From Newton's theory and Goethe's poetry to the reality of light and colour. Part 3

Let us begin by taking a good look at the screenshot below, which according to my mind is one of the best examples one could ever find to demonstrate how truly deficient still is the conventional view regarding the refraction phenomenon. Take your time and read everything carefully, for this is a most important and far reaching topic.

So, who's ready to declare unmitigated allegiance to any of the conventional points of view listed above? Anyone? Of course, those are entirely rhetorical questions, for the answers to them I already know quite well myself. There is nonetheless one thing that I'd love to really know for sure, and that is how many of you would agree that the last paragraph above is perhaps the most honest account any conventional physicist could offer on the issue at stake. Anyway, my personal opinion about that would at very best be a tepidly modern and lukewarm 'whatever'. That's because to my mind the issue of the refracted otter above is--as it has been since I was almost ten and a half years old--disarmingly simple, straightforward and therefore easily graspable. Now, whether you believe that, or not, I don't care. In any event, stay with me and I'll show you the proof, in my pudding.

The best way to give you a real taste of my pudding is for you to get hold of a large and full glass of water and to place it on a high table of sorts, ideally on the same level, or at least close enough to, your particular line of sight at this time. Next grab a long pen or pencil from your granddaughter's case, and then dip it vertically in the water all the way to the bottom, right in front of your eyes and just like it is depicted in the middle glass marked A in the picture I will drop below.

I have said what I'm about to say next many times before, but I will never tire to continue to repeat it into the future from time to time, simply because it's true and because over the years it has played a major role in my continuing development. It has always been pretty obvious to me that whatever kind of patterns most of the world were interested in and liked to talk about I invariably found boring, insipid or downright invisible or irrelevant. And naturally the opposite was also getting more and more evident every day. A perfect example of that nature had also occurred when I first heard about refraction in water. As soon as I experimented on my own with glasses of water and pencils, I never cared to follow the conventional methods of experimenting and thinking about--which by and large were conducted along the rationale depicted in the left and right glasses above, and with an inclined pencil that was apparently ''bending'' when under water. Instead, I was instantly fascinated by the rationale of a pencil dipped directly perpendicular to the plane of the bottom of the glass, and driven by the observation that the immersed part of the pencil wasn't 'bending' at all in the process--it was instead clearly severed from the rest of the pencil and 'moved' in space along the shortest path to the edge of the water. See the illustration below.

To my mind it was clearly obvious that this observational effect was really the one that should lead an investigator toward an understanding of what the so-called process of refraction truly was. As far as I was concerned all those conventional assumptions (different speeds for the travelling light in different media, at different angles, a.s.o.a.s.f.) were nothing but poppycock tales, good enough for most of  the mob, no good at all for the minority of free thinkers. Popularity, after all, is the hallmark of mediocrity, by definition--to paraphrase Dr. Niles Crane.

By the way, I forgot to tell you that by now you should verify my words and observe the so-called refraction in water from the perspective of a perpendicularly immersed pencil. More importantly, leave the conventional assumptions on the side for a little while and start thinking about the possible implications of this new perspective of observation. I can assure you that a careful examination will easily reveal a very rich and fertile field of vision and territory of potentialities. On the other hand, the continuing blind Newtonian fellowship that is still the dominant aspect of research in the field will become increasingly harder to handle and preach, unless a new generation shall find the courage and wisdom to say loud and clear "You've had your time, long and ample yet largely unproductive and dry. So, with all the respect we can muster we say that is nigh time for you to retire inside your own arid old skulls". For otherwise we will only expose more and more young and capable brains to such incredible abominations like the following one, in which a Science High School teacher ''proves'' to her students that a rectangular slab of glass refracts light as efficiently as a triangular prism.

Is there any need now to elaborate on how coherently one could explain the 'mystery' of the refracted otter building on the observation I made as a 10-year-old? I don't think so. Nonetheless, for the benefit of those rare free thinkers that might stumble across these pages one day I'll show you one old picture of the water refraction I've been talking about. The rest of the story you can surely develop yourself.

The human eye, or that of a camera, or indeed any other similar means of visual observation, are profoundly handicapped because of one and the same inherent inability: To be able to visually record and observe the reality out there in real time on a genuine three-dimensional screen. And that is a great handicap, make no bones about it. That, for example, is the primary overwhelming reason for our ingrained inability to build and imagine three-dimensional structures inside our brains with the same degree of success as we can do it with two-dimensional entities. It suffices to realise how debilitating that handicap is simply by watching a game of cricket, let's say, on the flat screen of a television set. Even with the most sophisticated devices we have at the moment we struggle to get an accurate picture about how long the 22-yard cricket pitch really is, or how far the slip cordon of the bowling side truly is behind the batsman at stumps.

Now, we are certainly very well aware of the factors that are fundamentally responsible for our prevalent handicap in visual observation and monitoring, and although we have managed to some extent to circumvent and partially overcome a small handful of the most debilitating side effects of our physiological shortcomings (for instance we may not be able to create three-dimensional structures mentally very well, but we can certainly do it very successfully in the greater universal reality, and increasingly more  in the abstract digital reality that we've been building in leaps and bounds all around). Effectively, due to our sense of sight being basically collected and decoded from the information gathered on a two-dimensional detector we are almost exclusively limited to a two-dimensional visual perspective of space. More specifically, we are almost totally prohibited from getting a visual perspective of the spatial depth. At a first sight that seems to be nothing more than a merely innocuous and inconsequential realisation. But to me that realisation led me onto a pathway full of new and exciting possibilities in its relevant field of study. See the two pictures below.

Intermezzo

From time to time someone I know leaves a certain kind of comments at the end of some of my posts. A 'certain kind' because they're all designed and meant for one, only, and the same reason, which I won't mention at this time nevertheless. Anyway, it so happened that yesterday I found a new one at the end of this post, and it is for that reason that I have decided to draw this impromptu interlude--so I would asap address it. The comment, in its naked nature, is both offensive and pejorative, precisely because it comprises nothing but a link: https://www.physicsclassroom.com/Class/refrn/u14l1b.cfm. 

Yesterday, when I first saw the 'comment' and visited the web page with that link, I spent quite some time drawing an elaborate plan about how I thought I should respond to it. Indeed for a few hours I drew diagrams (like a much better rendition of the diagram supplied on that page, which is effectively a crucial part of the conventional line of defence against attackers like myself on the reigning establishment and doctrine--see below) and earnestly considered a detailed explanation of my own, in which I was going to cover, address and respond to every single conventional line of reasoning and argument.

But, truth be told, the reality is that 24 hours is a bloody long, long time inside my private universe, and such a long amount of time is pretty much guaranteed to subject my decisions to a hard and unrelenting array of tests on any given occasion. And sure enough that is exactly what happened in the latest 24 hours of my life too. To cut a long story short, after a hard and intense process of deliberation I finally came to the conclusion that I shouldn't feel compelled to spend an awful amount of time and space in order to convince someone with an obviously limited ability for a strong and demonstrably fluent capability to reason, especially after they had already been provided with sufficient and eloquent bits of information that could have easily been strung together into a cohesive and coherent picture of the matter under question.

 What I will do instead is show you a new set of those eloquent bits of information that you can easily (well, relatively easily, at worst) put together and thus realise and appreciate my understanding of this phenomenon for what it really is, and does.

The crucial attributable factor in the entire process is the one photographed below, and everything else that is involved in the unfolding of the relevant experiment and observation is wholly dependent on it, as well as correlated with it.

The idea behind the process is that light always travels in a straight line following the shortest path within the boundaries of any medium when carries images of the objects that are oriented at the angle that's been designated as the normal. In effect, what happens in those cases is that the image of the object is refracted longitudinally, rather than transversally, along the shortest path towards the edges of the medium. A careful look at the picture above should be more than sufficient to convey the entire message.

The next set of data comprises three pictures that have been taken from three different angles, relative to that of the original object (which is of course the pencil immersed vertically in the body of water) as well as to its longitudinally refracted image. It's all so damn clear that you don't even have to think about it.

Finally, below I'll drop the last piece of information on the subject we have been discussing in this intermezzo, and about that I will not add a single word.

There is one more aspect of this pencil in the water experiment that I want to talk about in more detail, for it is of great importance and it reveals even more conspicuously the fact that the conventional theory that claims to account for it fully and without any problems is just blatant poppycock, as I had said somewhere above.

We'll begin by showing a couple of of the most popular conventional illustrations depicting the experiment, and interestingly enough they're both copies of diagrams from the Physics Classroom Website, whose link was posted as a comment at the end of this page by a so-called Secular Sanity. Have a look at those two illustrations below.

Let us first address what is stated in the last sentence of the illustration directly above:

The portion of the pencil which is submerged in water also appears to be wider than the portion of the pencil which is not submerged.

That is not necessarily so, and that in itself shows firstly that the conventional theory is really shooting in the dark and secondly it shows how truly unscientific that claim is. Lat me show you why that is the case. See the picture below.

See what I've done? I simply copied the image of the otter that was submerged under water and attached it to the part above the water. And, lo and behold--a perfect fit! Let me show you another example, below.

In this example I did exactly the same thing with one of the pictures taken by me and shown earlier in the intermezzo. And, sure enough, another perfect fit.

In the end the conventional physicist will have no choice but to realise that the reason for which in the two cases shown above, the images of the otter and pencil that are submerged under water are not fatter than the otter/pencil parts above the water due to the shape of the two containers that are holding the water, which are similar in both cases. Now that realisation should rightfully make her very unhappy indeed, whilst at the same time make me rub my belly with joy. For all that plays right into my hands.

While it's obvious that the conventional physicist has omitted to consider the overall shape of the body of water into which the images of objects immersed are known to experience refraction, it is not at all obvious why she has done so. For, let's not beat around the bush, if it was a genuine omission then she must be a dead set fair dinkum dilettante, and if it wasn't a genuine mistake then she can only be a con girl. And I, for one, don't know which is worse. Do you?

A common classroom demonstration involves placing a pencil (or similar object) in an upright position in a round glass of water. The pencil is then slowly moved across the middle of the glass from a centered position to an off-center position. As the pencil is moved across the middle of the glass, an interesting phenomenon is observed. The position of the pencil under the water is shifted relative to the position of the pencil above the water - the pencil appears broken. Additionally, the pencil as observed through the water, appears fatter than the pencil as observed above the water. 

Why is this phenomenon observed? Of course, the explanation of this phenomenon involves the refraction of light. But just how does the refraction of light cause the pencil to appear fatter and shifted to the side? The answer to this question is depicted in the animation below.

The above is the animation in question, unfolding from the left to the right. There is one essential point I want you to keep in mind. That the reason for the apparent fattening of the image of the pencil is that upon passing from the water medium into the air the rays of light are bending away from the normal. And I'll say okay to that, without asking any questions whatsoever. Then I will show the picture below and surmise that it must be for the same reason that the image of the straw that is submerged in the water appears fatter than the image of the straw above the water.

And just like before I will accept that explanation without any qualifications. The only thing that I'll do then is show the conventional physicist the picture below, and ask her to explain why in this case the rays of light refuse to bend away from the normal when they pass from the water into the air.

As I'll be waiting for her reply I'll remind you about my own explanation for the behaviour of light in any medium. Which is that light always travels in straight lines, following the shortest paths toward the boundaries of the medium. Then, to prove that my explanation accounts both qualitatively and quantitatively as well for the observed results of experiments I will present the following analysis.

Taking as reference the picture I showed just before the one above I took the following measurements with the straw placed at the centre of a perfectly round bottle filled with water.

Then, by using the Phythagorean theorem and the data extrapolated from the measurements taken I tried to see if I could account for the above observations by making use of my a priori explanation. Below you can see a comprehensive diagram of the results I obtained.

As you can verify and see the two paths of interest are those depicted in green, and they unquestionably are shorter than all others shown, with the exception of the yellow path--which is essentially irrelevant to the whole issue, anyway. Its only role was to help us determine the length of the green line, which is in fact the hypotenuse of the right angle that the yellow line is a part of. All given results are correct to two decimal places.

Finally, my a priori explanation easily and coherently accounts for the apparent non-fattening of the image of the straw submerged in the water held by a square or rectangular container. That's all about that, for now.

   

This morning I found another comment from Secular Sanity and this time I decided to leave it on. I will discuss this new comment in about two weeks from now, when I'll return from a short vacation.

Mr. Poradin Water in a curved container acts like a convex lens and focuses the light rays in a way that magnifies an object. Water in a square container acts like a slab of glass and focuses the light rays in such a way as make the object appear closer than the actual position. Consider an observer looking straight down at an object in water. The virtual image of an object in a medium with a greater refraction index appears closer. The image is virtual because it cannot be formed on a screen. The same is true in reverse. If the observer was underwater and looking straight up, the objects would appear farther than their actual position.

Wrong, Secular Sanity. As always you put all your eggs in the conventional basket without verifying to see if in fact that's a wise or safe choice. I, on the other hand, was born a perennial sceptic, so I never accept any thing whatsoever without subjecting it first to my own set of criteria. In the case of our current bone of contention if I am brutally honest I must say that it is highly disappointing if one fails to see how clearly the suggestion of the water in a curved container acting like a convex lens is totally inadequate in the particular cases we've been dealing with. Why? Because a convex lens magnifies an object at specific distances from its point of origin while in our cases the object appears bigger at any point of observation, including that where the container of water is placed. See the pictures below.

 

Moreover, according to conventional laws of refraction (and to the verifiable empirical evidence anyone could obtain) it would be absolutely impossible for an object like the one in the pictures above to somehow appear magnified by the refracted rays of light. See the two pictures below.

There is nevertheless one particular way to create a magnified object like the one shown in our specific cases. See the photos below.

And that particular case is precisely the one I had suggested earlier.

To whom it may concern

The four pictures below have been provided in order to show to those concerned why the conventional understanding regarding the refraction in water is inadequate to account for the observational results of those so-called "pencil in water" experiments. The pictures in question should be sufficient on their own to represent my non-conventional view on the subject in a manner that is both satisfactory and straightforward enough to convey the relevant message to those that may have been concerned about the entire issue at stake.

Let us make sense of the picture above. We have a triangular prism, equilateral (5 cm each side), a strip of black paper 2.5 cm broad and a camera placed on the same level at some distance behind. Let us account for every image seen through the prism, starting with that of the floor (the base) of the prism. The fact that it appears black is due to the image of the black strip of paper that has landed on it via the front side of the prism, which is the further side from the point of observation. I can tell you that it is about 145 px high and that it accounts for about 30% of the entire image of the prism.