# How does Newton's 2-prism experiment help to explain why light does not get dispersed into 7-colors in a parallel glass slab? [duplicate]

In a real parallel glass slide(with two prisms imagined to be touching each other to form a parallel glass slide),
The ray of light should pass through the Z in between without any dispersion or change in direction because the density in both of the prisms is the same(and they are touching each other). So Newton's experiment won't help in explaining this because in it, there is a vaccum(or air) in between and hence the change in direction of light. I hope that you are getting me, if not I'm ready to elaborate more.

[In case anyone is wondering that I did post a Q about dispersion earlier too, then that is true - but I did not get the answer of the question that I really meant to ask and hence this, I hope that you guys will help me better understand this.]

• Your picture is physically incorrect this way. The light continues to spread after exiting the prism. Direct recombination with just one other prism only works on the cover of Dark Side Of The Moon! Apr 12 '12 at 19:27
• At leftaroundabout - I didn't really understand what you meant. The picture is correct - the concept was experimentally proved by Newton in the early ages by first splitting light into seven colors and then recombining it using another prism. And @tmac - It is. It actually is a comment that I made that was sort of a question. And I did not get it answered and hence me posting this. I hope you get me....thanks! Apr 13 '12 at 14:53
• btw, does newton's 2 prism experiment prove the non-dispersion in a glass slab?? Apr 18 '12 at 6:36

So Newton's experiment won't help in explaining this

No, it does explain it.

First, I'd like to dispel a confusion regarding dispersion. In both cases (slab/prisms), we have no angular dispersion, but we do have lateral dispersion (image stolen from @Amu's post)

The colors do split up, and if you used a thin slit of light, you would get an outgoing slit with coloring at the edges (you may get a rainbow if it's thin enough). For a thicker "beam", adjacent rays overlap when they split, producing white light. But since the rays are parallel, the amount of dispersion does not change.

In a single prism, on the other hand, the rays don't come out parallel--they have an angle between them. And thus the lateral dispersion increases as you go further from a prism, giving a clear rainbow.

In double prisms, depending on the distances, you may or may not see dispersion on a screen.

Actually, the correct experiment is displayed by this xkcd comic:

Yep, there's an extra lens involved--which makes the situation reversible.

Alright, back to the question.

Imagine taking the double-prism in the diagram above and bringing the two prisms closer to each other. The dispersion in the center "z" will decrease till it becomes zero. And then, it becomes the same as a slab--it's as easy as that :). I think that the diagram you have is slightly wrong, I'm not sure--since it's not directly supporting this. I may have to look for some more diagrams and compare.

Remember that a zero-width film of any material has no effect on a ray of light, provided that there's no total internal reflection going on.

• I get it now - at least most of it, thanks. But I'll wait for your reply, nonetheless, so that I understand all of it. On a side note, a zero-width film doesn't exist right? if something has no width - how can it exist? And like you, I too am not sure if the diagram is wrong, since I've seen it on many legitimate science websites on the internet. Thank you. Apr 23 '12 at 8:47
• @alvasrawuther no, a zero-width film doesn't physically exist--but we can use it as a tool in certain situations like the above one. Basically you're taking a limit. Regarding the diagram, I said that it's slightly wrong, which can leas to a confusion regarding the angles. The correct diagram will be similar, but not the same--you may have seen one of these(cant find any atm). Apr 23 '12 at 9:01
• But you also said that a zero-width film has no effect on a ray of light. But that is not the case in the diagram. Apr 23 '12 at 11:42
• @alvas it is the case, you're not imagining the convergence (coming closer) of the two prisms properly. And, like I said, the diagram is slightly wrong. If I get time, I'll do a bit of digging tomorrow. Apr 23 '12 at 14:34
• @alvas: A zero-width film (or a film of negligible width, if you prefer) has no net effect on light passing through it. (It does have an effect on any light that might be reflected from it, but that's irrelevant to this question.) Yes, the light does refract when it enters the film and then immediately refract again when it leaves it, but those two effects occur at (nearly) the same time and place and exactly cancel each other out. It's just as if, while walking, you were to first turn, say, 30° left and then immediately 30° right: you end up going in the exact same direction as before. Jul 24 '12 at 17:01

Whenever light rays of different colors emerge from a refracting surface parallel to each other, they mix up to form white light. When they're not parallel to each other, such as after refraction from a single prism, they remain separate and we see seven different colors.

After the second prism refraction, the light rays emerge parallel to each other just as they were in the incident beam of light, and hence this looks like white light. Similarly refraction of a beam of light through a parallel glass slab produces rays parallel to each other.

Image source

In the image, the rays which make up the incident beam are shown far apart from each other for clarity. In reality, these rays are extremely close to each other and so are the emergent rays. Hence the adjacent red and violet rays, being parallel to each other, mix up and produce white light.

• Actually, reversibility doesn't quite cut it--the rays aren't parallel, so the concept of reversibility is moot, In fact, I don't even think that the rays recombine perfectly in a double prism with space between the prisms; they only appear to do so(parallel emergent rays). And since we don't have perfect one-dimensional rays, the dispersion is masked by the red-violet thingy you mentioned. The correct answer here is that you can assume a slab to be two prisms. Apr 17 '12 at 14:13
• @Manishearth But the path of light would be different if you assume two prisms - what happens to the extra bending at the boundary between prisms? And if you say that there's no extra bending because there's no air, then how is that any different from just a glass slab? It doesn't give a 'new' explanation.. :/
– Amu
Apr 17 '12 at 14:36
• a glass slab is a special case of parallel prisms, i.e. when they touch. There is no extra bending when they touch; but there is balanced deviation in all cases. When they don't touch, there still is an increase of dispersion. Apr 17 '12 at 15:08
• If Amu is right & @Manishearth is wrong, does that mean that Newton conducted a false experiment? That dispersion through a glass slab does not get explained through it? Thank you. Apr 17 '12 at 15:13
• Was the aim of Newton's experiment to explain lack of dispersion through a glass slab??
– Amu
Apr 17 '12 at 15:15