The most fundamental issue is that if you shine a large light source through a prism, you will get a bunch of overlapping images of the source in each color. If the spectrum is projected onto a screen close by, you will get red images at one end, violet images at the other, and in the center the images will overlap and produce white. Newton's spectrum is NOT an ellipse but an oblong of overlapping circles.
This, incidentally, explains your "paradox" of the white rectangle with colored fringes. When you split the rectangle in two with the pen, you get two large white sources, and on the screen each has a red and a violet fringe. The fringes fall on the black background where they're uncontaminated by competing light. In the middle the images of all the other colors overlap to create white.
So the only way to get really pure colors is to use a tiny source like a star. Since the spectrum of a prism is perpendicular to the length of the prism, a thin slit parallel to the length of the prism will also give a pure spectrum. Spectroscopes do this. Now there is a little overlap since the slit has finite width, but if the slit is very narrow it doesn't matter.
So let's say we have a very narrow slit allowing sunlight to pass through a spectrum and project on a screen to give a fairly pure spectrum. Violet light bends more, red less, so we have a spectrum with red on top and violet below. If you put your eye in the beam of colors you'll see just one color (actually a narrow range of colors). Let's say you put your eye in the green part of the spectrum. You'll see only green. The red light is hitting above your eye and the violet below. To see red light, we'd need a second slit positioned so its red light hits your eye. Since the red light from the first slit is hitting too high on your face, we need the second slit positioned below the first slit. And to see violet light, we need a third slit above the first one. So to get all three colors, we need three slits, and you'll see violet on top, green in the middle, and red below, just the opposite of what you see when the spectrum is projected on the screen. When you look at the sun through a prism, the violet and red parts of the spectrum come from different parts of the sun. Projecting on a screen and seeing the whole spectrum with your eye at once are two different geometrical situations.
I do think it's fitting to call the visual spectrum "Aristotelean." He had so many other things backward, why not a backward spectrum? And yes, I've been reading Aristotle.
There are numerous places on the text page links that confuse the physiological response of the eye or the photographic response of film with the spectrum itself. The fact that colors look different depending on the background is a physiological and neurological question, not one of physics. Goethe's "magenta" comes from overlapping the red portion of a spectrum and the blue portion of another, so of course it's not part of Newton's spectrum. Most colors are mixtures rather than pure colors.
I can't say too much more since I will be out of the office for a couple of weeks.
Steve Dutch
When I read this email for the first time I was furious. It was evidently clear that the man had hardly skimmed through my pages, before reciting some parts of the conventional theory like a litany. His reply was an affront, and I couldn't believe that someone who had expressed himself so eloquently in that “Note to visitors” would show such ordinary intellect when confronted by what probably appeared, to his gargantuan arrogance, like a questioning of God's marvels by a mere mortal. But then I remembered Leon Lederman's warning that a Ph.D. is an even less reliable measure of smartness than a Nobel Prize, and my fury eased. That's why I'd decided not to reveal this Professor's name until now, and that was also the reason for not elaborating too much (in the pages you've read so far) on the only reply I received from a real conventional physicist. And everything would have remained like that—were it not for that “explanation” I'd received from schrodingasdawg. Indeed the reason for my change of heart was my realisation that between those two replies, there wasn't much difference!
For those ready to look for stones at this point, let me explain what I mean. Schrodingasdawg's answer should be easy to be properly assessed by any of my ideal readers—so I'll not dwell on that. It suffices to mention that his “explanation” is not only manifestly incoherent—it does not use the Newtonian reasoning at the base of the conventional theory, either. The Professor's answer, on the other hand, uses the Newtonian concepts upon which the conventional theory is based, and if you have complete faith in the conventional theory you'll naturally tend to believe—even without a proper analysis—that the answer in his email must be correct. But, if you're one of those, keep reading, for you will have a beautiful (two-fold) experience. Firstly, you will realise—beyond the shadow of a doubt—that the conventional theory cannot answer any of my three challenges. Secondly, you will also realise that the apparent eloquence of the conventional explanation about what happens in prismatic experiments will suddenly begin to stutter, and then get totally incoherent, when confronted with prismatic set-ups which Newton (and his followers since) have omitted, or failed to consider. In what follows, then, I will take each point in the answer written above in red and I will analyse its merits, before leaving you the task of deciding upon its validity.
Before doing that, however, I will briefly repeat—for those who mightn't have watched my videos on YouTube—the three challenges I presented for any conventional physicist out there.
Challenge number one. It is a known observational fact that if one substitutes the screen in the basic prismatic experiment with a human eye (or the eye of a camera) the order of the spectral colours is reversed (from top to bottom). In effect, the spectrum projected on a screen has the ROYGBV composition, while the spectrum seen by the naked eye (or by the eye of a camera, etc.) has the VBGYOR composition. (See photo below.) My challenge: Use the conventional theory to explain how this observation is possible.
Challenge number two. In the basic prismatic experiment (with a small difference, which I'll mention in due time) where the spectral image is projected onto a screen, I interfere with the beam of light between the source and the prism, creating different images on the screen. (See photos below.) My challenge: Use the conventional theory to explain the coloured bands on the screen.
Challenge number three. In the basic prismatic experiment I block certain coloured bands after the beam of light emerges from the prism and yet I manage to create new bands of the colours I blocked. (See photos below.) My challenge: Can the conventional theory explain this observational fact?
These are the three challenges I presented on YouTube, and if you remember in my email to Prof. Dutch I invited him to explain, by using the conventional theory, their observations. Professor Dutch, however, did not provide specific answers to my challenges. He chose, instead, to offer an overview of my whole understanding on this topic as it was presented on my website. Interestingly, in his email he gives the impression that he answered my challenges too, although it will become clearly obvious that he completely misunderstood the first, could not see the subtlety of the second, and thoroughly ignored the third. But I will talk about these issues a little later. For now let me analyse each point in his email, beginning with the first one.
The most fundamental issue is that if you shine a large light source through a prism, you will get a bunch of overlapping images of the source in each color. If the spectrum is projected onto a screen close by, you will get red images at one end, violet images at the other, and in the center the images will overlap and produce white. Newton's spectrum is NOT an ellipse but an oblong of overlapping circles.
Let me begin with the last sentence in this paragraph. It is true that according to Newton the shape of the spectrum produced by a beam of light passed through a prism placed at minimum deviation is an oblong, which he believed to be formed by an indefinite number of overlapping circles. (I have talked about this in detail.) Nevertheless, in situations where the prism is not set at minimum deviation the spectra produced are elliptical, and since Newton's theory is supposed to account for all prismatic experiments the sentence above is quite inconsequential—even if it's, strictly speaking, correct. Observe, for instance, in the photos below the shapes of the spectra produced by three perfectly circular sources. (In none of the three examples the prism was placed at minimum deviation.)
The really interesting aspects of the email start with the first sentence: “The most fundamental issue is that if you shine a large light source through a prism, you will get a bunch of overlapping images of the source in each color. If the spectrum is projected onto a screen close by, you will get red images at one end, violet images at the other, and in the center the images will overlap and produce white”. What Professor Dutch is doing here is offering an explanation for what is seen in the photo below, which is part of challenge number two.
Now, I have to tell you that I did not use a large light source—I used a pinpoint source with a diameter of about 1 mm. The reason that no beam of light is observed is due to the fact that I did not use a lens to collimate the light. The field of light, therefore, had a conical shape with its tip at the source. This fact does not impinge at all on the Professor's explanation (in fact it helps with visualising what is described verbally). In the photos that follow I have depicted graphically everything Prof. Dutch said as a way of explaining what is seen on the screen. Thus, the first sentence (“The most fundamental issue is that if you shine a large light source through a prism, you will get a bunch of overlapping images of the source in each color”) is depicted in the photo below. I trust that there's no real need to explain how the photos depict graphically what the Professor said verbally, but where I will consider necessary I will, nonetheless. In the photo below, for instance, the coloured circles represent my source (which was perfectly circular), and they are overlapping. The size of the circles matters only in the fact that it is larger than the prism itself, which is indeed the case. I must also say that I have drawn six circles (in the spectral colours ROYGBV), although I will not argue the issue of how the conventional theory could explain why there are less colours observed on the screen.
“If the spectrum is projected onto a screen close by, you will get red images at one end, violet images at the other, and in the center the images will overlap and produce white”, says Professor Dutch next. The message is clear, even though it's quite abbreviated. I will be more precise, however, and I'll begin to account for the colours observed one by one—starting with the red. Below there is a photo onto which I've drawn the image of my source in the spectral red. Spend a bit of time thinking about how the red photons are refracted at a certain angle, and keep in mind that at this point the image on the screen would be represented by a red rectangle, which is really a graphic representation of the image of the prism projected onto the screen (see figure below right).
Next, let's think about how the orange circle (which is the image of the source in spectral orange) could fit into the previous image in order to account for what is seen on the screen. The most important thing is to understand that the orange photons are refracted a little more than the red ones, and in order to leave the band of red on the screen unaffected the orange circle should be refracted so much that its upper part would be right below the red band. You know what I mean? (Think about it, it should be easily understood.) If that were the case, however, there would be other problems that the conventional explanation would have to answer (like the curvature of the circle, which is not observed in any of the colours displayed on the screen). But I will not make a case out of this. I will simply say that at this point the image on the screen will have a red rectangle, with a smaller orange rectangle incorporated like in the figure below right.
The rest of the spectral colours follow the same line of reasoning, and below I have depicted them in the same manner. Beside each photo there is also a figure showing how the image on the screen evolved.
And now, if you've understood and followed the conventional explanation and the process I've used to verify if it's empirically valid, you should have no problem at all seeing that it cannot account for the image on the screen. That's because the image formed by the conventional theory could not have the blue and violet fringes! Indeed, according to the conventional explanation the image on the screen should look very much like the figure below. Should I explain why? No, I didn't think so.
(I must mention here, for those willing to split hairs, that the image above would only result if the concessions I made were possible. In reality that is impossible, and therefore the image that would be projected onto the screen would be a completely white rectangle, devoid of any colour. If you understood what I have said on this topic you won't have any trouble understanding why the image projected on the screen should be a white rectangle in my second challenge.)
This is what Professor Dutch has missed in his so-called answer to my “paradoxes”. He obviously did not think about my challenge at all—he merely repeated what the conventional theory says, being undoubtedly convinced that the theory can account for all possible observations. Well, the conventional theory is flawed, and badly so. In fact there are so many things wrong with the conventional theory that it fails in numerous other cases (some of them you have seen in the pages I've written so far, others you will encounter soon). In his email Professor Dutch continues with the same explanation as a way of answering my second challenge. Thus he says: “This, incidentally, explains your "paradox" of the white rectangle with colored fringes. When you split the rectangle in two with the pen, you get two large white sources, and on the screen each has a red and a violet fringe. The fringes fall on the black background where they're uncontaminated by competing light. In the middle the images of all the other colors overlap to create white”. With the arrogance of ignorance he wrote, quite pejoratively, '...your “paradox”'. Naturally, the same problems I've discussed above are plaguing the conventional explanation used to account for what is seen on the screen when I split the beam of light with a pen. (See example below.) Fortunately, I don't have to go through the conventional explanation again—for everything should be clear now.
The next two paragraphs in the email are concerned with providing an explanation for my first challenge. Alas, they are utterly incomprehensible. Three things are clear enough, though: Professor Dutch had never performed that experiment, he (more than likely) wasn't aware that Newton himself knew about this observational fact, and he did not have (quite naturally) any idea about its cause. To try to make some sense about his “explanation” would be a tiresome task for no gain at all—so I'll pass. But I will recall it below, for it is a genuine pearl.
So the only way to get really pure colors is to use a tiny source like a star. Since the spectrum of a prism is perpendicular to the length of the prism, a thin slit parallel to the length of the prism will also give a pure spectrum. Spectroscopes do this. Now there is a little overlap since the slit has finite width, but if the slit is very narrow it doesn't matter.
So let's say we have a very narrow slit allowing sunlight to pass through a spectrum and project on a screen to give a fairly pure spectrum. Violet light bends more, red less, so we have a spectrum with red on top and violet below. If you put your eye in the beam of colors you'll see just one color (actually a narrow range of colors). Let's say you put your eye in the green part of the spectrum. You'll see only green. The red light is hitting above your eye and the violet below. To see red light, we'd need a second slit positioned so its red light hits your eye. Since the red light from the first slit is hitting too high on your face, we need the second slit positioned below the first slit. And to see violet light, we need a third slit above the first one. So to get all three colors, we need three slits, and you'll see violet on top, green in the middle, and red below, just the opposite of what you see when the spectrum is projected on the screen. When you look at the sun through a prism, the violet and red parts of the spectrum come from different parts of the sun. Projecting on a screen and seeing the whole spectrum with your eye at once are two different geometrical situations.
You gotta love the last sentence above... And now, to the last couple of paragraphs:
I do think it's fitting to call the visual spectrum "Aristotelean." He had so many other things backward, why not a backward spectrum? And yes, I've been reading Aristotle.
There are numerous places on the text page links that confuse the physiological response of the eye or the photographic response of film with the spectrum itself. The fact that colors look different depending on the background is a physiological and neurological question, not one of physics. Goethe's "magenta" comes from overlapping the red portion of a spectrum and the blue portion of another, so of course it's not part of Newton's spectrum. Most colors are mixtures rather than pure colors.
In regards to the first paragraph I can only say “Congratulations”! The next paragraph, however, shows that Professor Dutch did not read my pages, for if he did he surely would have seen that I debunked the myth of eye's subjectivity. After all it is absolutely clear that I can explain every observational fact seen in subjective prismatic experiments by using the same—simple and coherent—line of reasoning. It is absolutely clear, as well, that I can predict with 100% accuracy what, where, and how, the spectral colours are displayed in any subjective experiment. These two facts cannot be denied. No conventional physicist can do that. I know that, and some of them know that too. Finally, the reference to the magenta shows once again that Professor Dutch did not care to read my pages at all, for his comment does not refer to anything I have written about it. As for the last sentence of the paragraph, I bet that the number of pure (primary) colours is, according to Newton, at least as large as that of the secondary colours. But, clearly, Professor Dutch has no idea why (according to Newton's theory) that must be so indeed.
If I only managed to get one reply from a conventional physicist, the American lady who had written to me about her obsession with the inverted spectrum had more luck. In the month of January 2010 I received a great number of emails from her, in which she was informing me that she had written to a number of physicists—mainly professors specialised in optics—and that quite a few of them had replied to her request for an official explanation about what causes the inverted spectrum seen in subjective experiments. Curiously, a few of the physicists she had contacted were not aware of the phenomenon! A couple of those she had written to were so helpful, on the other hand, that they offered her their cell numbers (presumably for a thorough analysis), although I have no information about how that most kind gesture eventuated. The most important thing I was to learn from her, however, was that a few of those contacted had apparently expressed their belief that the explanation developed by the lady was the correct one. Now, the truth is that I wouldn't have believed that if I did not see with my own eyes that at least one such Professor (from Berkeley, of all places) indeed replied unambiguously: “I think your answer is correct”. (I forgot to mention that the American lady—who asked me not to divulge her name—had attached to each of her requests a diagram depicting her explanation.) Having seen the diagram myself I could not believe that a physicist (any physicist) would possibly agree that that “explanation” could be correct. But I was definitely wrong on that. Professor Charles Schwartz (Berkeley, if you can believe it...)thinks that that “explanation” is correct. With such a backup, as you can imagine, the American lady found this opportunity too hard to resist, and in a couple of long emails she began to speak in statements, to fraternise with me about how it feels to be wrong, to mention in passing that she knew that certain things I misunderstood, to express her sympathy for the fact that I had worked so hard for nothing etc. etc. And that's when I decided to show you that explanation (not “explanation” because now it has credentials).
Naturally, I sent the American lady an email: “I'll discuss very soon your explanation for the inverted spectrum on my website. Keep you posted”. Two days later I have three or four emails. I am informed that the explanation is not entirely hers. (That's the only thing I really remember, although there were other things written in those emails.)
Anyway, below is the diagram with the explanation.
Now, there are a couple of things missing from the figure above. Specifically, an eye looking at the correct angle, as it was specified in the second thing missing (which was an instruction: “Please be sure to look through the correct angle obviously the opposite angle will be reversed”). But, of course, it is rather easy to figure out that the correct angle is the line that travels through the middle of the two spectra. I should also mention that adjacent to the above figure there was another picture, meant to clarify that there is a real light globe and a virtual one—with the virtual one being displaced as in the main drawing. There's no need for that picture, however, to understand what the explanation says, just there is no need for the eye to show us the correct angle.
Before anything else I want to say that I loved the missing statement in the drawing, especially the second part... “obviously the opposite angle will be reversed”. Obviously?! You gotta be kidding! We have discussed how a beam of white light conveys the image of the source in all spectral colours. Professor Dutch was correct in his description, and that description is the right description because it satisfies the most important criterion: that description renders the light white. Were it any other way, the light would be any other colour but white—in the most extreme case displaying the full array of spectral colours, precisely how such case is depicted in the drawing above, where the light is really a spectrum magically dispersed without a prism. You know what I mean?
But there are other things wrong with the “explanation” too, things I shouldn't even care to mention. Only someone who has performed the experiment numerous times and in many ways could be aware of those things. I say that because, for instance, you do not have to look strictly through the “correct” angle to see the inverted spectrum, because you can see it from different angles—which is a fact that eliminates by itself the “explanation”. Not only that, you should also know that you do not have to look at a strong source of light (necessary by the “explanation” in order to produce a spectrum after passing through the prism). You can look at a white piece of paper with a minimum light (that means that there is no beam of light to create a spectrum after travelling through the prism, which also invalidates the “explanation”) and you'll still see an inverted spectrum. Or, you should also realise that if you use a camera exactly at the “correct” angle, you will never be able to make a photo like the one below left. That's because you'll invariably hit one of the colours of the continuous spectrum. Think about it, and see the rest of the photos below.
Leaving aside the rest of the things wrong with the "explanation" (for there are even more of them), I want to answer the most important question on this topic : Can the conventional theory provide a clear answer to the inverted spectrum observed in the so-called subjective experiments? The simple answer to that question is “No”. If the conventional theory could have provided an answer, chances are that Newton himself would have found it. After all, he was the creator of the theory, he knew that the inverted spectrum existed, yet he failed to offer an explanation (even when directly confronted by Lucas). It should be manifestly obvious that Newton would have loved to explain that observation, but that his own theory deprived him of any chance of finding an answer. But what about the many generations of physicists since? Why hasn't any of them seen what I have? The answer to those questions is also simple, and it's clearly evident from the attitude invariably displayed by those physicists I have contacted. Indeed, it is manifestly evident that all physicists I (and the American lady, for that matter) have contacted did not even consider the possibility that the conventional theory may be flawed, venturing instead into concocting some 'on the run' “answers”—which, in the end, only managed to uncover their prejudice, arrogance, ignorance and lack of wisdom. Of course, there's nothing I can do about their own actions, or in-actions, but I can certainly continue my work and develop new strategies that—hopefully—might force them one day to come out and defend their moribund theories. In the meantime I will make public the names of those I have contacted and of those who offered answers. Below you'll find such an answer, offered by another physicist who answered to the American lady, Kurt Gibble:
The prism deflects blue light more than red light. When you look at the light on the wall after it has passed through the prism, this is what you see. That's the easy one to visualize. Now, if you look through the prism, the blue light from the object was deflected by a larger amount than the red. Of course your eye (brain) doesn't know that blue is refracted more than red. Assuming both were deflected the same, then it appears that the blue was actually on the other side, reversed as you say. In optics, the image on the wall is called a "real image." The light source that you see when looking through the prism is a "virtual image." There's a page on Wikipedia about virtual images and lenses - it might help a little.
Now Kurt, what on earth do you mean? “... if you look through the prism, the blue light from the object was deflected by a larger amount than the red.” Kurt, if you look through a prism the blue light appears along the top of the “object”! How could it have been deflected by a larger amount than red, which appears along its bottom?! I love, nevertheless, your profound insight that the brain doesn't know that blue light is refracted more than red, even though you lot have been brainwashing the world for three and a half centuries that that is the case!! One would think that at least some brains would have learnt that by now! Write to me if you're offended by my assessment of your “explanation”, and prove that you know what you're talking about, because so far you've only been speaking in tongues.
Today I have become aware of another explanation for the so-called reverse spectrum observed in the basic subjective prismatic experiment, and although it is identical in principle to the explanation I've already discussed (the one backed up by Professor Schwartz, from Berkeley) I'll show you this explanation, too. The reason I'm doing it (even though the arguments I mentioned in relation to the other “explanation” apply here just as well) is because the new explanation comes with seemingly relevant conclusions provided by the author—beside a diagram. The author, by the way, is a Ph.D. who works for a major university research laboratory in infrared optics, and who offers answers to general questions in optics at www.allexperts.com. His, or her, nickname is Optics C. Without any further ado, let me show you the questions and answers he offered.
Physics/Answered Question
Expert: Optics C
Subject: Reversed spectrum
Question: Why does the spectrum reverse when you look at the light source through a prism? When the light shines through and hits the wall or paper the blue is through the thickest part of the prism but when you look through the prism you see the red at the thickest part. I know that there is displacement of the object or light source but how does the displacement cause the spectrum to reverse?
ANSWER: I tried to think about this one for a while, but the reason is clear when you draw the rays in a diagram. Yes, blue light is bent more than red light by a prism. Thus, the blue part of the spectrum is on the thicker side of the prism.
When you look through the prism, you are mapping the space behind the prism to a "virtual space" that is affected by the dispersion of the prism. This is easy to do on paper. Draw a line from the object (say, a point of light) to the prism, then draw "red" and "blue" lines from the prism to a screen. Now, draw the red and blue lines backwards, as if there were no prism present. The lines cross at the location of the prism. As you go back from there, the blue line appears to be coming from the narrower side of the prism while the red line appears to be coming from the thicker side. In other words, the red "virtual" object will appear on the thicker side of the prism and the blue virtual object will be on the thinner side.
Best,
OC
---------- FOLLOW-UP ----------
QUESTION: At first sight, I thought this was a great answer, but I have received a variety of answers from other professors. I also posted it at www.physicsforums.com and no one seems to agree that this is the correct answer. Will you take look and give it some more thought?
Answer: My first instinct was to reject your question, but I'll jump in with reservations. First, asking the same question to multiple scientists will always get you multiple answers. They are probably mostly correct, but not always. The peer review process is necessarily interactive. If you as a group of scientists the same question, and they can all discuss the question, you will get a unified answer, and it will likely be much better than any of the individual answers. This is the basis of peer-reviewed publications.
To the point, my answer is correct but was lacking an illustration and was somewhat obtuse. Check the following figure:
You can see that the orientation of the red and blue "virtual" objects in relation to the prism. Note that I don't have to draw an eye and obsess over how light is refracted by your eye. Knowing the orientation of the virtual objects is all that matters.
Best,
OC
As you can see from the diagram above, Optics C's explanation is basically identical with the earlier one, so the arguments I raised against that “explanation” are valid in this case as well. I'd like to pay attention, however, to a few points in the verbal explanation above—for it amazes me how easily many experts are led astray by their gross misunderstanding of simple concepts, often without even realising when they begin to speak in tongues (in gibberish).
“When you look through the prism, you are mapping the space behind the prism to a "virtual space" that is affected by the dispersion of the prism”... Fortunately, this is—apparently—“easy to do on paper”. And thus Optics C then says: “Draw a line from the object (say, a point of light) to the prism, then draw "red" and "blue" lines from the prism to a screen. Now, draw the red and blue lines backwards, as if there were no prism present”?!?... Why, Optics C? What justification do you have (beside your obvious desire to find some way of explaining an inconvenient observation through a conventional theory) for drawing those lines? What physical concept are you illustrating through that action? Surely you don't intend to use those imaginary lines that you draw (totally ad-hoc), as real lines that would illustrate spectral rays? But that is exactly what you're doing next! And thus it becomes evident that you don't even understand what virtual means! You don't realise, either, that when you look at your so-called blue and red virtual sources, you're actually looking at the real source—which you have substituted with non-existing entities! That ultimately means that you either claim that white light is dispersed without any aiding gadget into its constituent colours(like in the previous “explanation”), or (even worse) that your virtual sources do not exist, although they are images of the real source seen by the eye! Think about it! Think about the child-like question your “explanation” ought to answer, especially after your remarks in the follow-up question: Do my virtual objects exist? Then, if your answer to that question is “Yes”: How did they come into being? (Look for something other than your backward extension of imaginary lines.) And if your answer is “No”: How can my eye see things that do not exist?
There is much I could talk on this subject, but the fact is that I find it tiresome and totally unrewarding to discuss issues one should basically resolve for oneself—before offering one's expertise to others. Fortunately, there is a much simpler way of assessing the validity of would-be explanations on this topic. I have already mentioned that simpler test, and I'll do it again shortly. Before that, however, I'll ask you to have a look at the diagrams below—for they will help more than any written explanation in understanding the origin and nature of the inverted spectrum.
Firstly, in the diagram below I have crossed out the ad-hoc backward extension of the spectral rays projected onto a screen. There is no need of them, in order to explain—coherently and comprehensibly—the origins of the inverted spectrum and the reasons for its observation. Secondly, in the diagram I have inserted the eye in the place from where the inverted spectrum is supposedly observed—according to Optics C's and, in general, to the conventional-Newtonian explanations. And, finally, I have depicted below the manner in which the image of the source of light is conveyed from its point of origin to the prism. I have discussed this before, and therefore I shall say no more about it here.
Now, surely it isn't too hard to realise that when you look through a prism at a source of light, that is exactly what you see! It might seem silly to mention such an obvious thing, but in view of what I've been hearing (from people who ought to know these things) I feel that I should specify that fact. Thus, when the eye in the diagram above looks through the prism at the source of light denoted as “real”, it sees precisely that—albeit, as if that image came from the place where Optics C placed his virtual sources. A direct consequence of that fact is that the image arriving at the prism from its point of origin follows the manner I have already discussed (and as it was described by Professor Dutch in his email). That is the way the conventional-Newtonian theory describes the process, and that is basically my own understanding as well. I have depicted that process in the diagram above, with the image of the source in each spectral colour extending from the source (the real source, as specified) to the point of entry in the prism. Now, when the eye looks through the prism it sees the same field (and the same process) along the virtual path, too. Within that context, then, a would-be explanation for the inverted spectrum must be developed—and Optics C's “explanation” fails that test spectacularly. In fact, Optics C's “explanation” fails even without considering those things, and some of you should be able to pinpoint here why I say that! Indeed, had Optics C thought carefully about all the factors involved (and, especially, had he performed the experiment a few times and in a few different ways) he would have realised that if one looks through a prism with one's eye oriented exactly as in the diagram, one wouldn't be able to see anything beyond the point where the light exits the prism! That's because, at any conceivable point between the red and the blue lines, the observer's eye can only see the image of the source in a particular spectral colour. I have already mentioned this too, and any physicist should have also known this fact—since the conventional-Newtonian theory asserts that the resulting spectrum is continuous. In view of these facts, any explanation which requires the observer's eye to be in the path of the spectrum is undoubtedly a failed explanation. That, in turn, means that Optics C's explanation (which demands the eye to be precisely in that position) is really nothing more than a failed attempt—an “explanation”.
And so, arriving at this point, I will now show below a diagram of the things I've discussed thus far. A diagram that should be self-explanatory. A diagram that shows how simple is my own explanation for the so-called inverted spectrum observed in the basic subjective prismatic experiment, and how naturally it hangs out. And, furthermore, I should not forget to mention that my explanation does not only account for the inverted spectrum: it also accounts for all possible prismatic observations! This is, indeed, a highly desirable side-effect, in perfect agreement with Feynman's description of what a good theory should do—enable us to extract more from it than what it takes to be put in. Without any comments, then, below is a diagram (constructed in the manner of Optics C's original diagram) of my own understanding of the factors responsible for the existence and observation of the inverted spectrum (VBGYOR). (I have deliberately omitted to draw the process that "lifts" the third dimension into the view of the observer. I have also placed the eye in the position from where the inverted spectrum is best observed.)
The time has come to answer those three challenges of mine, through my own understanding of the nature of light and its behaviour in prismatic experiments. Let me then begin with challenge number one. I believe that anyone who has read with attention my pages, and who has used a prism to look through at the drawings in the previous chapters, has had little trouble understanding what I have written thus far. After all, between my understanding and Newton's theory there are only a couple of differences. Nonetheless, those few differences translate—in the end—into a completely new theory. Let's use a simple example to see the differences between my understanding and the conventional-Newtonian one. Below there is a rectangular source of white light.
If you look with the naked eye at that source of light above you will simply see a white rectangle. However, says the Newtonian-conventional physicist, although your eye (your brain, ultimately) can only see (register) the image of a white rectangle, that image is nevertheless formed by a very swift succession of images of the rectangle in every spectral colour. (This description may ruffle a few conventional feathers, but I am willingly taking that chance.) We have met this Newtonian description in that email from Professor Dutch, and I've already confirmed that—in principle—I agree with it. There are, however, some significant differences between my understanding of these issues and the conventional-Newtonian view. One of those differences is concerned with the number of spectral colours—a handful in my understanding (less than a handful, in fact: My understanding will ultimately show that only three spectral colours are necessary to explain all observations), an indefinite great number in Newton's.
The other, most significant, difference between the conventional view and mine is concerned with the order of the spectral colours, which convey the image of the source from its origin to its point of interception. Thus, in the conventional understanding there is no specific order of the spectral colours that carry the image of the source of light. Indeed, the conventional assertion is that a cross-section of the beam of white light will simply show a superposition of all images of the source, in all spectral colours and without any specific order. (In fact the conventional theory seems to suggest that the order of the spectral colours is absolutely random. That suggestion is a consequence of the emission theory of light, which is a highly controversial theory whose predictions never really agree with empirical data.) In my understanding, on the other hand, the images of the source of light follow a distinct spectral order, which is none other than VBGYOR—with red leading and violet ending the spectral array. (This is a totally new idea, revolutionary and therefore heretical, which—amongst other things—eliminates the need for the emission theory I've just mentioned.)
Now, at this point one should rightfully ask me: What is the basis for your assertion that the spectral images of a source of white light travel in that order? To that question I have a compelling answer: That assertion is based on a specific property of the prism that can be easily verified—namely the fact that, uniquely, a prism allows the observer to get a vectorial perspective of the third dimension (the dimension normally prohibited to the naked eye). I have discussed how that characteristic property of the prism is proved, and the order of the spectral colours is experimentally observed to always be the same: ROYGBV (displayed on a vector running from the point of observation toward the source), or VBGYOR (displayed on a vector, or direction, running from the source toward the point of observation). To refresh your visual memory look through a prism (with the vertex pointing upwards, although oriented at a 45 degree angle) at the white rectangle above from a distance of about 0.5m, and you will readily see the order of the spectral colours.
The reason I asked you to orient your prism at a 45 degree angle was because that orientation does offer a better perspective of the way the spectral images of a source of light are arranged in the VBGYOR order (from the source to the observation point), or ROYGBV (from the observation point toward the source). If you look at the white rectangle above through a prism oriented directly with the vertex up, however, you will see an image similar to the one below, with the spectral colours displayed in the same order.
The other fundamental difference between my understanding and the conventional-Newtonian theory is concerned with the reasons for the spectral display projected onto a screen, after the beam of light passes through a prism. According to Newton, the spectral colours that form the white light are refracted by a prism at their own individual angles. To Newton this idea appeared to be unquestionably true. Indeed, that idea appears to have been proven by his experimentum crucis, and Newton put all his faith in the conclusions he derived from the results of that experiment. And there is no question that the results of that experiment are quite persuasive. But there is also an undeniable fact that Newton's conclusions have actually created more problems than it solved. The problems it created are so many, and so obvious, that I still find it incredible to believe that for over three centuries no one took the time to find an alternative explanation for the results of the so-called experimentum crucis. After all, many should have been wary of the fact that Newton's own explanation for the results of his crucial experiment has brought nothing else to the table, beside that (seemingly plausible) hypothesis. On the contrary, his whole theory of light and colours has brought with it only contradictions, caveats, and controversies. And indeed that fact is even more accentuated when the more phenomena one tries to explain by using his theory, the more one realises just how much those contradictions, caveats, and controversies increase in number and level of difficulty.
Now, since Newton's theory provides a plausible explanation for his crucial experiment, it is manifestly clear that any opposing theory must provide an explanation at least as plausible for its results. It's either that, or one could think (suggest?) that there might be a way to merge Newton's wanting theory with my own. I, however, do not believe at all in that possibility. I do not believe in that possibility for a number of good reasons, which I won't discuss them now, though. One of those reasons, however, is because I firmly believe that I can explain the results of the experimentum crucis without invoking different “refrangibilities” for those so many spectral colours required by Newton's theory. At this point there is worth remembering an extremely important fact. It is not a trivial matter that the spectral colours, which are purported to have been refracted the second time in the crucial experiment at exactly the same angles as they were refracted by the first prism, are only approximately respecting that rule. For instance, the blue light is refracted more than the red light, but as for being refracted at exactly the same angle ... that “truth” is merely more or less true. And this is truly a nutritious food for thought.
There is a very simple way to explain the results of Newton's crucial experiment. And that way is not only simple; it is also structurally logical and theoretically desirable. Consider the particle of light, the photon. If you were to imagine the photon as a particle, how would your mind see it? How would your mind imagine, say, a blue photon? Would your mind imagine it as a sphere of blue light and, structurally, like a ball bearing? I really hope that you do not imagine it like that—for it really couldn't be like that! A particle—any particle—could not have the same density at its centre as at its boundaries! A particle should have its highest density at the centre, and from that point outwards the density should progressively diminish. And, of course, there is a conversely similar situation with the wave aspect of a particle. A blue photon, therefore, could only exist in the forms I have depicted below—as a particle on the left, and as a wave on the right. And, thus, nothing else is needed to explain the results of Newton's experimentum crucis. Not only that, by using my explanation I have no problem accounting for some inconvenient observations (like that of Mariotte, and others, who noticed thin bands of red accompanying violet after the second refraction, which obviously should not happen).
And now for my explanation for the ROYGBV spectrum observed when the refracted beam is projected onto a screen, which is depicted in the animation below. The angle of refraction in the animation is exaggerated (and pointing in the opposite direction to the conventional one), in order to emphasise that light, in general, tends to follow the shortest path through the prism, (as it was theoretically predicted by Fermat, and as it was evidenced by some of my earlier experiments). Sure, in the basic prismatic experiment the beam of light exiting the prism is refracted at an angle less than the incident, but the exiting beam of light does not contain all the photons that were part of the beam that entered the prism. How do I know that? Simple. If you perform the basic prismatic experiment with a very narrow beam of light (which is obtained by using a lens, of course) and you pass that beam through a prism onto which you have drawn a line (like in my earlier experiment) you will not only see a beam being refracted at the known angle—you will also see an image of the line that appears at a totally different angle. And, needless to say, that image must have been carried by photons that must have been refracted through the prism at that angle.
I believe that those who have understood what I have written so far should be able to see not only the differences between my understanding and the conventional-Newtonian theory, but also the similarities. And perhaps the most important similarity in question is the almost identical way in which the image of the source, conveyed in every spectral colour, explains the observational results seen in most prismatic experiments. There is, however, one crucial difference between the two explanations: The conventional theory stipulates, uncompromisingly, that the image of the source conveyed by the spectral colours displays the spectral image after it passes through the prism; my understanding, on the other hand, asserts that the image of the source conveyed by the spectral colours displays the spectral image before entering the prism. Need I explain what I mean? OK, consider what will be observed if we use a source of light like the white rectangle we looked at through a prism on the previous page. To make it easier there's that rectangle below.
If you look through a prism, oriented with the vertex straight up, you will see an image like the one below on the left. If you, however, let the light from such source pass through a prism before projecting it onto a screen, you will see an image very similar to the one below on the right.
Now, virtually the same conventional description used to explain the image above right (remember the email from Professor Dutch), minus the refraction part, I use to explain the image above left. In fact, the image above right is the upside down version of the one on the left. So one should ask at this point: Could it be that both explanations are correct? Could it be that each explains a different situation, and that consequently each is necessary in order to account for different experiments? The last question might appear valid, since the image above right is the result of what we call an objective experiment, while the one on the left is the result of a subjective experiment. But although that may look as a fair compromise, I totally reject it. That's because I can use my explanation to account for what is seen in both kinds of experiments, whereas the conventional explanation is unable to do the same! And this is the test par excellence that ultimately shows which “understanding” is superior. In fact this is also the fundamental requirement any theory must meet—to explain everything known hitherto, and to explain those new things that the previous theory cannot. Think about it.
P.S. I've just realised that I have forgotten to discuss one of the most important (if not the most important) aspect of Newton's theory of light and colours. I'm referring to the elongation of the spectrum in prismatic experiments where the prism is placed at minimum deviation. That elongation, which according to the wisdom in Newton's time should not occur, is in fact the spectral oblong of overlapping circles mentioned by Prof. Dutch, if you remember. That elongation is also one of the most discussed aspects of the theory, by Newton himself—and, even more, by his followers. If you remember, Newton had discussed that elongation with Lucas, when he'd insisted that the oblong projected onto a screen (or wall) must be 5 ½ longer than its breadth. Newton had also observed that his oblong had perfectly straight sides—which was an observation that forced him to invoke virtually an infinity of spectral colours, each with its own degree of “refrangibility”. And that idea has remained the same for three and a half centuries, despite some dubious facts that should have certainly been noticed by someone since. Here I will give you just one such fact.
According to Newton's theory, the oblong spectrum is a consequence of the heterogeneous refraction of the spectral colours that take place in the prism. In effect, Newton had a perfectly circular source of light, hence the purported oblong of overlapping circles. Since the oblong projected onto his wall was 5 ½ times longer than wide, and since there were no other things contributing to the transformation of that shape from its point of origin (which was the exit side of the prism) to the wall, apart from the natural and equal spatial extension due to distance, an elongation of the spectrum should have been observed right at the exit side of the prism. Do you know what I mean? You should. That means that on the side of the prism where the beam of light enters the prism an observer should see a circle of light, while on the exit side the observer should see an oblong. The problem is that there are set-ups with prisms at minimum deviation where both the entry and the exit sides of the prism show exactly the same shape for the image of the source! Indeed I have conducted such experiments and have made that observation. Moreover, since Newton's theory is supposed to explain all prismatic experiments, any set-up should show an elongated exit image. Yet the situation is the same in those cases also. Now, Newton, with his convoluted set-up, could not really make the observations I mentioned. The contemporary conventional physicist, however, with his sophisticated optical benches and equipment, should have easily seen what I have!
Finally, if you have understood what I've been discussing in the last few pages you should be able to see how naturally my understanding explains the oblong spectrum seen in set-ups with prisms at minimum deviation. Just replace the white rectangle in my example above with a perfect circle, and then think how that image is passed through the prism before being projected onto a screen. Think how perfectly straight the edges of that image are (after all it is the beam of light itself, which is like a shaft that forms that image) and how there's no need to invoke a myriad of colours to render those edges straight. And if you are a conventional physicist who, for some reason, cannot see how beautifully simple and natural my explanation for the Newtonian oblong is, write to me and I'll make a diagram for you.
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