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