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.
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.
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.
Before concluding today's discussion, I want to share with you a last couple of important things which are closely related to prismatic experimentation. First, let me show you three more pictures about the second experiment we have discussed today. See below.
These three views from above of the objects involved in the second experiment should help us all get an even firmer grip on the subject of prisms and about how they manage to gather so amazing bits of information from their surroundings. Look carefully and notice how each of the two main faces of the prism gathers all the information that's laying beneath the whole base face of the prism.
See then how in the third picture, in which the prism is laying down diagonally across the strip of paper and oversteps its boundaries, the two active faces are still able to collect and transmit all the info data that's on display, including the two bare corners that then become four, due to their own individual displays.
Think then for a little while, and you should understand why those two "windows" of the prism are so truly amazing--for in stark contrast to real windows they are able to give the observer a complete perspective each, of the entire inner ground flooring of the prism. And then, as if that weren't impressive enough already, notice how they both raise and hold their displays at an angle that makes them visible from any vantage point around. Wow!
Finally, please spend just one more minute thinking and you will surely realise that all those amazing things are simply and clearly made possible and accomplished because of one--and that's one only --reason: the mere slant at which the two opposing faces are oriented in the space.
And now, really--truly--finally, let me show you what I didn't when we talked about the real reasons behind the results we had seen in the first experiment covered in this post. (By the way, I am dead tired, so I'll keep it really sweet, quick and short:)
Due to the inherent slant at which the front face of the prism is laying, and in addition to one of its distinctive peculiarities (that which restricts the field of observation to the space that is laying ahead in a direct line and parallelly with its particular plane of inclination--remember our most recent discussion, which is recorded in the paragraphs just before the current illustration above) the only things that would become observable through that front "window" of the prism would be those that are part of the landscape that is delimited by lines that are running at 90° relative to that plane.
That's all I'll say, in words, about that, but in order to make sure that you will understand the point I'm making I have also conducted a relevant experiment, whose visual result is right below, for scrutiny.
Hooroo, I'm off to bed.
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!
These three views from above of the objects involved in the second experiment should help us all get an even firmer grip on the subject of prisms and about how they manage to gather so amazing bits of information from their surroundings. Look carefully and notice how each of the two main faces of the prism gathers all the information that's laying beneath the whole base face of the prism.
See then how in the third picture, in which the prism is laying down diagonally across the strip of paper and oversteps its boundaries, the two active faces are still able to collect and transmit all the info data that's on display, including the two bare corners that then become four, due to their own individual displays.
Think then for a little while, and you should understand why those two "windows" of the prism are so truly amazing--for in stark contrast to real windows they are able to give the observer a complete perspective each, of the entire inner ground flooring of the prism. And then, as if that weren't impressive enough already, notice how they both raise and hold their displays at an angle that makes them visible from any vantage point around. Wow!
Finally, please spend just one more minute thinking and you will surely realise that all those amazing things are simply and clearly made possible and accomplished because of one--and that's one only --reason: the mere slant at which the two opposing faces are oriented in the space.
And now, really--truly--finally, let me show you what I didn't when we talked about the real reasons behind the results we had seen in the first experiment covered in this post. (By the way, I am dead tired, so I'll keep it really sweet, quick and short:)
Due to the inherent slant at which the front face of the prism is laying, and in addition to one of its distinctive peculiarities (that which restricts the field of observation to the space that is laying ahead in a direct line and parallelly with its particular plane of inclination--remember our most recent discussion, which is recorded in the paragraphs just before the current illustration above) the only things that would become observable through that front "window" of the prism would be those that are part of the landscape that is delimited by lines that are running at 90° relative to that plane.
That's all I'll say, in words, about that, but in order to make sure that you will understand the point I'm making I have also conducted a relevant experiment, whose visual result is right below, for scrutiny.
Hooroo, I'm off to bed.