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.
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 magnaeupon 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.
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.
