On some of the most important (yet seemingly unknown) attributes of the triangular prism

Today I'm going to show you two prismatic experiments that will reveal some attributes of the triangular prism that I have never seen discussed in any textbooks.

The first experiment involves an equilateral triangular prism (with each side 5 cm long), a camera to record the observations and a vertical marker. See photo below.

To help you get a better understanding of the whole setup please have a look at the figure below.

So, we have a camera facing a triangular prism whose apex is pointing to the right and whose base is on the same line with the camera. I can tell you that the camera is positioned at a distance of 10 cm from the prism, which insures that the entire surface of the prism is visible, and nothing more than that. We have also a vertical marker, which is held in the position indicated in the diagram above by a holder of sorts.  The purpose of this experiment is very simple. In effect, we shall move the vertical marker in 1 cm incremental steps, taking snapshots at every one of them to see what happens. I forgot to mention that, as you had seen in the first picture above, I have taken a couple of measurements of the image of the prism. Those measurements are in number of pixels, which are correspondent with the size of the images used (1800 x 1013).

That's all there is to this experiment, but before proceeding to the first step I'd like to ask you to take a minute or two in order to try to see if you can anticipate what the results will be.

Step 1. The vertical holder is moved to position 1, which is exactly at a distance of one cm from the prism. We take a snapshot and drop the picture below.

Step 2. Photo below.

Step 3. Picture below.

Step 4.

Last step, 5 cm distance from the prism. See relevant picture below.

Okay, these are the results of this experiment, so let me ask you now: Did you in any way anticipate what you've just seen? And if you did, how do you think that these observational results occurred?

For those who did not anticipate those results, and who perhaps are wondering a little about how could they have been generated, I will now show how they have come to be. Please have a look at the illustration below.

At this point I can almost hear some voices saying: "Aaaah, so that's how those images occurred. Big deal! After all we have known for hundreds of years that light expands spherically, haven't we?". I hope that you are not, however, one of those voices. Why? Because if that were the reason per se then we should observe the same results occurring in slabs of glass, not just in triangular prisms. But the plain reality is that we can only see results like those we have seen above in prismatic tools of observation. So, the reality is a bit subtler than some of us tend to think. Before getting into that, however, let me show you another interesting bit of the reality out there. Without any extra commentary please watch the two-minute video below.

For the second experiment we'll use a camera, the same prism as in the previous experiment, and a rectangular piece of paper (5 cm wide and 10 cm long) marked at every cm along its length. (See the picture below.)

First we lay the piece of paper horizontally on a flat surface. Then we position the camera at the same level with the flat surface used upon which our cutout paper is laying, making sure that we leave a fairly large gap between them (in our case a distance of 7 cm separated the front of the camera and the paper).

As you can see in the picture above there is a shelf at some distance behind the paper (at 49 cm, to be exact) upon which we placed a marker of sorts, for reasons that will become obvious in a moment. Finally, we carefully place our prism on the strip of paper, lining it up in such a manner as to perfectly cover the first half (the first 5 cm) of the paper field. Then, when satisfied with the whole setup, we take the first picture and drop it below.

Pretty interesting results, don't you think? Let me ask the same question now, as I did in the first experiment: Do you think you can make sense of everything that is seen in this first picture? Oh, how I'd love to hear your answer, if you had one! But since that is rather impossible (as at the time that I am typing these words, at least) let me try to provide an answer to the story above (which leaves you with the luxury of finding out in the privacy of your own mind if your assumed answer would have been right, or wrong). (Needless to mention, by saying what I've just said implies, rather unashamedly, that I do know what is taking place above.)

Now, there is a lot of information in this first picture, but the truth is that any careful observer should be able in the end to extract it all, really. Nonetheless, the truth is also that the conventional physicist of the last 350 years has rarely, if ever, ventured further than those so-called objective experiments, which have been based overwhelmingly on Newton's own experiments--especially on his experimentum crucis. To the other kind of prismatic experimentation--that which has been dubbed subjective--he (the conventional physicist) barely paid much attention at all, treating it with a rather large dose of condescension and contempt. For that grave error in judgement he has paid, and is still paying to this day, a very high price indeed. Anyway, let us get back to the matter at hand.

What we have captured in the picture above is a subjective prismatic experiment. We've used a camera to detect and record what is basically a conglomerate, an aggregate, a sum, of information that is displayed all at once onto one only screen. The information that is on display, however, comes from three different sources. Those sources are the three active faces of the prism: the front face (the one facing the camera), the back face, and the base face.

Now, perhaps the most amazing attribute of the triangular prism is the fact that in spite of those three active faces being diametrically opposed in spatial orientation, they are all and always visible and on display at the same time. This is a characteristic that is unique to the triangular prism, I believe (but don't quote me on that). To make things easier to explain, and understand, please have a look at the picture below, in which I have added some extra information designed to help us all, in both explaining and understanding what the picture is actually telling us.

The most important thing to take in first is that those three red letters are there because they mark the respective displaying areas for each of the three active faces of the prism. Now I suspect that most of you would be able to accurately identify at least one of the three, which is most likely the C area, showing what's on display on the face of the prism that I had called earlier the base face. But what about the other two areas, do you think you know which one is what?

In fact the answer to that question is relatively simple and straightforward: A is showing the display offered by the front face of the prism while B does the same on behalf of that I called earlier the back face. Every bit of information that is contained in our picture is ultimately due to the interplay that is on display at all times between the images provided by those three active faces of the triangular prism. Some of those bits are easier to see or discover, others are much trickier to find. For instance, in our current picture, from what is displayed in the B area one may not necessarily find easy to determine where the other two numbers (namely 1 and 2, respectively) that rightfully belong to its display are hiding. (Incidentally, they are laying horizontally on the area I marked with a little red arrow, which is visible just below that inverted bit of the 5 that is partially displayed.) Or, in fact, one may find even more difficult to understand how such a sharp reflection as that of the shelf and the marker on it, which is clearly seen in the C area, could possibly be generated by a transparent surface that is sitting on a piece of paper that is lined, marked and numbered at every cm along its centre. A reflection of such quality can only be produced by a high-quality mirror, and in our case it certainly looks like the base face of the prism has managed to do that in spite of its being far from what one could call a high-quality mirror.

The reality is that here are many more issues related to the subject of prismatic experimentation than one could discuss in one post. But a couple of the most important of those issues one should certainly be able to manage, and for the rest of this post I shall try to do just that.

Without doubt the most important attribute of the triangular prism is its ability to gather (and provide for the observer) through its three faces a lot of information, not only from its immediate surroundings but also from places far, far away indeed. One of those uncanny attributes of the triangular prism is its ability to gather information from the third dimension of space, which is normally forbidden to the naked eye, and in the process to also provide the observer with a direct perspective of that information. Alas, that potential observer is certainly not a conventional physicist, for he (alas, again) has forfeited that possibility a long time ago, when he (alas, once more) decided to forever remain a disciple of those prismatic kind of experiments that he had dubbed (alas, one final time) objective. To show you that what I am saying is absolutely true let me give you a concrete example. What you will see below is a direct exchange of emails between myself and a conventional physicist called Dr. Markus Selmke (whose name is surely most  familiar by now to many of you).

Fourthly, my dear Markus, it is clearly obvious that you (and most likely everybody else in a position similar to yours) are completely unaware 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. 

And after reading the above please have a look below at those attachments I had mentioned.

 

Anyway, all I'll add to this little story is that I haven't the foggiest how anyone could offer a more obvious demonstration that what I said about that particular ability of the triangular prism was correct.

Getting back to our current experiment, what I'd like to do next is show you a number of other pictures concerned with this second experiment, in which the prism is moved back and forth relative to the fixed position of the paper strip, in order to see how that changes what will be seen on display. Before doing that, however, I'll show you first a handful of other photos that are related to our experiment, but which have been taken in the context of a different setup, under a different illumination. The first of those five photos is basically the same with the picture we used earlier. Have a look below.

In the second picture below the prism (but not the paper strip) has been moved forward 1 cm. If you look carefully at what has changed in the shown display you should be able to make a good sense of how the prism works.

In the third picture the prism was moved 1 cm backwards from its initial position. Observe.

In the fourth the prism was moved 2 cm forward from its initial position.

In the final picture taken in this particular setup the prism was moved 2 cm backward from its initial position.

Next, I will drop below a quick succession of 14 photos without any commentary, thus tacitly inviting you to figure out on your own under what exact circumstances they were taken.

The triangular prism is much more than an experimental device--it is an amazing tool of observation. It has been known for hundreds of years, and used extensively in optical research for the last 350. It is also a very simple object, and one would expect that after so many years of continuous research and scrutiny man would have managed by now to learn and extract from it every single bit of usefulness, potentiality and information it could ever carry within. But the sheer reality is very far from that, let us not kid ourselves. And since we're here, now, let us become truthful and strong enough for once to point our accusing finger in the direction of the party that's been wholly responsible for that embarrassing, humiliating failure. For, after all, that's hardly any secret, and we know it. Enough with weaving legends and erecting statues for the mortal gods. We've been around long enough to know and do better than that. C'mon!

Before concluding today's discussion, I want to share with you a last couple of important things which are closely related to prismatic experimentation. First, let me show you three more pictures about the second experiment we have discussed today. See below.

  

These three views from above of the objects involved in the second experiment should help us all get an even firmer grip on the subject of prisms and about how they manage to gather so amazing bits of information from their surroundings. Look carefully and notice how each of the two main faces of the prism gathers all the information that's laying beneath the whole base face of the prism.

See then how in the third picture, in which the prism is laying down diagonally across the strip of paper and oversteps its boundaries, the two active faces are still able to collect and transmit all the info data that's on display, including the two bare corners that then become four, due to their own individual displays.

Think then for a little while, and you should understand why those two "windows" of the prism are so truly amazing--for in stark contrast to real windows they are able to give the observer a complete perspective each, of the entire inner ground flooring of the prism. And then, as if that weren't impressive enough already, notice how they both raise and hold their displays at an angle that makes them visible from any vantage point around. Wow!

Finally, please spend just one more minute thinking and you will surely realise that all those amazing things are simply and clearly made possible and accomplished because of one--and that's one only --reason: the mere slant at which the two opposing faces are oriented in the space.

And now, really--truly--finally, let me show you what I didn't when we talked about the real reasons behind the results we had seen in the first experiment covered in this post. (By the way, I am dead tired, so I'll keep it really sweet, quick and short:)

Due to the inherent slant at which the front face of the prism is laying, and in addition to one of its distinctive peculiarities (that which restricts the field of observation to the space that is laying ahead in a direct line and parallelly with its particular plane of inclination--remember our most recent discussion, which is recorded in the paragraphs just before the current illustration above) the only things that would become observable through that front "window" of the prism would be those that are part of the landscape that is delimited by lines that are running at 90° relative to that plane.

That's all I'll say, in words, about that, but in order to make sure that you will understand the point I'm making I have also conducted a relevant experiment, whose visual result is right below, for scrutiny.

Hooroo, I'm off to bed.

About the refraction and dispersion of light in my own universe. Part 2.

(Or why a physicist should be acutely aware of the KISS paradigm and have the same degree of  understanding as that of a master sharpshooter)

The KISS paradigm is an invention of the common thinker, but no physicist should ignore it on that particular basis. The KISS paradigm is fully defined by just one very brief message: Keep it simple, stupid. That is certainly the most frugal yet the most nutritious piece of insightfulness that I'm personally aware of, so I will take this opportunity to reiterate it for those of us that need it more than anybody else. So, to myself, and to anyone else who needs to be at all times fully aware of the wisdom of KISS, let me say it once more before going any further:
                                                 

 Hey, keep it simple, stupid!

Learning to be always aware and mindful of the KISS paradigm goes a long way in becoming a great physicist, but it does certainly not enable one to go all the way to the absolute top. To greatly increase the odds in that endeavour one must also master a complete understanding of the quintessential understanding of a sharpshooter. Let me explain.

A sharpshooter is deeply aware that being able to hit a target at some distance away is hardly a complete and undeniable evidence of an absolute proof about a marksman's particular degree of accuracy at any point in time--including the one when it actually took place. In fact, the reality is that a genuine master sharpshooter will always be fully aware that being able to hit a target at pretty much any distance away will still fall decidedly short of becoming an absolute evidential proof of any particular shooting event, at any conceivable point in time. Let me now explain why that should be so.

One may have a perfectly tuned weapon, a superb 20/20 vision, a freakishly steady arm and smooth triggering finger, as well as a perfect record of hitting the designated targets, but even in such case one should clearly understand that all those things have been possible due to the relatively large degree of tolerance that exists in one's particular occupation. A minimal error at the release point combined with the width of the target may ensure that a hitting event will become reality, which is why a master sharpshooter should never forget the reality of that particular reality.

Conversely, a physicist should never forget that even when one of his particular beliefs appears to hit other targets in his field, that state of affairs still falls short of being an absolute proof about its complete validity. On the sheer basis of that understanding alone a physicist should never begin adjusting and changing the sizes, the positions, or the distances of the relevant targets in order to maximize the apparent accuracy of his forecasts and predictions, for however seemingly warranted such act may be deemed at some point in time, in the long run and within the grander scheme of things that will quickly snowball from a first straw on the back of a camel to the last one that will eventually break its back. Alas, he's already done that, and indeed many a time, on indeed many a case, and indeed in many a subject and field, so by now the world has no other choice but to wait for the time when the conventional zealotry will systematically fail to hit even the closest targets within their aiming sights, which will then become obvious enough factual events to be finally noticed by those that today are just running around in circles, as blind as their catastrophically short-sighted and commensurately overrated army of contemporaneous prophets.

There are two major reasons for which the evolution of the optical physics had reached a dead end many years ago. The first is the incredible rigidity with which the basic tenets of the Newtonian understanding of refraction and dispersion has been adopted and then enforced in all related topics and fields. The second is the sheer magnitude of the fundamentalist zeal that has been the primitive force behind all decision making since Newton's own time in the living Universe.

Needless to say, the subsequent consequences of the unchallenged absolutism with which the reigning establishment has operated and ruled for more than three hundred years have unsurprisingly resulted in a painfully fusty modern world.

Now, let us think for a few moments about the most significant attributes of the Newtonian theory of light and colours. 

1. White light is a homogeneous mixture of all the colours seen in a typical spectrum.

2. Each particular colour of the spectrum has a different degree of refrangibility in a medium.

3. Red has the least degree of refrangibility of all the spectral colours, violet has the highest, and all the other colours have their own particular place between the two.

These are the basic tenets of the Newtonian understanding of light and colours, but they are by no means exclusive. To those three fundamental tenets above there exists an additional and significant number of other theoretical attributes that are playing a role in the optical conventional saga of Newtonian kind. 

One of those, which is to my mind more significant than all the others combined, is concerned with how the spectral colours are distributed within the boundaries of the so-called white light. It is this particular issue with which I'll begin the presentation of my own understanding of the refraction and dispersion of light.

It is pretty much impossible (at least to my mind) to understand how the spectral colours are distributed within the boundaries of a beam of white light. For instance, when we are told that those infinite numbers of monochromatic colours that make up the white light are superimposed onto each other, to my mind that means nothing, really. To other minds, on the other hand, that doesn't seem to create any problem at all, apparently. Take for example the video you will see below in a moment. To the mind of its creator, who is some teacher (I presume) for some sort of Education Institution, which has a You Tube channel called ABC Zoom, not only the problem I mentioned earlier is fully depicted and explained in her three-minute video, but no less than the entire subject of refraction and dispersion in a prism.

Needless to say, any depiction of any thing that exists and is part of the Universe we have come to know and understand (to a very modest extent, absolutely, but certainly to a greater-than-zero extent, just as well) in any shape or form similar to the one that is believed to govern over the nature of light at this point in time makes my blood boil with rage and my mind swing between equal bouts of crying and laughing bitterly in despair.

Where the hell has anyone seen anything, anywhere, anyhow, in the world we know manifesting or displaying an existence like the one depicted in the pictures below?

What the hell does it even mean that an infinitesimal ray of white light is formed by an infinity of different monochromatic colours, which are all superimposed onto each other while they all also oscillate transversally to the direction of propagation?

How can anyone possibly fail to see that absolutely everything in this Universe (every speck of matter, every known force, every bit of space and time) exist and display the same two kinds of distributions, spatiotemporal extensions, propagative manifestations...?

Now, some of you may have realised that one or two issues we touched on today I had already discussed in one of my past posts. If you are one of those people, you'd probably be aware then about how I believe that the spectral colours are superimposed onto each other in a ray of white light.

Thus, firstly I should make clear that according to my understanding the total number of the spectral colours that combine together and, in the process, create the so-called white light is three. And to that I should add that those three are none other than the Red-Green-Blue trio of primary colours. I have decided to believe that on the basis of some good reasons, which will become evident as we'll walk along these pages for the next 4-5-6 weeks.

The RGB spectral components are superimposed onto each other in the manner that I depicted graphically in the two pictures below.

The first picture is actually a copy (albeit, smaller in size) of the one I had shown you in that older post I had mentioned earlier. The second one is in most aspects identical to the first. However, as you can see it does contain some additional information. Specifically, in that picture I have included what I consider to be the relevant wavelengths of the three spectral components, and I have matched them with the actual lengths of their respective illustrations, which are of course expressed in number of pixels.

According to my understanding, then, the blue spectral component of the white light (which in the picture above has a length of 450 pixels) has a wavelength of 450 nm, the green component a wavelength of 540 nm, and the red one of 650 nm, respectively. (Don't ask me why those particular values, yet.)

At this point let me remind you that the vertical RGB bars are meant to be observed through a triangular prism (oriented with vertex pointing to the observer's left) from a distance of about 1 m in the case of the first picture and of about 2 m in the other case.

That's all I wish to say about my understanding of the composition of white light, for now. From here we'll proceed next straight into the subject of how I see the refraction and dispersion of light happening inside a triangular prism. Stay with me, for I am sure that you'll all love the rest of this post. I promise you that without any reservations.

According to my understanding that which we call a ray of white light is actually a tripartite assembly of hues distributed and superimposed onto each other longitudinally, running therefore along and upon the same line with the direction of propagation, or travel. It is because of that reason alone that any observing apparatus (be it a human eye, a spectrometer or an intercepting screen of some sort) will always register a white display of light upon encounter. It is also precisely for the same reason that most monitoring devices we have used in our scientific explorations simply cannot observe that tripartite distribution of colours. Think carefully about that: there is generally not any conceivable way for an eye to see along its own line of sight. True? Well, in general true enough, one could say, but...

But with one most spectacular exception. Which is...??

Which is the optical tool we call the triangular prism.

The triangular prism is the only device I know that offers the observer a visual perspective of what is happening not only on the two-dimensional screen of an eye, of a camera, or of some other detecting contraption, but also about what takes place along the third dimension of space, which extends along the same direction with the observer's own line of sight. 

Of course, there's nothing new about that, as far as I'm concerned. In fact, that is one of the oldest things I learned since my choosing this particular path in life. So, having already written about it more than ten years ago on these pages, today I shall not spend even a minute more discussing it again.

I have chosen the picture above to become a template for the presentation of my understanding of light refraction and dispersion in a prism. I have done so for a number of very good reasons, which we'll discuss quite extensively in this post as well as in the next one or two that will follow. One of those reasons is of course the fact that it illustrates with a reasonable degree of accuracy the basic prismatic setup in which the prism is placed at (an almost) angle of minimum deviation. But I have to tell you that by no means that particular reason was amongst the few that in the end were to become the deciding ones. We'll talk about that in due time, however. For now, let me invite you to the first act of our current journey.

In this picture I depicted how I see the distribution of the spectral colours propagating within the boundaries of the incident beam of white light before entering the prism. There is only one thing that should be clearly understood about that. Simply, that although the distribution of the spectral colours is extending longitudinally (relative to their direction of travel) at this point they still continue to oscillate transversally (relative to the same, of course).

Upon coming in contact with the prism, the wavefront--the leading part of the travelling beam--experiencing an increased resistance in its advance is forced into a commensurate change of direction (of orientation, really) which naturally can only happen in the manner illustrated in the picture. This sudden change of direction means that at this point the RGB spectral components of the wavefront are no longer distributed longitudinally relative to the beam's direction of propagation, but somewhat transversally to it instead. And this new state of affairs comes, quite naturally, with some additional and consequential effect. Which simply is that at this point the RGB trio is no longer oscillating strictly transversally to their direction of propagation, but in effect that they are waving now in a longitudinal direction too. Think about that, and I believe that no one should have too much trouble seeing how the events I have briefly described can quite naturally occur simply because the wavefront of the light had changed its spatial orientation relative to its vector of propagation.

But, if it happened, why it happened, how it happened, and for what reason exactly did it happen--if indeed it happened...

Following the events of the previous act the leading part of the beam is driven onto the typical rectilinear path that is characteristic to the propagation of light, systematically interfering with the atoms of the prism and in the process continuing to adjust its spatial orientation as it advances by following the atomic geometrical structure of the dialectic medium it travels through. The manner in which the wavefront advances within the prism is closely followed and replicated by each subsequent quantum that are tagging close, behind.

As the leading part of the beam is approaching the middle of the prism its spatial orientation relative to the direction of travel is increasingly changing until it reaches a status that is almost perpendicularly lined up with the axis of propagation. Then, after passing that point it begins changing its orientation again, but this time in a direction opposite to the one experienced in the previous leg of the journey.

Finally, the rest of my personal vision of the refraction and dispersion of white light in a prism is quite straightforward and therefore it does not necessitate any additional commentary on my part. It suffices to be illustrated as in the two pictures above. There is neither any need of me to explain the image created by the spectral colours after their exit from the prism.

All of a sudden, I've become so tired that I could fall asleep right here, on the floor, under my desk. It's not so much because I have been working all night--for I am thoroughly and comprehensively used to that. It's rather for some other two most beautiful, most satisfying reasons, which in fact have managed to please and sooth my soul to such an extent in the very near past that I can't help myself from still staying with you for an extra handful of minutes, so I could tell you a few things about that.

Firstly, let me tell you that in the last 6-7-8-9 weeks, or more, I found myself having to go back in time about ten years now, in order to renew and reassert myself again with the works and subsequent polemics created by all the attackers and defenders of those two men called Isaac Newton and Johann Wolfgang Goethe. You see, the truth is that it's been that long indeed since my last genuine foray inside their working minds and hunting territories. It had been, after all, my genuine belief until the recent times, that there was nothing else that I could wish to explore about their respective contributions toward a better evolution of mankind.

To cut a pretty long story a little shorter, it so happened that in the last few weeks I've come to learn that there has been, in the relatively recent past, a pretty strong revival of the debate about to whom of the two mortally sworn enemies of the last 200-400 years should rightfully be given that much disputed and fought over proverbial bone of contention.

Now, according to my mind--and in as far as I have always been concerned--that issue had never been an issue in the first place, anyway. That proverbial bone should rightfully and undoubtedly be given to Newton. To my great surprise and chagrin, however, it has become apparent in the recent times that there is a rapidly increasing number of new Goethean proselytes determined to prove somehow that Goethe's vision of colour and light is at the very least as good a theory as Newton's. And that of course was to my mind a more than sufficient reason on its own to put me back into the saddle, so to speak, for I have never had a doubt that however wrong Newton had been in his optical investigation, when it comes strictly to the reality per se there is no way that Goethe's contribution to the subject could be anywhere even in the same ballpark--let alone on a par--with Newton's.

So, for the last 6-7-8-9 weeks, as I mentioned, I spent my time downloading papers, articles and books that have been written more recently than any other I had known, and read and read one after one after another to see on what kind of actual bases is the newer Goethean following hoping to put their idol onto an equal pedestal with Newton (if not higher).

About that, that will be all, for now. The rest--the meaty part--I will discuss next time, in detail.

Secondly, I want to tell you what happened even more recently than that. In fact, as recently as yesterday, early in the morning.

As I was slowly laying down my own understanding of refraction and dispersion, I was increasingly looking at, and at the same time thinking about, that reflected part of light that is so obviously extending (in the template picture I had chosen) in a vertical direction and at a right angle to the refracted part inside the prism.

I decided to end this post now, even if it admittedly is a little abruptly. Nonetheless, I will pick up this thread again pretty soon. In the meantime, try to think a little about the pictures below. Until next time, hooroo from Down Under.