Reversed spectrum through prism?

[Debstar]

There is a debate going on regarding this subject, and many different physics professors, who have a PhD in optical physics, are providing different answers. It looks like they are getting destroyed in the debate which is rather silly. I have been watching and I am very curious about the correct answer. The question is a child like (why is the sky blue) but all the answers are completely different. I was wondering if anyone else would take a crack at it. If you could provide the math that would also be helpful. I am just a stay at home mom with an insatiable curiosity. Here is the question. Why do the colors of the spectrum reverse in order when you look at the light source through a prism? When the light shines through and hits the wall or paper the blue is towards the base of the prism but when you look through the prism at the light the red appears where the blue should be. I know that there is displacement of the object or light source but how would the displacement cause the spectrum to reverse? Why would the virtual image be reversed? The only reason I can think of is that our eyes trace it back in a straight path and it crosses over but this doesn’t seem like a sufficient answer. A few professors have agreed with my answer but it is getting destroyed in the debate. Any other ideas would be greatly appreciated.

 

[torquil]

I may not have understood the problem, but here goes...

The light from some light source, through a prism, will spread in the usual way, e.g. onto a white screen.

If the ray of light is infinitely thin, each point of the screen will be reached by light coming from one specific angle. As the ray of light is made thicker, each point on the screen will be reached by a some close "neighbouring" colours from a small continuous set of angles. The incoming angles at which these different coloured light rays will reach a given spot on the screen will be the opposite to the spectrum of colours on the screen. This is easily seen by just drawing a picture and remembering that blue is deflected more than red.

It's not necessary to calculate anything, a simple drawing will prove it.

Torquil

 

[Debstar]

Thank you for your answer. The whole truth is that there is this man who has a strange website. At first glance he appears to be a crank but if you notice all of the answers from the professors you will see that he has a few valid points. His site is long and drawn out but if you skip to the part regarding his work you will find some of the answers that he is debating. I hate to confess but I am the American lady he is referring to and I am a tad bit obsessed with finding the correct answer. Will any of you take a look at it? I must warn you that it is a very arrogant, and an almost crankish site, but with just three simple challenges. Will you please try to look past all the craziness and help me figure out the answer. He also has a Youtube video called prismatic experiment. He is strange but he is pissing me off. Please help! www.jaccuse.info[/URL]

 

[torquil]

These observations are nothing new, they follow directly from the conventional theory by applying some simple geometry.

A simple drawing where one considers all the collection of rays that will impact a single spot on the white screen will explain all these observtions. You don't need a PhD in optics to explain it or to be a physics professor, because this is just a very basic physics and geometry. I'm afraid this guy has gone to great lengths writing about this effect that is quite easily explained...

The explanation is basically what I wrote in my first response. To apply it to the cases with the knife is easy. In short, each point on the white image is composed of different coloured light coming from different angles (this is possible because the incoming light on the prism is not an infinitely thin beam). The contributions at each point are ordered by angle in the same way you see the spectrum by looking into the prism with your eye. At the points that are influenced by the knife edge, half of these contributions are removed, thus creating a colour instead of white.

A simple geometric drawing will show that the colours will be as observed by this man. A drawing is worth a thousand words, but I don't know if I want to go to the trouble of drawing, scanning and posting for this.

EDIT: Just so people know which observations I am explaining:

http://www.youtube.com/watch?v=zNvE_X5JIcQ"

Torquil

 

[Claude Bile]

Hi Debstar, welcome to PF!

Exercise caution when using online resources that have not been peer-reviewed! You are far better served using textbooks or scientific journals. Websites tend to be avenues for people to express their more "fringe" views on physics.

If this fellow had a valid point with Newtonian physics, he should be able to frame his succiently describe his point using mathematical arguments in 1-2 paragraphs. The fact he uses such long-winded drawn out arguments (I count 25+ paragraphs and 10+ images) serves to obfuscate rather than clarify and reinforces my suspicion that he is a crackpot.

Claude.

P.S. I have a PhD in optical physics!

 

[Debstar]

Thanks to the both of you. I was thrown for a loop by the variety of answers that I received from Professors. I am usually very good at checking my sources, but every now an then, my curiosity leads me down a road less traveled. One great source that I use for math is the Khan Academy. He is an excellent teacher and a non-profit organization. He is trying to figure out ways to keep the site self sustaining. It is an amazing contribution especially to curious stay at home moms. Thanks again! I really needed peer-reviewed validation. Claude, am I to assume then that you agree with Torquil’s answer?

 

[uart]

Oh my god, that guys stuff is reminiscent of an Osama Bin Laden video.

Debstar, to easily understand the prism reverse spectrum "paradox" please take a look at the two figures I have attached.

In the first figure we have just the light source(s) the prism and the screen. Instead of just one source we have a number of sources arranged in a "T" shape so that we can detect the up/down orientation of the image as a whole. Without a lens of course there won't be a sharp focused image, but if the light sources are very directional then you will get roughly the image as shown (with blue displaced toward the wide end of the prism as expected). BTW, I made these figures quick and nasty by just showing red and blue, obviously you can fill in the other colors in between.

The eye (or camera etc) does not work like the above. Here we require a sharp image even if the light is not already focused into narrow beams, here we require a lens. We can't avoid the lens when viewing this, it's built into our eyes so there's no way around this. We will not see the image as shown above when viewing the prism directly, we must see as per what's shown in the second figure.

In the second figure I have shown the same experiment but with the inclusion of a lens before the image is projected onto the screen (or the retina in the case of viewing this directly with the eye). Notice something VERY important about this result. The image is inverted (this is common knowledge ok, a lens always does this) but what is interesting is that the red-blue shifting is NOT inverted, blue is still displaced toward the wide end of the prism. You can prove this easily enough by simple ray tracing, or alternatively you could say that this occurs because the lens corrects for the multi-path divergent light rays from the source (which is what it's designed to do and which produces a focused inverted image) but it doesn't correct for the red-blue shifting caused by the prism (as the lens is not designed to do this). In any case we have the situation that relative to the orientation of the image we now have the opposite orientation of the red-blue shift. Of course the eye (and camera's and all other optical equipment* which uses lenses) invert the image a second times so that we see it the right way up – and this of course means that we will see the red-blue shifting the wrong way. Honestly that's all there is to this so call paradox.

*Note. The eye inverts the image simply by the way it's wired to the brain, otherwise we'd all see everything upside down. A simple film camera for example has the film loaded into the camera upside down relative to it's orientation when developed. Binoculars and terrestrial telescopes use a series of 90 degree reflections to right the image. Only astronomical telescopes usually leave the image inverted.

I hope that helps. :)

 

[Debstar]

That is funny! There is a little resemblance. I took an online ray tracing optical course and you can compare a convex lens to a prism because the top half is basically the same shape. In the course it indicated the distance rule is positive for a real image and negative for a virtual image. To locate the image it is where the outgoing rays or their trace back rays converge. In this case the out going rays never converge only the trace backs, so the image will be a virtual image, which is always inverted. Is this what you are trying to convey?

On the flip side of the craziness, being a layman myself, I can empathize with the rebellious attitude. Have you ever tried to explain to a layman the concept of the big bang theory? The Redshift, the Doppler effect, the Expansion Model, all indicating that the entire universe was derived from a single point smaller than a pin head, or even the history of how Maxwell’s equations came about. That since light is a transverse wave, we needed a semisolid substance, not just a fluid, because a fluid can’t hold a sheer force. That’s why the idea for an ether was born. I think it was Thompson who tried to build a mechanical model with rotating fluid because vortex rings can be very stable and offer more resistance. Maxwell liked this idea and begins to add to this model, which lead him to understand how light is connected to electromagnetism. He is able to calculate what the speed for a transverse wave would be in this model and is within 1% of c. Analogies never deliver airtight insight, that why we say, his physical discription are the equations themselves. It was difficult for even the most well known intellectuals to grasp. He used mostly Cartesian notations, because he did not like vector notations, and France and Germany were using laplacian notations, so it was difficult to translate. Hermann Von Holtz agreed with his results but even he could not grasp the actual physical conditions of this statement. I think Maxwell indicated that this field was primary and charges and currents secondary, the charges and currents were not physical entities themselves but a consequence of this field. Many remained in denial and did not want to give up the concept of ether. Even Einstein did not contribute to ether and there were many who never accepted General Relativity. There was no concrete payoffs to allow you to understand practical mechanics. I think Michelson and Lorentz never even came around to accepting GR. The simplicity, unity, elegance, is what came into play for those who did. Analogies themselves can sometimes be more harmful even though we need them. Just look at the child like cartoon versions of Special and General Relativity. Then you come across all of the people in the history of physics who out of egotism have falsified their work, Hendricks Schon is a good example. Then you have to look at the personalities of the greats themselves. I am sure that one could come up with some type of clinical disorder for even Newton.

I feel that if the average taxpaying layman were to understand the whole of the Hadron Collider, and how much money is being contributed, especially during our current economic crises, he might not choose to add to this exploration. Then there are the theories themselves which seem a little crazy, examples are parallel universes, the variable speed of light theory. etc. We all have our favorites, and we can see the beauty in Newton’s and Kepler’s laws, but there are many with over the top imaginations. This is why my curiosity forages in diverse places every now and then. We all try to gather bits and pieces of information to create a story that explains our sense of “I” and our surroundings. I feel it is important to have as many different perspectives as possible to contribute. So I always appreciate everyone’s ideas and opinions.

Is what I indicated above what you are conveying? If anyone else has anything to offer I would love it, because like I said, I have received tons of different answers. Thanks to everyone for helping a bored, high school graduate, who is a simple curious housewife, aka (slave). I'm glad that everyone here is so polite and respectful. I have teenagers so they remind me everyday of my stupidity, so I don't need anymore reminders. Thanks again!

 

[russ_watters]

Here's how I would word it: It's because you're standing in front of the prism instead of behind it. Just like with a mirror: right and left are reversed! Or...How do you go from looking at the screen to looking through the prism? Turn around!

 

[Debstar]

Very interesting! I thought about that as well. Similar to the T-shirt analogy. How the letters place a perfect stamp on the mirror, and if we could see through the persons shirt it would have the same orientation. I like it. Does anyone else? Is anyone currently in a physics course where you are able to ask your professor? I asked this question on www.allexperts.com , and I didn't even give him my thoughts, he has a PhD in optical physics. Here is the 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.

Claude, you are recognized as a senior science advisor and you have a PhD in optical physics. What is your professional opinion? Which answer so far is closest to the truth? Thanks again for all the great input!

 

[Claude Bile]

Torquil is right.

If you had an infinitesimally thin strip of light as a source, you would only ever see one colour. The colour you see depends on the position of your eye.

Real sources however are not infinitesimally thin, they have a finite width. So, from a fixed position, you see "red" from one part of the source, while you see the "blue" from another part of the source. Since the blue light refracts more, it has a steeper "trajectory", and thus will appear to come from the top of the source, while the red comes from the bottom.

Claude.

 

[torquil]

Analogies never deliver airtight insight, that why we say, his physical discription are the equations themselves.

Analogies themselves can sometimes be more harmful even though we need them. Just look at the child like cartoon versions of Special and General Relativity.

This is very true! One example of this was a question here on the forum by someone who had taken the "rubber sheet" analogy of gravity too seriously. I.e., he had thought that gravity worked exactly like an invisible rubber sheet near the so-called "invariable plane" of or solar system (just learned that word from wikipedia...).

But as you say, analogies are needed. I think it is important in order to improve understanding.

Torquil

 

[Debstar]

My understanding is flawed. I am having trouble comprehending how this would not tie into ray tracing. There is displacement of the objects when looking through the prism right? Would it be considered a virtual image since the rays only converge on that side? Does this explain away the effects that he shows in the pictures, presenting the word HELLO, and the one with the black line drawn on the prism? Does the dispersion of light not lead to chromatic aberration when tracing the rays back? Understanding light, and the causes of color is not an easy task for me, but I do enjoy it, so please bear with me. I watched the “Walter Lewin” videos at MIT. He said, that when you take 8.02 you think you know what light is. Then you reach 8.05 and you realize you have know idea what light is. All you know is how to manipulate difficult equations that allow you to predict what it will do. All I want is to understand all the causes of color but I’m having a little trouble. Is this site considered a safe source? Do most of the users have the credentials that they claim? I just want to make sure. Check-Check-Double Check... Thanks!

 

[DaTario]

Hi,

I will try to answer you original question, believing my answer has some new insight, not given here.

When seeing the spectrum on the wall, you are likely to see aberrations, as only a perfect one ray light will produce on the wall the perfect rainbow. No ideal sources will throw some blue intensity at the same position where some green intensity is being thrown.

When you collect the prism's output radiation directly with your eyes, you are collecting necessarily light from a series of different rainbows, as, if there were just one ray, you would observe only one color (hipothesis: point like eye aperture). Therefore, the red impression will come from a low ray, as the red associated angle is small. The blue impression will come from a higher ray, as blue deflection is greater.

Hoping to have helped,

Best wishes

DaTario

 

[uart]

My understanding is flawed. I am having trouble comprehending how this would not tie into ray tracing.

You mean like this (see attached image). Yes I think that is the easiest way to demonstrate this so called paradox. BTW the ray trace in the attachment was drawn to scale (as in angles measured and Snell's Law accurately applied) in a CAD drawing package. It clearly shows why the relative orientation of red and blue parts of the image are the way that they are when viewed directly.

 

[Buckleymanor]

That is funny! There is a little resemblance. I took an online ray tracing optical course and you can compare a convex lens to a prism because the top half is basically the same shape. In the course it indicated the distance rule is positive for a real image and negative for a virtual image. To locate the image it is where the outgoing rays or their trace back rays converge. In this case the out going rays never converge only the trace backs, so the image will be a virtual image, which is always inverted. Is this what you are trying to convey?

If you put one prism close to another the spectrum dissapears.
So if you place one prism close to your eye (because it's comparative to a prism, well the top half) does the spectrum allso disappear in this instance.
I would try it but I ain't got a prism.