Red and Blue refract in opposite directions in objective experiments too

 

According to the conventional understanding there are two kinds of prismatic experiments: subjective and objective. The subjective experiments are basically understood to be those in which the observer is thought to be interfering with the experiment. The objective prismatic experiments are understood to be those in which the observer is thought not to be interfering with the experiment. Thus, if the experimenter is looking through a prism at a source of light, what he sees is deemed to be a subjective observation. Conversely, if the experimenter is looking at some screen upon which a prismatic image has been intercepted, his observation is deemed to be objective. Furthermore, if the experimenter substitutes his eye with the eye of some recording device, like a camera, the observation thus acquired is still considered to be subjective. If, on the other hand, the experimenter uses a camera to record a prismatic image captured on a screen, the observation acquired is considered to be objective. 

Now, with all these things being said, I want to ask the conventional physicist what kind of observation is the one captured in the image below.

Think carefully before trying to sell me a hybrid story (half subjective, half objective, blah, blah) for there is a prismatic image intercepted by the same screen upon which your so-called objective image is recorded. And if you're still defiant and start concocting other stories to try to justify your position, I will show you even more confronting images that will make your skin crawl with the fear of your time coming to an inevitable end. Images like this

and this

and this

Needless to say, the conventional physicist has treated the so-called subjective experiments much differently than those so-called objective ones. This is of course another Newtonian legacy, and it is a most unfortunate one. Somewhat ironically though Newton believed that the same rules governed and applied to both. In spite of that, however, the reality is that he took little time to examine the subjective observations with the same care as he did with the objective ones. One significant example of this fact is the manner in which he treated the observation that in subjective experiments the spectrum is inversely displayed--VBGYOR, instead of ROYGBV (from the apex of the prism to the base). Apart from mentioning that fact, in passing, he did nothing at all about it. And that failure, again, has reverberated to the present day. To such an extent that today's conventional physicist's 'explanation' for that observation is such a cacophonous verbiage of nonsense that it makes me want to howl to the moon every time I hear it. And believe me, I have heard it so many times over the years...

Newton's failure to treat the so-called subjective experiments with the same degree of care as he treated the objective ones is by and large the main cause for the staggering level of prismatic ignorance that is prevalent today. From the hundreds (perhaps thousands) of examples that I could give you about that fact, in the end I have chosen only one. It is a personal example and it happened a few months back at the Physics StackExchange forum. It began when I posted the question below.

My question attracted two answers.

I don't want to spend any time at all discussing the 'answers' given. That wasn't my intention in the first place for showing you this particular example. The main reason for that decision was to highlight what should be the most valuable insight one should extract from this little piece of factual reality. The overarching lesson of this story is to see that the vast majority of us invariably fail to see that the simplest truths are the hardest to discover. The question I had posted to that forum should have been comprehensively answered in less than 100 words by pretty much anyone who had even a superficial knowledge of Goethe's and Newton's work. So much so, I say, that any ordinary thinker (with even a superficial knowledge of the works I mentioned) should have instantly realised that when it comes to providing a consistent explanation for the observation in question Goethe's wins hands down, beyond the shadow of a doubt. For those unable to see the truth of this matter even now the only thing I have to say is this: I'm sorry that it is I who had to inform you that you're definitely not a thinker. That doesn't mean that you couldn't be a physicist. Quite the contrary, in fact, for to the best of everybody's knowledge, there hasn't been thus far even a single physicist--of the conventional kind, let us specify--who's managed to see that small piece of the bloody truth in the last 350 years. So, I have said, once and for all, but if there's anyone who thinks that he knows better don't cower in the safety of shadows. Come forward, out here, in the open, under the lights and scrutiny of all--or otherwise keep your mouth firmly shut. Forever.

From Newton's theory and Goethe's poetry to the reality of light and colour. Part 2.

In the last post I said at a certain point that I would expect a physicist with Goethean leanings and familiar with my work to confront me with an array of arguments and questions. So, let's begin with those.

Taking into consideration your own explanation of how the Newtonian theoretical understanding, when it is combined with your view that in subjective observations R and B are apparently deflected in opposing directions (whilst, at the same time, G is not deflected at all) can account for all combinations of the observable boundary colours, why do you assert that Goethe's theory of colours cannot achieve that goal itself, when in principle it is identical to it. Effectively, can you tell me what difference there is between the idea that B deflects in a direction toward the apex of the prism, R towards the base, and G stays put, and Goethe's proposal that in a subjective prismatic experiments the object under observation is displaced in the direction of the prism's apex, which in the process creates the known boundary colours due to the overlapping of light over darkness at one end and darkness over light at the other?

Yes, I can tell you what differences (for there are more than just one) there are between my Newtonian explanation for those so-called boundary colours and Goethe's. In order to do that let us look at the picture below, which is a copy of the original picture from Goethe's Theory of colours, as we'll read the cited paragraph below it (which is shown in a different font).

Goethe's Figure G.II.2

If we cause the white disk to move, in appearance, entirely from its place, which can be done effectually by prisms, it will be coloured according to the direction in which it apparently moves... If we look at the disk G.II.2.a through a prism, so that it appear moved to G.II.2.b, the outer edge will appear blue and blue-red, according to the law of the figure G.II.1.B, the other edge being yellow, and yellow-red, according to the law of the figure G.II.1.C. For in the first case the white figure is, as it were, extended over the dark boundary, and in the other case the dark boundary is passed over the white figure. The same happens if the disk is, to appearance, moved from G.II.2.a to G.II.2.c, from G.II.2.a to G.II.2.d, and so throughout the circle.

Ignoring for the time being the parts highlighted in red, the first difference between my Newtonian explanation and Goethe's becomes immediately apparent when we compare his picture and verbal explanation with what would be my own graphical depiction and verbal explanation of a similar observation. See below. 

Now, the plain reality is that to any physicist who nurtures a belief that Goethe's theory is validly describing the nature of light and colour it should have easily become apparent that his explanation of the experiment depicted in the figure G.II.2 is fatally deficient right from the outset. Can you see why that is in fact the case? 

It's all most simple, straightforward and obvious, really. Thus, in effect if Goethe's understanding of this particular prismatic observation were correct, on the one hand the blue area in my diagram should contain the cyan part as well, whilst on the other the yellow area in my picture should contain the red part too. Keeping in mind that our blue Goethe called blue-red, the cyan Goethe called blue and the red he called yellow-red, take a good look at both pictures above, look through your prism at the white circles in both pictures again, think for a while if you still cannot see what I'm talking about, and then, finally, if you're still mystified by what I said in this paragraph please stop reading these pages immediately, for you're not equipped for that task.

Goethe's entire theory of colours rests upon one crucial idea. Which is that in order for any colour to become apparent a source of light viewed through a triangular prism must appear to have been displaced from its original place over a dark boundary. And fundamentally it is precisely here where the entire theory can be shown to categorically fail, as we will demonstrate by the end of this page. To that end we shall now turn our attention to another subjective prismatic experiment from his book.

If we attentively examine these opposite coloured edges, we find that they only appear in the direction of the apparent change of place. A round figure leaves us in some degree uncertain as to this: a quadrangular figure removes all doubt.

The quadrangular figure G.II.3.a, moved in the direction G.II.3.a G.II.3.b, or G.II.3.a G.II.3.d, exhibits no colour on the sides which are parallel with the direction in which it moves: on the other hand, if moved in the direction G.II.3.a G.II.3.c, parallel with its diagonal, all the edges of the figure appear coloured.

Goethe's Figure G.II.3

Thus, a former position is here confirmed; namely to produce colour, an object must be so displaced that the light edges be apparently carried over a dark surface, the dark edges over a light surface, the figure over its boundary, the boundary over the figure.

Now, having cited this particular experiment in its entirety we shall add to it a couple of paragraphs that will help in making the whole issue clearer. See below.

The colour which is outside, or foremost, in the apparent change of an object by refraction, is always the broader, and we will henceforth call this a border: the colour that remains next the outline is the narrower, and this we will call an edge.

If we move a dark boundary towards a light surface, the yellow broader border is foremost, and the narrower yellow-red edge follows close to the outline. If we move a light boundary towards a dark surface, the broader violet (which Goethe had also called blue-red) border is foremost, and the narrower blue edge follows.

And since Goethe's own diagrams are hardly accurate depictions of what the observer truly sees through his prism, below we shall also display a much more accurate rendition of the original picture above.

On the dumbfounding reality that no one's noticed for more than 200 years

Consider the following facts.

Goethe published his Theory of colours in 1810. His book is still in print today, as it has been since its inception. A countless number of people have read it, with the vast majority of those being either professional physicists or philosophers. Thousands of those readers have written thousands of books about it and many of them have made it the principal source of their entire life and fortune. Thousands of physicists have subjected it to a level of scrutiny that is characteristic to most scientists, regardless if they were doing it as disciples or as opponents. Thousands of physicists, philosophers, artists and other kinds of professional people from all around the globe are, as we speak, passionately lobbying either for or against Goethe's theory of colours.

And yet, as a perplexing matter-of-fact, in total spite of all that multitude of factors the world is still bitterly divided over Goethe's theory. Why, people, why is that still the case when I have managed on my own to determine the reality on that matter in a mere handful of very short years? Why?

This is the reality that to my mind is so incredibly dumbfounding that in spite of all the best intentions I can muster I still find the entire issue intolerably inexcusable. And now, with all that being said and publicly recorded, let me show you how easily we can establish--beyond the shadow of a doubt--whether Goethe's Theory of colours bears any scientific validity, or not. Stay with me. 

Remember my earlier remark that Goethe's entire theory rests upon one quintessential idea: That the colours seen in any prismatic observations are direct consequences of the apparent displacement of an object from its original position that is effected by a prism. And thus, since that is the ideam magnae upon which Goethe's entire theory of colours unconditionally depends (and therefore ultimately either lives or dies) a careful and objective scrutiny of it shall be more than sufficient to show us in the end how we all, as the current living world, should present it to those that will come tomorrow.

I'd love so much to be able to see inside your brain at this point, for no longer than perhaps half an hour or so. The reason I would love that is because upon a first examination about how one could definitively prove either the validity or indeed the invalidity of the ideam magnae one may rather easily find that, if pushed in a corner, one may choose to resort to a number of arguments that could really make the task of a would-be prosecutor, so to speak, very difficult indeed.

Let me give you a concrete example of what I'm trying to say. Consider a physicist with strong Newtonian beliefs who would argue that the ideam magnae is purely a concocted story, towards which Goethe had been inexorably driven by his preconceived beliefs and to which he had also added a known and unavoidable observational fact. By contrast, he would continue, Newton's theory of light and colours has a solid physical basis and it was in the end arrived at by adding to that empirical basis only later some logical inferences, which Newton nonetheless continued for many years to subject to a rigorous experimentation. Then, in the final part of his argumentation he could make use of a diagram similar to the one shown below...

...and then he could begin explaining that the picture above depicts what a subjective observation of the green and white rectangles at 1 would reveal to the observer who's looking through his prism oriented with its apex pointing to the left beginning from an initial distance of about 70-80 cm (2) and then gradually increasing the distance until seeing the image depicted under number 5, when the distance between the point of observation and the screen of his computer's monitor would be approximately 3 m. He could then continue by explaining that there is a good reason for using the green rectangles in addition to the white ones, for it can be proven that in subjective observations objects of that colour do not appear to be in any way deflected--or displaced, if you like--by a prism if they are observed against a black background, which makes them perfect points of reference in prismatic observations of that nature. 

To cut a long story short, a Newtonian defender could offer all the arguments I have already discussed in what would be a pretty consistent and compelling presentation about the strong points of Newton's theory of light and colours. For no one in his right mind can deny that there is simply no more persuasive theory out there (which could fully account, as a most pertinent example, for all the colours that are displayed by the white rectangles numbered 2, 3 and 4). Think about that. In earnestness.

Finally, in summing up, a Newtonian defender should point out to the Goethean one the fact that there is, at the very least, one most dubious thing in Goethe's own explanation for the results of a subjective observation. Which is this. 

Now, let's make no bones about it, the plain reality is that even if one accepts the ideam magnae right from the outset and as it really is (meaning without any evidence behind it) there should be not a single doubt about the fact that the entire issue not only looks and sounds bad--it also smells bad (meaning it has the typical smell of a blatant lie). Let me tell you why no one should even dare to suggest that what I've said is not in fact a fact. 

Take first a look with the naked eye at the white rectangle 1 in the picture above, look at it next through a prism (oriented and from a distance as those specified), verify what you have seen is basically what's shown along the sides of the white rectangle 2, and now start reasoning along with me.

If you believe that Goethe's theory is right, when you look at the white rectangle 1 through a prism do you believe that you see those colours because the prism has literally moved the white rectangle from its place to another place? Do you? At this point I see that a great many of you have suddenly fallen into a kind of silent trance. Now, regardless of what your answer really was let me show you next another picture, and then ask you the same question again.

There are many things which to the majority of human brains appear to be absolutely clear and rather obvious, if they're explained by other brains with apparently more knowledge than theirs. Then, there are other things which to a select minority will suddenly get clearly understood and obvious, when a couple of other brains paint different images of that same thing which they had neither seen nor contemplated until then. There are also some things which to some lone brains out there they far too often appear either clearly wrong when to all others they seem absolutely right, or vice versa, for good measure. And this thing, let me tell you, is without question one of those.

To my mind Goethe's ideam magnae (great idea) is so incredibly naive and silly that in many ways I feel like I'm being bullyingly pushed into a dark corner and insolently spat right on the face '"You can think what you want and you may do what you think, but let me tell you that you can never prove that a prism cannot displace a white object surrounded by a black background from its original position--which in the end means that you will never be able to completely eliminate my idea as a possible cause for the colours seen in prismatic experiments". And, in/as/from a strict and most perverse principle/matter of fact/perspective, that is pretty much true. 

But there is always more than one way to skin any particular cat. So let me accept Goethe's ideam magnae without any qualification and ask you to take another look at the picture above. See how much the prism appears to have displaced the relevant part of the metal rod from its true position? That is a big displacement, considering how close it appears to be to that face of the prism. Observe next that the displaced part of the rod is bordered on its vertical sides by the two familiar Y-R (on the right side of the rod) and C-B (on its left side).

Now, at this point I want to ask any Goethean with a solid understanding of the theory of colours if they can provide a sound explanation for the results displayed in the picture above. Especially I'd love to hear how they would link into a consistent explanation the amount of displacement of a refracted object with the widths of its boundary colours, which is a subject Goethe wrote about in his book (albeit, in a very brief and superficial account and a quite vague mode of expression for a writer of his calibre). To my mind it's been clearly obvious for many years now that one of the murkiest parts in both the conventional/Newtonian theory and also in Goethe's is that concerned with the image displacement in prismatic observations. There's also another most interesting fact about that particular issue. That in diametrical contrast to the prevalence of that reality, to my mind that subject was one of the easiest of all to understand, assess, investigate, make sense of and eventually resolve to the extent it uncompromisingly demands from all the other things that come under its scrutiny. This particular subject is very important for a number of reasons, so I will next spend a fair amount of time to discuss its most important attributes and implications.

Many years ago, when I was taking baby steps into the realm of physics and its many territories, I designed my very first experiment in order to verify and determine--once and for all--whether the mainstream theoretical understanding regarding the nature of light in prismatic experiments was true, and therefore correct in assertions. The experiment in question was the one pictured below, and after conducting it I came to my first definitive conclusion. Which was that the conventional theory regarding the behaviour of light in prismatic observations was blatantly and uncompromisingly wrong, and therefore incorrect in all its related assertions.

Can you imagine the reason that had driven me towards what I still believe to this day to have been the right conclusion? In any event, the reason in question was the inevitable consequence of the following line of reasoning. Thus, according to the best of my understanding, if the conventional theory were correct, then instead of the apparent gap that was seemingly created by the prism into the black cardboard held right behind it, in the picture on the left, there should have appeared a black area extending downwards, in the direction of the prism's base. That should have indeed become an observable consequence due to the uncompromising assertion that light rays/photons carry the image along the paths they travel, which are determined by the natures of the media they travel through and from, and which in our case should have been angled in the direction mentioned a moment ago. As in regards to the other picture above, the effect that should have become manifestly evident would have been one of a diametrically opposite nature and extension. I don't think that there's any need of me to say more than that. There is however one other thing that is by far more important than any other conceivably related in some way to our current topic, and that particular thing is certainly worthy of attention, as we'll see in just a moment or two.

There is no doubt whatsoever that the issue of image displacement in prismatic observations is still too hot for the conventional physics to handle, which is a truth that I have known for too many years to even care about these days. Nevertheless, there are quite a few other truths that I have known for a very long time, and let me tell you that about those I've always cared so much that I have dedicated ample time over the years to pay them the attention they deserved and learn how to eventually live with and along them peacefully, serenely, for a little while yet.

About ten years ago I found myself embroiled in some contentious discussions with a number of people who were trying their hardest and best to convince me that I was wrong in basically everything I said. Today, when we appropriately live in the symbolic year for exquisite hindsight, I am in earnestness becoming more aware each day about how and why those many differently coloured events from my past are finally finding their rightful place into my living present. It is a cathartic cliché, but today I don't mind that--for those are, in truthfulness, two words I never used before.

One thing amongst the many I had heard from others is central to the mainstream view concerned with the image displacement in a prism. That particular thing is the ideam magnae at the core of the conventional understanding regarding the topic of image displacement in prismatic observations, and it is encapsulated in the paragraph below.

Although a prism displaces light towards its base, when the refracted light is projected backwards it makes the object appear as though it originated in the opposite direction of this displacement. Consequently, we say that the image created by a prism is displaced towards the apex of the prism. This point is extremely important and worth reiterating: A prism deviates light towards its base and images toward its apex.

And since we know that a picture tells a thousand words, I'll next drop below not one but a couple of them.

I hated the ideam magnae right from the time it came into my world. I hated it, first and foremost, because the message it's proclaiming has always rung inside my ears with a droning semblance of trustworthiness. Which, to my mind, had not one grain of. Then I hated it because in due time I came to realise that for all intents and purposes it was next to impossible to either defend against or to defeat it by using only logical argumentation and by appealing to one's reason. But just hating something bears no fruit and brings no yield. So I stopped doing that, and then gradually managed to extend my outlook and field of vision into the subject I loved................

Anyways, let me start again. 

We have already seen and heard the fundamental basis--the bedrock, if you like--upon which the entire conventional understanding regarding the nature of image displacement in prismatic observations integrally rests and depends. To all that at this point I'll add the diagram below, which comes from Newton's Opticks. The reason I am showing you this particular picture is to emphasise the astonishing fact that in the matter of image prismatic displacement there has been no change at all in 316 years. Now, upon hearing that one may conclude that the most logical explanation for such a long status quo must be a solid and persuasive indicator that the entire subject of image displacement in prismatic observations is correct. "Nothing happened because there's no need of anything else in that matter" one may declare.

The sheer reality about that matter however is poignantly different, as I'll show you next.

Armed with a solid understanding of the conventional theory concerned with the nature of image displacement in subjective prismatic observations we proceed to examine the picture below.

It shouldn't take long at all to see that the image displacement in this picture could not have been in any shape or form caused by the spatial orientation of the camera that took the picture. That's assuming that you have read all my pages and understood what I've been talking about. But the reality about that possibility is, more than likely, very unlikely. In view of that I decided that for the rest of this post I will try to link my present work with that of the past (which means that this particular post is going to be rather long, and that it will take quite some time to lay it all down as such).

There are a number of very good reasons behind my saying that it shouldn't take long to conclude that the conventional theory is definitely inadequate to account in a coherent and cohesive manner for the results observed in the subjective experiment pictured above. Before starting in earnest to discuss them though I'd like to point them all out for you and thus give you a chance to try to anticipate on what kind of ground and foundations have my beliefs been built. And I'll do that by using the means shown below.

So, in the upper part of the picture I have highlighted in different colours the parts of the image where the eye of a keen observer should notice visual anomalies, so to speak, which if properly assessed and understood can point out and lead the investigator to some of the most sought-after answers in the field. Nevertheless, in reality things are of course always easier said than done, which means that in order to have any chance of resolving in that way some complex matter one needs much more than just a keen eye and a Ph. D. But let's not waste our time in discussing those kinds of peripheral issues.

I want you to look first at those two-line segments in the picture, and try to think in what way could they be connected. I personally first thought about that little subject many years ago, and I am quiet proud to know that I elucidated fully, on my own, and beyond the shadow of a doubt. Incredibly, I've never ever seen that topic being discussed or mentioned anywhere at all, at any point in time. The subject I'm referring to is the perhaps most obvious prismatic peculiarity. See below.

Why is the base of the prism so clearly on display for the observer's eye when by all known accounts it simply shouldn't, couldn't, wouldn't. Right? Wrong. Obviously. To my mind then it became right from the start imperatively necessary to find out asap via what processes or factors does that particular aspect of the prism become an absolute matter of fact. In the end, I can assure you that the answer to that question turned out to be rather easy to uncover, as you will see in a moment.

The reason behind the fact we are discussing is straightforwardly simple, and you should be able to deduce it (if you don't already know it, that is) as soon as you take a good look at the picture below.

Every conceivable subjective observation through s prism is determined by the interplay of the two active faces of the prism, which due to their particular orientations enables the observer to get a perspective of whatever there may lay along the spatial dimension that is normally forbidden to the naked eye. I'm talking here of course by what we call the third dimension of space--its depth. Thus, in our case the base of the prism becomes visible due to the inclination of the face of the prism, which virtually is a window that is facing at an angle the floor, if you want. And this is also the real reason for which there is a displacement of objects viewed through a prism toward its apex. I'll give you now a few moments to think about that while looking at a beautiful depiction of that process in the picture below.

It certainly is an idea the brain accommodates very comfortably, for when it's analysed by using the common sense as a yardstick it passes all the tests with flying colours. But it's not only satisfactory to that kind of scrutiny. It is also successfully passing the more stringent demands of a scientific investigation. Consider for instance this particular line of investigation. Can the idea put forward here account in some quantitative measure for the observable results of all relevant subjective experiments? The answer is yes. One concrete example could be the one I offered many years ago, which was depicted in the picture below.

I took two 45⁰ prisms (of the size specified on the left) and after placing them as shown in the picture on the right I drew two lines that should indicate the exact amount of displacement the observer would see, if the idea at the centre of the issue was correct. Then in the middle of the picture I placed a diagram that depicted the entire line of reasoning from a geometrical perspective.

My understanding of our current topic of discussion meets all the demands required by what we call a good scientific theory. (That is a realisation I only began to see in the relatively recent times, after many years of a chaotic struggle with things I didn't know and within an inhospitable and unfamiliar environment that I didn't understand.) It is a good theory for a number of reasons, of which the first and foremost is the fact that it is fully verifiable. And that is, as I nowadays understand, the quintessential attribute of a good theory. By contrast the long reigning conventional understanding is far from being a good theoretical view of the phenomenon of image displacement in prismatic observations. That's because, let's be frank about it, it does not offer any direct means for a quantitative verification. (Which, by the way, is the same crucial flaw in Goethe's vision of the colour phenomena.) A simple examination of the textbooks on the matter will immediately reveal that fact. Indeed, when I first started reading the conventional textbooks in physics, I was stunned to see the virtually total absence of mathematics in their presentation of the subject, which is a very rare occurrence, as we know. But if that was the first event that had struck me as highly odd, soon enough a second one I came to learn about proved to have even a more astonishing effect on me.

These two diagrams are official depictions of the conventional understanding and they can be seen in numerous places online. (Check out OptiCampus.com for example.) Nevertheless, the message they are conveying is manifestly--and easily demonstrable--incorrect, wrong, false and untrue. Yet beside myself I have never seen anyone else do it (demonstrate it).

I did it on a few occasions over the years, and in a number of different ways. For instance, the first couple of times I did it by using the experiment depicted in the two images below.

Let me briefly explain what the two pictures are showing. I first drew a line across one face of a prism at exactly halfway, then I began to slowly turn it around and observed how the image of the line was moving at a higher point in the direction of the apex. My argument against the conventional understanding then was that I did not have to adjust the line of sight of the camera (or mine as an observer, for that matter) in order to notice the apparent displacement of line's image, which is clearly evident in the pictures I took. In effect I therefore proved that the observer does not have to place his eye in and along the line of refraction to see the displacement of an image in a prism.

Then on another occasion I used the experiment pictured below.

Taking as point of reference the well-known effect of the total internal reflection of light in a 45⁰ prism, I drew a line across one of the straight faces of such a prism at exactly the halfway mark (as shown in the middle picture above) and upon rotating the prism around I saw that in total contrast to what an observer would have conventionally expected, the image of the line was still displaced in the direction of the apex. And since this yet another observational fact that flies right in the face of the conventional teachings we feel quite entitled to say "There's something rotten in Denmark, my people".

This experiment, when it is combined with its complementary counterpart below, provide the most eloquent evidential example sustaining my understanding about the real causes behind the phenomenon of image displacement in prismatic observations.

On the inclined face of a 45⁰ prism I drew a horizontal line at the halfway point. (Left picture.) Then, without changing my line of sight, I turned the prism around and looked at it with its straight face in front. (Right picture.)

The result of such experiment is that the observer will see the image of the line in the same place, along the middle of the prism. In other words, there is no displacement in this case. An obvious question then arises that demands an unambiguous answer. Why is there no displacement observed in this case when in its counterpart there definitely is one? The conventional understanding simply cannot answer that question. In fact, it fails to provide a consistent explanation for either. The conclusion is clear, straightforward, direct and in the end definitive: The conventional understanding cannot answer that question. According to my understanding, on the other hand, in the first case of this two-fold experiment there is a displacement of the image of the line toward the apex of the prism because the observation is carried out through an inclined 'window', whereas in the second case the observation is conducted through a 'window' that is straight, which really means that it has a spatial orientation running parallelly to the spatial orientation of the observer.

This post is turning out to get much longer than I had anticipated. So, in the interest of everyone concerned, I have decided to conclude it here and continue the presentation of my work in the next post, which will be Part 3 of the titled subject. See you then.

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.