papers are published, meaning that invariably you are consistently forced to leave the page you're reading in order to look at some diagrams or figures, then forced again to return for a little while until the next piece of reference comes into play...a.s.o.a.s.f. to the last word. Ha!) I'll ask you now to read it once again, with care, and then to take once more a close look at the beam of light that runs inside the 'sphere' on the refracted (or bent) pathway it has been forced to follow (see the picture below).

Now, if you have looked at the part of the beam of light carefully you would have been most likely able to discern (albeit, barely) that indeed the two edges of the refracted beam appear to be formed by some very thin lines of two different colours: one "blueish" (running along the upper edge) and the other one "reddish" along the lower edge of the beam. To help somewhat in making the whole issue a little clearer I have added to the original picture the two-coloured arrows on display. (Some of you may have noticed however that the upper arrow seems to be rather more 'violetish' than "blueish". I did that for a very simple reason, which is that the actual colour of the edge itself is rather more 'violetish' than "blueish". This fact will become more evident shortly.)

I must tell you now that when I first read the 'explanation' that Dr Selmke spat in my direction--with the apparent conviction of either an absolute prophet or that of an undeniably complete moron--I found it pretty much impossible to believe. Are you going to ask me why? Really? Okay.

Firstly, because even if one were to accept the explanation given without any questions (and I can assure you that the explanation given is very far from being in any way thoroughly evident and truly unquestionable) the simple and clearly obvious fact is that the so-called dispersion colours that are edging the beam of white light are displayed in the wrong order! In effect the reddish edge is where the blueish one should be, and vice versa.

Secondly, because those thin coloured edges of the beam of white light that is bent inside the 'sphere' are inherited attributes from the incident white light that strikes the refracting 'sphere'! Look again at the picture in question, if you need to.

But, by a long shot, the most far-reaching aspect of what we've seen and discussed on this topic is the reality that in absolute spite of the fact that both those coloured edges of the white beam are clearly in the wrong place to give the results that the conventional theory ascertains, the incredible thing is that those results still appear to be thoroughly fulfilled nonetheless! Think about that, carefully, for believe me it is worth doing it.

At this point I'd like to show you a few screenshots I have taken of the paper from which the picture above, and a host of others that I have shown in some past posts, have been extracted. As you will see I have highlighted some of the more significant parts of it and I hope that some of you will take the time to read them. Following that I will also show you enlarged pictures of the four different experiments that were carried out by the authors of the paper (with the fourth one providing a most interesting perspective into one of the conventional tenets of the rainbow theory and mentioned by Dr Selmke in the email we've been discussing in this post).

Let me now show you two enlarged pictures of the the experiments depicted in pictures 13 and 14 above. You have already seen the enlarged rendition of the first experiment, which is shown above in figure 12, and we have discussed the issues raised by Dr. Selmke. As you will see below the same state of affairs is conspicuously evident in the second and the third experiment.

Finally I want to direct your attention to the fourth experiment, which is shown on the relevant screenshot in Figure 15. In that particular experiment you would have seen (if you read the highlighted segments in my screenshots) that the two authors had used direct sunlight, instead of those tungsten light bulbs they had used in the previous three. According to the authors the divergence of the solar rays (which has a value, according to the reigning theory, of 32') had been carefully measured and monitored in all experiments, including the one in which real sunlight was used. In regards to this fourth experiment, for example, they specifically mention the following:

Rotating the apparatus in a way that the light does not enter the acrylic cylinder the path of the beam is clearly visible and its divergence can be measured. The values obtained varied between 28'±10' and 36'±10', in agreement with the accepted value of 32'.

Now, before getting into the matter that I want to conclude this post with I must tell you once again that when I read this paper for the first time, I was even more shocked than in the other incident that I mentioned earlier about Dr. Selmke's pitiful remark about those reddish and blueish edges that 'proved' my 'obvious' misunderstanding of dispersion. I was even more shocked because what to me was a very simple, a most obvious and an embarrassingly monstrous blunder, to those who have been given the role of teaching and leading the humanity to new levels of progressive development, understanding and intellectual evolution the frightening reality of not being aware of even some of the simplest and easiest bits of knowledge that one could possibly become aware of today must invariably be shocking to any living soul of this world! But let's see what you think after reading the last bit of this post.

Let me first show you an enlarged view of that fourth experiment, which was shown in Figure 15 of the last screenshot above.

Now, can you see what is the most obvious difference between this picture and the other three you have seen? It's not the number of extra rainbows, of course. It's that somewhat triangular protrusion that extends from the centre of the acrylic cylinder towards the rim of the apparatus. Do you know what that is? You should, if you're a physicist. Do you know how it got there, how it came to be? You should, if you're a physicist. Does it bother you that it has no explanation whatsoever in the paper that shows it? It should, regardless of what your occupation may be.

That 'protrusion' is a visual manifestation of the extension of the optical field of the acrylic cylinder of the apparatus described in the paper, which for all intents and purposes is a converging lens. At the tip of the 'protrusion' is the focal point of the lens. There are many more important aspects of this optical feature of a lens and in due time I will discuss them further. For now, though let us direct our attention to how this particular feature of a lens came to materialisation in the picture above.

There is one way and one way only in which the particular optical field of a lens that is seen in the picture above can become visible: by passing of a beam of light through the centre of the lens. And that's not all either, for there is another uncompromising requirement that needs to be working at the same time with it: the beam of light that passes through the lens along its central line must be highly divergent. By "highly divergent" I mean a beam with a much greater degree of divergence than that of the conventionally accepted value of 32'. This fact is easily demonstrable, and I will do it in a moment. For now though let us remember a couple of very important factors that are of relevance to the matter at hand.

First, let us not forget that according to the authors the experiment had been conducted in such a manner that no light was allowed to enter the acrylic cylinder. Second, let us remember that according to the authors--and the conventional understanding--the divergence of the lights used in all four experiments was equal to, or less than, the conventionally accepted value of 32'. It is also worth remembering that those conventionally accepted divergent beams are in all cases the incident beams that extend in all four cases from the slit denoted S to the particular point where they enter the acrylic cylinder in each experiment.

How could one then explain the strange display seen in the picture above? you may ask.

Easily, I say in reply. Have a look at my rendition of the picture above, first.

Observe how the black line that I inserted in the original picture extends in a direct line from the tip of that unwanted 'protrusion' to the middle of the same slit that was used to direct the conventionally divergent beam of sunlight towards the top of the acrylic cylinder. The conclusion therefore is unavoidable: the conventionally accepted value of the solar ray's divergence must be wrong. (As I personally believed, btw😉) I will refrain from saying any more than that now, but I can promise you that I'll revisit this topic at some future point.

Finally, let me show you three pictures of mine that are highly relevant to the topic we've been discussing above. The first of the three shows what the optical field of a spherical lens looks like when it is created by what I'd called earlier a highly divergent beam of light. The second shows what the same field looks like when it is created by a beam of light with a divergence similar to that that is conventionally accepted. The third one shows what the field looks like when it is created by a beam of light with a divergence similar to that that is conventionally accepted when it grazes the top of the lens, like in the picture above.

That's all for now. Take care and think carefully before believing anything of any body, at any point in time.

On rainbows. Part 8 (Or about what I learned from the wisdom of Yogi Berra)

"You can observe of a lot of things just by looking"

In the last month of last year I was suddenly sent an email by that superciliously stooping mediocrity called Dr. Markus Selmke. Written in the same duncishly patronising tone he managed to arouse enough interest in me to make me answer it as commensurately as I was able to contrive on a boring, hot summer day. Anyway, to cut a long story short it suffices to say that over the best part of December we exchanged perhaps a half dozen emails, out of which I'll show you the two most relevant ones below.


Dear Markus,

Thank you very much for your last email, I found it peacefully refreshing, honest, and thoughtful. Let me say that I appreciated that, and to that let me add that I'll try to reciprocate my own emails from now on commensurately. (Nonetheless, I would like to reassure you, in case that I will fail to fulfil that promise at all times, that even in those cases there will never be any ill-conceived thoughts or malice behind them--only my inherent shortcomings and flaws, most likely.)

OK, with that being said let me now address the much more important issues that you have brought to my attention in your latest email.

I wrote all that, again harking back to the toptic of the central scientific method, because this is actually what struck me the first time I read a post in your blog in reaction to your first e-mail: I remember that you displayed what to me amounted to a sweeping display of disrespect to the scientists working in the field and dismissal of their findings, assuming on their part indiscriminately a combination of blind obstinacy and downright stupidity.

Although what you said is basically true I would like to ask you to allow me to defend my position by letting you know that what I did was nothing more than responding in kind. You may not be aware of that fact, but I can assure you that in every instance when I contacted ANY conventional scientist I was invariably met with such a degree of blatant and self-assumed infallibility, supremacy, superiority, and obvious contempt for those of us that 'merely' form the rest of the world that I have always truly believed and felt that I was not only rightfully entitled to reply, react and respond in exactly the same manner myself, but that in fact I had a God-given right and duty, as an inviolable and unquestionable equal, to show how shallow, unremarkable, ordinary and yes, sometimes stupid, they themselves are. If you want you can read in some of my past posts about some of my interactions with such people, and then you may be able to see for yourself just how plain and stupid some of them can in fact be.

I have also explained in the past why especially the rainbow theory is practically beyond any reasonable doubt in its general form. 

I respectfully disagree with your assertion. For a number of good reasons. First and foremost because if the conventional understanding would be correct then the rainbow would be a real image, which in turn would then completely dazzle the eye of an observer. Since that is not the case I believe that the current theoretical understanding of rainbows is intrinsically flawed. This, incidentally, is an easily demonstrable fact, both theoretically as well as empirically. From a theoretical perspective one has only to realise that if the rainbow would be produced via the conventional way then in effect when it is asserted that the observer sees a rainbow because the sun rays are emitted, refracted and intercepted by his eye in the conventional manner what is practically stated is that when the observer looks at the rainbow he looks, for all intents and purposes, directly at the sun! And for an empirical perspective all one has to do to see that what I'm saying is correct is simply try to put his eye in the path of a ray of light that is refracted in the conventional manner by some 'raindrop'! 

Secondly, if the conventional understanding was correct then the only possible rainbow display would be one arching upwards toward the heavens, instead of downwards toward the ground. This is also an easily demonstrable fact. All one has to do is observe what kind of caustic is created by the southern part of any typical raindrop refraction. [Of course, the conventional understanding has been periodically altered and tweaked, in order to account somehow for new and inconvenient observations, but the plain and simple truth is that there are now so many inconvenient observations out there that there is no way that they can all be somehow accounted for by the conventional theory, so most of those inconvenient observations are 'discreetly' ignored and swept under the carpet. Let me give a concrete example; in case you'll try to reply to my argument above by invoking the counter-arguments depicted in pictures 25 and 26 (see attachments) I will ask you to see the Pictures 1 and 2 (see attachments), which thoroughly dispel what is depicted in the 25 and 26 pictures. In fact the plain truth is that there are now so many factual observations of rainbows that not even the most fundamental conventional requirements for the existence of rainbows--like the formerly indispensable Cartesian angle, for instance--are any longer required in order to create rainbows.]

There are many more reasons, beside those I mentioned, that have convinced me that the current theoretical understanding of rainbows is fatally flawed, and in time I will discuss most of them in my blog. For now though I only want to add to the above the following: even you, Markus, must admit that the current picture of the rainbow phenomena is so cumbersome, so convoluted, so full of holes and so incredibly bombastic and cacophonic in certain parts that it just simply cannot be part of the physical reality we know. Finally, on this subject, please tell me, Markus, why couldn't the rainbow instead be a direct consequence of the observations I recorded in pictures 22 and 121?

Which brings me to your claims on prismatic experiments. If you wish to discuss visual perception, then the audience (and journal for publication) should likely be the field of psychology or neuro-science. I am no expert here, and neither is the vast majority of physicists. If, however, you claim to have uncovered a new behaviour of light (like: green light does not get refracted), then you must quantify it and adhere to the language of physicists, as well as putting your work as described before in the context of the field. Also, the physical non-refraction of green light would be counter to a myriad of other works in the field and in contradiction with the working principles of modern optical technology. I had read your “paper” (I put it in quotes, because it is not published in a peer-reviewed journal) concerning your prismatic experiments. I did not find it to be intelligible to me as a physicist (I provided concrete points if I remember correctly), likely for the very different take on the scientific method you have and the very diffrerent languages you use in this relation as described before, and apparently no other physicist did. Which would explain why it was not published. I am afraid that you would rather have it (I remember getting that feeling when reading it also) be because of a malign conspiracy on the side of the physics community. I would hope that maybe you come closer to see that this is not the case. At least I have that hope now that I have read your last e-mail.

Dear Markus, I must tell you that in a stark contrast to the rest of you email I found the paragraph above greatly and disconcertingly disappointing. For the following reasons. Firstly, because it is clearly evident that you have either not paid enough attention to the things I had said in my previous email or, alternatively, that you have just relied exclusively on the statistical figures that appear to show that the vast majority of claims made by non-scientists are wrong and therefore not worth considering by people who think they are in the know. Take for example the second sentence in the paragraph. It is plainly obvious that you did not consider at all the fact that a subjective prismatic observation is not merely and strictly a matter of visual perception--it is also fully confirmed and corroborated by photographic and spectroscopic apparatuses and detectors. Moreover, if your assertion had any truth in it at all then astronomy and spectroscopy should not be part of physics but "of psychology and neuro-science" instead.

 Secondly, even though you claim to have read my "paper" you obviously did not care at all to verify if my claims were valid or not, in spite of the fact that the entire process involved a mere one minute glance through a most basic triangular prism. Even more disconcertingly, however, was your completely baseless and unwarranted implication that since my observation runs seemingly counter to "myriad of other works" it must somehow be nothing but wrong.

Thirdly, you have obviously no qualms whatsoever why my "paper" was not published, yet you are blissfully ignorant of the fact that I asked (in vain) for help and assistance to bring my "paper" in line with the formal requirements and even offered to let my discovery be published simply as an anonymous and authorless news item. Additionally, even though all reputable physics journals proclaim that they are not interested in any incremental work at all, only on new and significant pieces, not one journal out of the 15 or 20 I contacted found the fact that the very first experiment in Newton's Opticks was finally proved (after a mere span of 350 years of hitherto ignorance) to have been decidedly wrong, to be considered as having any new or significant value!

Fourthly, my dear Markus, it is clearly obvious that you (and most likely everybody else in a position similar to yours) are completely unware that the simple and ubiquitous triangular prism is much more than just some optical object that appears to disperse white light into its conglomerate colours. For instance it is also a cheap and simple device that enables an observer to get a clear and unobstructed view of the spatial dimension that is basically absent from one's natural sense of sight--the spatial depth (see attachments).

Regards.

 Figure 25

 Figure 26 

  Picture 22

 Picture 1 

Picture 121

Picture 2

Dear Remus,

I have also explained in the past why especially the rainbow theory is practically beyond any reasonable doubt in its general form. 

I respectfully disagree with your assertion. For a number of good reasons. First and foremost because if the conventional understanding would be correct then the rainbow would be a real image, which in turn would then completely dazzle the eye of an observer.

I don’t know what you mean by that. Image formation is not a concepts or framework that lends itself to the discussion of the rainbow phenomenon. Without going into the details (which are discussed in any given optics text book, e.g. Born & Wolf’s Principles of Optics, or more accessible: Eugene Hecht's Optics), image formation requires a point-wise one-to-one mapping from some object plane to an image plane. In the scenario of the rainbow, all one could reasonably discuss is a highly distorted image at infinity mediated by the mapping in the angular coordinate. See for instance:
p.120 - 122, R. L. Lee, Jr. and A. B. Fraser, "The Rainbow Bridge: Rainbows in Art, Myth, and Science” (Pennsylvania State U.P., University Park, PA / SPIE Press, Bellingham, WA, 2001). (e.g. https://books.google.de/books?redir_esc=y&id=kZcCtT1ZeaEC&q=image#v=snippet&q=image&f=false)

However, even in the approximation of the sun as a point source at infinite distance (which as we have discussed before is a good approximation), this mapping is to an entire polar angular "ring domain”, and a diffuse one at that (there is a caustic with an intensity diverging as 1/sqrt(theta - 42°), and one such caustic for each color). This is what you can see with a flashlamp at home as well. So, if you wish to make the claim that the “image” would dazzle the eye of the observer, I would expect 1) some quantitative discussion (rainbow theory accomplishes just that and is able to predict the intensity of the measured rainbow) 2) some details, sketches and calculations in the framework of geometrical optics (since this is the framework in which precise meanings and definitions of the word “images” have been given) on what image exactly you are talking about.

Since that is not the case I believe that the current theoretical understanding of rainbows is intrinsically flawed. This, incidentally, is an easily demonstrable fact, both theoretically as well as empirically. From a theoretical perspective one has only to realise that if the rainbow would be produced via the conventional way then in effect when it is asserted that the observer sees a rainbow because the sun rays are emitted, refracted and intercepted by his eye in the conventional manner what is practically stated is that when the observer looks at the rainbow he looks, for all intents and purposes, directly at the sun!

You are, with the limitations mentioned above, 100% correct! Still, you entirely omit the aspect of intensity. The rainbow's intensity is influenced by a multitude of experimentally verified factors, the most important ones being 0) solar irradiance of the rain volume / atmospheric scattering & absorption of light on their way towards the rain, 1) rain drop density along the line of sight, 2) absorption & scattering along the line of sight, 3) reflection & refraction coefficients for the ray paths responsible in a given direction (line of sight), i.e. a product of Fresnel coefficients averaged over all polarizations (again, an approximation, since the sun’s light is being polarized by atmospheric scattering, see for instance https://en.wikipedia.org/wiki/Haidinger%27s_brush), 4) rain drop size distribution (see measured and theoretical raindrop-size dependence of "rainbow scattering” → Mie Theory & supporting experiments). All of this has been done in the past, and noone ever reached the conclusion you have (without considering these factors), so you will find sceptics when confronted with your uncorroborated claim. This has nothing to do with your persona, but is rather explained by the lack of confirming evidenc provided on your side.

And for an empirical perspective all one has to do to see that what I'm saying is correct is simply try to put his eye in the path of a ray of light that is refracted in the conventional manner by some 'raindrop'! 

This experiment does not support your claim. In fact, people have measured rainbow intensities and found them to conform with the "classical theories”.

Secondly, if the conventional understanding was correct then the only possible rainbow display would be one arching upwards toward the heavens, instead of downwards toward the ground. This is also an easily demonstrable fact.

No one ever came to this conclusion. I find the geometry of the classical explanation / theory to be in perfect accord with the natural phenomenon and home / classroom experiments. So does everyone else who has thought about it. I really don’t know how else to put it. But either you see something which is inexlplainable and unintelligible to the rest of the world who have thought about the experiment, the explanation and the theory, or you got it simply wrong. By Ockham’s razor and simple probabilistic reasoning, given the predictive success of the classical theory in all quantitative aspects of the phenomenon in the lab and in nature, as well as the satisfaction the theory and explanation gives to the rest of the world who thinks about it, I choose to assume the latter. But most importantly, I do so because it makes honestly 100% sense to me when I think about it independently. In my mind it truly fits snugly and nicely together that the rainbow is an arc around the antisolar point and that an illuminated flask produces the rainbow caustic cone you can intercept by a projection screen. It all fits, to me and to the rest of the world?

All one has to do is observe what kind of caustic is created by the southern part of any typical raindrop refraction. [Of course, the conventional understanding has been periodically altered and tweaked, in order to account somehow for new and inconvenient observations, but the plain and simple truth is that there are now so many inconvenient observations out there that there is no way that they can all be somehow accounted for by the conventional theory, so most of those inconvenient observations are 'discreetly' ignored and swept under the carpet.

You speak of modifications of a theory. What you describe is not a sinister, mean, conspirational plan to conceal facts but the typical progress of science. When and if a better theory is discovered, the old one is replaced. Sort of, although in many instances the old one will remain useful and valid as an approximation, just like the Cartesian theory is still a valid, beautiful and useful theory with its well-understood limitations. I think we talked about the progress of the understanding of the rainbow phenomenon, although it is worth mentioning that you keep being focused and talking about the 17th century theory status of the scientific understanding of this phenomenon since the beginning of our discussion.

Let me give a concrete example; in case you'll try to reply to my argument above by invoking the counter-arguments depicted in pictures 25 and 26 (see attachments) I will ask you to see the Pictures 1 and 2 (see attachments), which thoroughly dispel what is depicted in the 25 and 26 pictures. In fact the plain truth is that there are now so many factual observations of rainbows that not even the most fundamental conventional requirements for the existence of rainbows--like the formerly indispensable Cartesian angle, for instance--are any longer required in order to create rainbows.]

Counterarguments are always welcome. 

I will ask you to see the Pictures 1 and 2 (see attachments), which thoroughly dispel what is depicted in the 25 and 26 pictures. 

I do not see how these 4 pictures should be in contradiction to each other. Honestly.

In fact the plain truth is that there are now so many factual observations of rainbows that not even the most fundamental conventional requirements for the existence of rainbows--like the formerly indispensable Cartesian angle, for instance--are any longer required in order to create rainbows.]

Again, I do not know what you allude to. I do not know of a single observational fact that puts the classical rainbow theory into question (the twinning phenomenon I mentioned before being compatible under assumptions of certain drop-size distributions). Nothing of what I have read or seend from your experiments changed that so far. The Cartesian ray is still a helpful and valid concept in understanding the rainbow. It is true, however, that ray theory got superseded by wave theory, if you mean that? But geometric optics remains a valid and useful approximation.

There are many more reasons, beside those I mentioned, that have convinced me that the current theoretical understanding of rainbows is fatally flawed, and in time I will discuss most of them in my blog. For now though I only want to add to the above the following: even you, Markus, must admit that the current picture of the rainbow phenomena is so cumbersome, so convoluted, so full of holes and so incredibly bombastic and cacophonic in certain parts that it just simply cannot be part of the physical reality we know. Finally, on this subject, please tell me, Markus, why couldn't the rainbow instead be a direct consequence of the observations I recorded in pictures 22 and 121?

As you know, I came to no such conclusion. Noone else did. So again, either you got it wrong or the rest of the world. The latter adhered to the scientific method and produced theories which are falsifiable, testable and quantitative. They are incredibly acurate and have an enormous predictive power that has convinced and compelled the rest of the world. Also, as I mentioned before, it is routinely used as a quantitative analysis tool for liquids in refractomery, and in remote sensing applications for meteorology.

Regarding the pictures, I have troubles interpreting them as you did not attach any description or details for the experimental setup in which they belong. I am sure that they can be explained in terms of geometric optics and will have some relation (in one way or another) to the rainbow phenomenon. As a means of explaining the natural phenomenon, they don’t help me personally.

so much on rainbows… Which I like as you would probably guess from my educationally geared publications on that matter.

Dear Markus, I must tell you that in a stark contrast to the rest of you email I found the paragraph above greatly and disconcertingly disappointing. For the following reasons. Firstly, because it is clearly evident that you have either not paid enough attention to the things I had said in my previous email or, alternatively, that you have just relied exclusively on the statistical figures that appear to show that the vast majority of claims made by non-scientists are wrong and therefore not worth considering by people who think they are in the know.

I am sorry if I have caused distress. I am afraid that it will still remain unavoidable that conflicting opinions of people in a conversation will cause some of it. I am glad, however, that we can cut the unpleasant vulgarities.

I will grant that to me and most likely to many other scientists, the fact that a paper comes from a respectable researcher of a given field will give a certain credit of trust in advance of reading a given publication. The reason will simply be the knowledge that said researcher will have shown in the past to be able to advance science, corroborate any made claims and adhere to the scientific method. However, that being said, any given publication is met with much the same scientific scrutiny as any other. i.e., it is evaluated against the backdrop of the literaure (is it new), its significance (is it interesting / important?) and whether all claims are corroborated by suitable experiments or calculations / derivations. All that is checked first by an editor to sort out all the obvious outliers (flat-earthers, contrail conspiracy belivers, etc.), and secondly by the review process (which is often double-blind!). Every once in a while someone publishes a nice paper without being affiliated with a research institution. Take for instance this recent publication: https://aapt.scitation.org/doi/full/10.1119/1.5075717, at least I belive this to be from an independent scientist. So although you keep insinuating that there is an evil plan to keep people like you out of science, it is rather a filter effect produced by the nonability to adhere to the strict standards of science. They were part of my last e-mail, but in short you first have to show that you understand the current status in the field before you either dispel it or advance it. Then you will have to cogently corroborate every claim you make.

Take for example the second sentence in the paragraph. It is plainly obvious that you did not consider at all the fact that a subjective prismatic observation is not merely and strictly a matter of visual perception--it is also fully confirmed and corroborated by photographic and spectroscopic apparatuses and detectors. Moreover, if your assertion had any truth in it at all then astronomy and spectroscopy should not be part of physics but "of psychology and neuro-science" instead.

You misunderstood me. Spectra are an important tool and source of information in science. But these are measured spectra.

Secondly, even though you claim to have read my "paper" you obviously did not care at all to verify if my claims were valid or not, in spite of the fact that the entire process involved a mere one minute glance through a most basic triangular prism. Even more disconcertingly, however, was your completely baseless and unwarranted implication that since my observation runs seemingly counter to "myriad of other works" it must somehow be nothing but wrong.

It is indeed a probabilistic thinking I was using in part. Importantly: in part. Substantially, I have addressed my concerns on your article in the past, I believe. The fact that it was rejected by as many as 20 or so journals reassures my of my personal assesment at that time that it did not adhere to the scientific method and the requirements discussed above. If I find the time I’ll get back to it if you so wish.

Thirdly, you have obviously no qualms whatsoever why my "paper" was not published, yet you are blissfully ignorant of the fact that I asked (in vain) for help and assistance to bring my "paper" in line with the formal requirements and even offered to let my discovery be published simply as an anonymous and authorless news item. Additionally, even though all reputable physics journals proclaim that they are not interested in any incremental work at all, only on new and significant pieces, not one journal out of the 15 or 20 I contacted found the fact that the very first experiment in Newton's Opticks was finally proved (after a mere span of 350 years of hitherto ignorance) to have been decidedly wrong, to be considered as having any new or significant value!

I think they rather came to the conclusion, as I wrote above, that the claims you made were uncorroborated by the experiments you described, or that the text was not in the language of science and thus unsuitable for publication. Whatever you think you have discovered, you will either need to make it intuitively and unequivocally intelligible (to me it wasn't) or put it into the context of the current understanding and discourse within the expert literature / community. You can also go to conferences and try to find colleagues who share your concerns if you think the valid filter mechanism described above impacted you wrongly (I do not believe so).

Fourthly, my dear Markus, it is clearly obvious that you (and most likely everybody else in a position similar to yours) are completely unware that the simple and ubiquitous triangular prism is much more than just some optical object that appears to disperse white light into its conglomerate colours. For instance it is also a cheap and simple device that enables an observer to get a clear and unobstructed view of the spatial dimension that is basically absent from one's natural sense of sight--the spatial depth (see attachments).

I really am unaware of this. Also, I do not know what you just said. What I do know is that the above is not a scientific statement, so I will take it as an odd phrase. The pictures show some probably nice experiments with a prism. They show refraction and dispersion. I also like prisms and have some at home. 

If you wish to learn about the origins of color dispersion, I suggest a good read about Maxwell’s equations and solid state physics. Eugene Hecht’s book is perfect also for that, and includes a lot of fun home experiments... 

Best Regards, and happy holidays,

Markus

Before anything else let me tell you how back where I come from the common thinker deals with the type of self-assumed superior sods like the Selmke dude. He, or she, starts by explaining that what will follow is a line of reasoning which in Romanian is called "pe babeste". Loosely, that means "like an old woman. Now, although I do not think that I have ever mentioned this Romanian kind of reasoning there is no doubt in my mind that there is an identical type of common wisdom in every other country, culture, or tribe that has ever existed on earth. So, without any further ado let me reply to a few of the objections that have been raised by the Selmke dude above "pe babeste".

I don’t know what you mean... ...on what image exactly you are talking about.

According to the conventional wisdom the rainbow is nothing more than sunlight refracted in a raindrop (as in the picture below) that subsequently enters the eye of the observer.

That, Selmke dude, means that the rainbow is a REAL image that travels from the sun to the retina of the observer! Now, you may invoke and claim that there are a million things that change the particularity of the light that enters the eye of the observer from the specific sunlight at its point of emission, but whatever factors may contribute to that alleged change that you see as all-explanatory I can guarantee you that it should still dazzle the eye of the observer, regardless! How do I know that? I know because I have had the privilege to see it in the many, many experiments I have conducted in order to learn what to believe and what to reject. So convinced I am of what I'm saying, Selmke dude, that I dare you to look directly at a refracted ray of light that is emitted by a source of light whose particular intensity I will let you chose without any objection. Do it, Selmke dude, I dare you! (For the other readers, please have a look at the video below. Incidentally, the source of light in the video was a $2.80 LED flashlight whose AAA batteries were pretty much drained of power.)

Still, you entirely omit the aspect of intensity. The rainbow's intensity is influenced by a multitude of experimentally verified factors, the most important ones being 0) solar irradiance of the rain volume / atmospheric scattering & absorption of light on their way towards the rain, 1) rain drop density along the line of sight, 2) absorption & scattering along the line of sight, 3) reflection & refraction coefficients for the ray paths responsible in a given direction (line of sight), i.e. a product of Fresnel coefficients averaged over all polarizations (again, an approximation, since the sun’s light is being polarized by atmospheric scattering, see for instance https://en.wikipedia.org/wiki/Haidinger%27s_brush), 4) rain drop size distribution (see measured and theoretical raindrop-size dependence of "rainbow scattering” → Mie Theory & supporting experiments).

To a large extent what I have said above applies here as well. To all that, however, it is worth adding a picture as reinforcement. This is still part of the "pe babeste" reasoning, although you'll have to figure yourself what message the picture below conveys, Selmke dude.

I will ask you to see the Pictures 1 and 2 (see attachments), which thoroughly dispel what is depicted in the 25 and 26 pictures. 

I do not see how these 4 pictures should be in contradiction to each other. Honestly.

So Selmke 'honestly' can't see how those four pictures are in contradiction to each other. No problem, Selmke dude, I'll help you with your sight impairment, but I must tell you that there is absolutely nothing I can do about your mental one. With that you'll have to ask God. (Oh, sorry, I forgot you are an atheist, so there's no help for you in that respect. Bugger!)

Let us look once again at (the conventional, hand-drawn, theoretical, non-real) picture 26, below, and then let us compare it the (real, unconventional, empirical, photographed) picture 2, right below the 26.

The difference between the two pictures couldn't be clearer (Selmke dude excluded, of course). In the real picture there isn't even a hint of the rainbow's coloured bands being created in the conventional manner. Instead it looks as clear as daylight that each water droplet changes its colour entirely once it passes through the spectral bands that are obviously created by the sunlight that shines on the water drops! Any other explanation than that is perversely insane, Selmke dude! Let us not forget also that there is not one piece of relevant experimental evidence that the conventional physicists could lay down on the common table to back up their phantasmagorical concoction they call 'a theory that is practically beyond any reasonable doubt'.

In fact the plain truth is that there are now so many factual observations of rainbows that not even the most fundamental conventional requirements for the existence of rainbows--like the formerly indispensable Cartesian angle, for instance--are any longer required in order to create rainbows.]

Again, I do not know what you allude to. 


Have a good look at the pictures below.

They all show rainbows snapped very early in the morning, when the raising sun is basically at the horizon. Let us now see what the conventional theory says about these very early rainbows.

So, according to the conventional theory at that time of the day the primary rainbow should be at a height of 42 degrees in the vault of the sky. A close inspection of the four pictures above, however, (especially with the help of an image manipulation program, like Gimp 2.1, which allows you to measure angles with a great degree of accuracy) reveals that not one of the four rainbows obeys the conventional law.

Additionally, since we are here, at this point I'll ask you to have yet another good look at those four pictures with early rainbows and to try to estimate at what distances do you think those rainbows are from the observer. (I know, the conventional story says that rainbows are at infinity--whatever that means, for they're not referring to the "infinity" photographers are meaning--but we, as common thinkers, believe that rainbows appear where the rain happens to fall relative to the observer.)

Now, staying within the same setup as the one described above in Picture 28, let us consider for a few moments the following consequential facts that the conventional theory unavoidably leads to.

At a distance of 40 km between the observer and the falling rain according to the conventional theory the primary rainbow must be at a height of 27 km and the secondary one at a height of 32.7 km. Alas, the reality is that there are no rain clouds at those heights.

At a distance of 20 km between the observer and the falling rain according to the conventional theory the primary rainbow must be at a height of 14.36 km and the secondary one at a height of 17.44 km. Alas, the reality is that there are no rain clouds at those heights either.

At a distance of 10 km between the observer and the falling rain according to the conventional theory  the primary rainbow must be at a height of 7.3 km and the secondary one at a height of 8.85 km. Alas, the reality is that there are still no rain clouds at those heights...

Secondly, if the conventional understanding was correct then the only possible rainbow display would be one arching upwards toward the heavens, instead of downwards toward the ground. This is also an easily demonstrable fact.

No one ever came to this conclusion. I find the geometry of the classical explanation / theory to be in perfect accord with the natural phenomenon and home / classroom experiments. So does everyone else who has thought about it. I really don’t know how else to put it. 


Since a picture tells a thousand words have a look at the one below without any comment from me.

Incidentally, I bet that the reason behind the so-called Circumzenithal Arc is due to the factors that are responsible for what is depicted in the picture above. Watch this space.

But either you see something which is inexlplainable and unintelligible to the rest of the world who have thought about the experiment, the explanation and the theory, or you got it simply wrong. By Ockham’s razor and simple probabilistic reasoning, given the predictive success of the classical theory in all quantitative aspects of the phenomenon in the lab and in nature, as well as the satisfaction the theory and explanation gives to the rest of the world who thinks about it, I choose to assume the latter.

This is my favourite paragraph from Selmke's email, for the simple reason that he cites Ockham's razor as a philosophical principle, or argument, that is supposedly making the conventional theory more plausible than my own understanding of the rainbow phenomena. Really, Selmke dude?😂😍

Anyway, let us remember what Ockham's razor is, exactly.

Occam's razor (or Ockham's razor) is a principle from philosophy. Suppose there exist two explanations for an occurrence. In this case the one that requires the least speculation is usually better. Another way of saying it is that the more assumptions you have to make, the more unlikely an explanation. Occam's razor is the problem-solving principle that essentially states that simpler solutions are more likely to be correct than complex ones. When presented with competing hypotheses to solve a problem, one should select the solution with the fewest assumptions. (Wikipedia)

Now, since you all presumably  know the main arguments that have been attached to the fundamental framework of the conventional theory of rainbows over the last 700 years, you shouldn't have any problem at all to judge whether the conventional understanding is simpler than mine, which I'll now drop below for your undoubtedly objective assessment.

Before concluding this post I want to tell you a little story about a certain paper written by Selmke Markus, Ph.D. This paper, which you can find here, covers that vitally pressing and truly avant-garde issue of rainbow experimentation with round bottomed flasks! And guess what? It only took the guy six months to write it! Of course, it also goes without saying that some-one, or maybe some-it, found the subject compelling and important enough to reward such significant contribution to mankind's patrimonial future with an equitable reward. Long live the physicists who are not afraid to apply for grants by redoing what had been done 700 years ago! Isn't it stupefyingly odd that in this day and age rainbow experiments are conducted with gear made in the 14th Century? Isn't it even more incredible that the best rainbow laboratory experiments and visual data has been by and large fed online by my own set of optical tools, which I bought from flea-market stalls and discount stores? Some time ago, when I was helplessly and longingly looking online at a decent source of light that was well beyond my penurious pocket I was thinking that if I were given a chance at even a relatively modest sum of money I could in no time at all acquire a hollow spherical ball made out of high quality glass, thin and almost fully enclosed, that I could fill with water and take the most beautiful and accurate pictures of caustics, bows, dark bands and spectral dispersions  the world will ever see. Or, in an even better world, if I was to have access to a bigger amount of money I am quite sure that in less than a year I could develop a domestic apparatus that could feasibly put a miniature rainbow in any household with a love for the beautiful phenomenon. In the meantime though let us revisit for the umpteenth time those 700-years-old flask experiments that are still the bedrock of the conventional rainbows.