Rainbows are not Vampires - Comments

[Buckleymanor]

I agree that rainbows are not 3D objects. Our difference is simply that I prefer to extrapolate the light rays back to infinity. For me raindrops are merely mirror particles at a finite distance, they are certainly not the location of the rainbow. Extrapolate the light rays back to infinity to find the virtual object. The celestial sky is the location of the rainbow. Everybody sees the rainbow at the same location in the celestial sky.

I am not sure if they are not 3D objects.If you stood in the same position and took a series of photos of the rainbow would the rainbow appear as a sphere when the photos were combined together.Provided there was enough time to do it.

 

[Orodruin]

Why do you have the sun coming off-axis in your diagram, I wonder?

You can have a rainbow without having dusk or dawn, but yes, the cone axis should be aligned with the incoming sunlight. The center of the circle on the celestial sphere is going to be antipodal to the sun and therefore generally below the horizon. This is also why the mirror image of this circle looks like it does in the attached photo.

I wouldn't call my diagram a 'reflected' rainbow - it isn't formed by the same raindrops as the main bow and it isn't a 'reflection' of the main bow.

Yes it is! Even if it has not passed through the same drops. The image is on the celestial sphere, not at the raindrops. This is also crucial for understanding why it appears reflected in the lake in the photo. The rays AC and A'B' both extend to the same point on the celestial sphere, since they are parallel.

 

[spareine]

Why do you have the sun coming off-axis in your diagram, I wonder?
That photo is impressive but it shows the secondary bow being symmetrical about the horizontal*. In your diagram, the secondary bow would appear to include point C, which is not symmetrical about the horizon. Your diagram isn't clear about how (if) the image in direction AC ever appears as an image in direction of B'.

May be this helps: the proportions in my diagram are misleading. The rainbow circle is infinitely far away, whereas the size of the water is finite. The red rainbow B is centered at the antisolar point C. The green reflected rainbow B' is centered at the the reflected antisolar point C'. Bow B and bow B' are mirror images with respect to the celestial horizon. (Bow B' is a curve, it doesn't 'include' point C. I am not sure what is meant by an image in direction AC; C is the antisolar point)

I think the inverted bow in the photograph is formed by droplets above the lake surface and rays from the sun that are reflected by the the lake and then by low level droplets. That would account for the symmetry.
I wouldn't call my diagram a 'reflected' rainbow - it isn't formed by the same raindrops as the main bow and it isn't a 'reflection' of the main bow. In fact, it there were only a shallow layer of drops in the air, the 'reflection' bow would be formed but the main one wouldn't.
There is some doubt about your explanation and it would help to resolve it if you could quote another source / reference.

In your diagram and my diagram the light ray reflects at the water surface between the raindrop and the eye. Therefore it is part of the reflected rainbow. The reflected rainbow circle and the reflection rainbow circle are part of the same celestial circle (42º around C' ). However they rarely occur simultaneously.

 

[OmCheeto]

You don't have to arrange the rain to come at the right time of the day and month you could make a spray with some with water and a hose.

That's how I make them.

I am not sure if they are not 3D objects.

Ha ha! The semantics of science. The two "nots" cancel and your phrase becomes; "I am sure if they are 3D objects".
Which, if you throw out the "if", looks suspiciously like "I am sure they are 3D objects".
I suspect they are 3D objects.
Where the hell is @Janus when you need a ray-trace guru??!?

If you stood in the same position and took a series of photos of the rainbow would the rainbow appear as a sphere when the photos were combined together.Provided there was enough time to do it.

Now that sounds like a grand experiment!

ps. Rainbows are complicated. I like that about them.

 

[anorlunda]

The point that there are different raindrops causing the rainbow for different observers is a point well taken. But I do not think this is very different from two people looking at the same object through different mirrors

If two people look through different mirrors, they see the same color object. If two people see light from the same drop at different angles, they see different colors.

I still think we are just debating semantics. The "object" in question to an optics expert is the sun, but the common language meaning of "I see a rainbow" is that people think of the rainbow as the object. They may not be optically correct, but that is what they mean by the word rainbow.

 

[spareine]

Just semantics? Using the rainbow circle it was easy predict the shape and location of the reflected rainbow and the reflection rainbow in this thread, and the prediction was confirmed by a photo. So far attempts failed to predict the same using the rainbow cone.

 

[Orodruin]

If two people look through different mirrors, they see the same color object. If two people see light from the same drop at different angles, they see different colors.

Yes, but this is not the issue. If two people look through a mirror, the light from a given object is reflected at different parts of the mirror too. The question is not which raindrop reflected what - the question is where the virtual object is and the answer to that is "in the celestial sky". There is no difference to the mirror case here, if you remove the part of the mirror one person sees an object through, the person will not see it and if you remove the raindrops a person sees the rainbow through the rainbow will disappear.
The raindrops are not where the virtual image is.

I still think we are just debating semantics. The "object" in question to an optics expert is the sun, but the common language meaning of "I see a rainbow" is that people think of the rainbow as the object. They may not be optically correct, but that is what they mean by the word rainbow.

They would be perfectly optically correct. The rainbow is a virtual object in the celestial sky. You just need certain conditions to be fulfilled in order to see this virtual object - just as you need a mirror present to see a mirror image.

 

[sophiecentaur]

You don't have to arrange the rain to come at the right time of the day and month you could make a spray with some with water and a hose.

But the Sun needs to be shining - or you need a very bright light source at some (∞) distance.

 

[Orodruin]

But the Sun needs to be shining - or you need a very bright light source at some (∞) distance.

So? This is always the case - you need a primary object and the necessary optical setup in order to have a visual virtual object. Here we are talking about a virtual image of the Sun and so naturally the Sun needs to be shining. If it does not or if the necessary optical setup (raindrops + proper line of sight) is missing, you will not see a rainbow. If you do not have a source or if you do not have a mirror, you will not see a virtual image of the source in a mirror.

Edit: All the post you replied to was saying was that you did not have to wait for the correct optical setup (i.e., raindrops). Of course you still need the source, but the optics you can add manually (given line of sight ...).

 

[sophiecentaur]

@spareine
I think I am getting this now. I struggled a bit to find exactly what your unconventional diagram was getting at but the mirror image approach does make some sense. I would still like to see what goes on above the lake's surface in a bit more detail (3D) than in my diagram.

 

[spareine]

In an old PF-thread, 'Drove through the rainbow',[1] your were the proponent of the view that a rainbow is not the raindrops and not the cone, but a virtual image at infinity, even behind a hill, because it follows from parallax and geometrical optics. I am still wondering why you are so hesitant about that view in this thread.

 

[sophiecentaur]

In an old PF-thread, 'Drove through the rainbow',[1] your were the proponent of the view that a rainbow is not the raindrops and not the cone, but a virtual image at infinity, even behind a hill, because it follows from parallax and geometrical optics. I am still wondering why you are so hesitant about that view in this thread.

I don't see any inconsistency there. The thing that generates an image can be anywhere and so can the image. You don't see the drops and you can't see the cone (shape) because you are looking along it from the vertex. All you see is an image that is a long way away (parallax). I don't think I have changed my view at all. You can see a rainbow 'against' the dark ground in front of you but that doesn't mean the image is that close. Your brain does its best to place it in space and the cues point to the ground, even when parallax is telling you otherwise, because the bow appears (to me at least) to be moving over the ground as I move.
This conversation is fizzling out now - like a damp firework - everything has been said except the ray diagram of the light paths above the ground showing how that inverted bow is formed. I can sort of go along with your mirror image idea; it certainly ought to be right.
There was an issue about spurious rainbows that don't fall on the expected cone (s) but the particular circumstances would need to be quoted; for instance, there could be a strong ray of reflected sunlight and that could produce its own bow.

 

[OmCheeto]

... You can see a rainbow 'against' the dark ground in front of you but that doesn't mean the image is that close. Your brain does its best to place it in space ...

This is really confusing. The rainbow here is definitely between me and the guy in the black t-shirt. But the image isn't?

Scratches head for 10 minutes...
Ok. I think I understand both viewpoints now.
The raindrops are just acting like a bazillion, somewhat complicated little mirrors.
We could replace them with much larger standard mirrors, such that they all reflected the sun at you.
Then it would be obvious that the images you were seeing, were in fact, the sun.
But then...
We could argue that the guy with the rainbow shorts is just a bazillion little atoms, which are not very good mirrors, in any sense of the word.
But he does reflect sunlight, and we don't call him a reflection of the sun.

So I'm going to go back and agree with anorlunda, that we are arguing semantics, rather than science.

...
This conversation is fizzling out now - like a damp firework - everything has been said except the ray diagram of the light paths above the ground showing how that inverted bow is formed. I can sort of go along with your mirror image idea; it certainly ought to be right.
There was an issue about spurious rainbows that don't fall on the expected cone (s) but the particular circumstances would need to be quoted; for instance, there could be a strong ray of reflected sunlight and that could produce its own bow.

Well, it may be fizzling, but it's generated a few new questions in my brain. Unfortunately, I think it would take me a week to figure out how to ask the questions, such that people could understand what I was asking.

Ever since I caught the image of my rainbows intersecting at ≈90°,

I've been curious if I could position mirrors to create a complex rainbow image of Mickey Mouse.
Might be impossible. Maybe not impossible. Looking forward to summer.
Perhaps I'll study up on optics, and do some maths first.

 

[Orodruin]

The rainbow here is definitely between me and the guy in the black t-shirt. But the image isn't?

No, the rainbow is the image and it is further away than the guy. It is just your brain telling you it is not because the guy is not blocking it, but this is a very different effect than the concept of where the virtual image is located, which is determined by the divergence of light rays coming from the virtual image.

But he does reflect sunlight, and we don't call him a reflection of the sun.

Not it the same way a raindrop or mirror does. We do not go around calling everything we see at night a mirror image of the lamps. You need a more ordered reflection which let's you construct a virtual image.

 

[OmCheeto]

No, the rainbow is the image and it is further away than the guy. It is just your brain telling you it is not because the guy is not blocking it, but this is a very different effect than the concept of where the virtual image is located, which is determined by the divergence of light rays coming from the virtual image.
...

You are all crazy. I think I'll go finish reading my book, on evolution.

 

[sophiecentaur]

No, the rainbow is the image and it is further away than the guy. It is just your brain telling you

The rainbow is such a powerful and romantic image that we (our inate powers of perception) fail to analyse what's really going on. It's a paradoxical situation and something that evolution never hepled us tp deal with. It's along the lines of a cheap and cheerful reflection hologram which is so convincing that we feel we could touch it. We have learned, since birth, to deal with reflections in a plane mirror but even they will fool a dog, cat or bird (or human, in the right circumstances.

The rainbow here is definitely between me and the guy in the black t-shirt

That's what your brain is telling you but we all know that "seeing is believing" is no way to approach Science.
And you picture of the garden hose effect can probably be explained by the fact that the globs of water coming out of a hose (that close to it) probably consist of long cylinders of water and not spheres. Different beasts altogether" (Altogether- "different beasts!")

 

[spareine]

So I'm going to go back and agree with anorlunda, that we are arguing semantics, rather than science.

Well, in linguistics semantics is about meaning, which is useful even in science. In the article Anorlunda said that two persons cannot see the same rainbow. Does that mean he would also say it is impossible for a single person to keep seeing the same rainbow, either at rest or while travelling?

 

[sophiecentaur]

Well, in linguistics semantics is about meaning, which is useful even in science. In the article Anorlunda said that two persons cannot see the same rainbow. Does that mean he would also say it is impossible for a single person to keep seeing the same rainbow, either at rest or while travelling?

If you and I are looking at a sphere, from different angles, we see diferent parts of the sphere. Paint the sphere with red and blue dots and we may see different red and blue dots. Our experience could be totally different, the only common thing being that the Sphere is the same. Someone else has asked if the rainbows in two different towns are the 'same' rainbow. They are both caused by light from the same Sun but does that make them the same? If we are both looking at the letters "PF" on a sheet of paper then we would agree' it's the same "PF" but what if we are looking at a hologram that shows a P in one direction and an F in the other? We are looking at the 'same' hologram but seeing different letters. You may see a blue ray from one raindrop while I see a red ray from the same drop. There is no 'answer' to the question but the point about 'different rainbows' is very instructive because it makes people realize that it's not just drawn in the sky with a brush. If we were to refer to this as 'duality', perhaps that would be acceptable to both the big endians and the little endians on this thread. Frankly, my dear, I don't . . . . . .

 

[OmCheeto]

The rainbow is such a powerful and romantic image that we (our inate powers of perception) fail to analyse what's really going on. It's a paradoxical situation and something that evolution never hepled us tp deal with. It's along the lines of a cheap and cheerful reflection hologram which is so convincing that we feel we could touch it. We have learned, since birth, to deal with reflections in a plane mirror but even they will fool a dog, cat or bird (or human, in the right circumstances.

That's what your brain is telling you but we all know that "seeing is believing" is no way to approach Science.

I will have to think about this some more.
Perhaps someone should start a survey: Where is the image of the rainbow?
To make it simpler, perhaps we should reduce it to one raindrop, as natural rainbows are a mess of parallax, angles, a 3D refraction screen, and a non-point source of light.
I was thinking about someone's comment; "No two people see the same rainbow". This got me thinking, and I came up with the question; "At what distance, do each of our eyes not see different rainbows"? Perhaps we should shut one eye when talking about rainbows. That would cut the confusion in half, at least for me.

From anorlunda's image, It is my vote, that the "rainbow image" should be located at the surface of the south pole of the raindrop, where the light finally exits.

And you picture of the garden hose effect can probably be explained by the fact that the globs of water coming out of a hose (that close to it) probably consist of long cylinders of water and not spheres. Different beasts altogether" (Altogether- "different beasts!")

I'm fairly certain that the water hose "water shape & flow selection device" was set on "mist", so the globs of water would have been nearly spherical.
Likewise with my "Hippies & Rainbows" image. Everyone was standing under a "mister", as it was somewhat hot that day.

The picture of my 90° intersecting rainbows was caused by a reflecting source.

The second bow being created by the sun reflecting off of the convex back window on one of my cars.

So according to anorlunda; "I think you mean "reflection" rainbow, not "reflected""
It is an example of a natural, and a reflection rainbow, captured in a single image.

 

[Orodruin]

Perhaps someone should start a survey: Where is the image of the rainbow?

This, like most of physics, is not a subject for popular vote. A virtual image is something with a clear physical meaning (and as in many other cases it does not always correspond to what you would use colloquially) and this meaning will definitely not show up in a two-dimensional photograph as a photograph can never convey the divergence/convergence of the rays.

To make it simpler, perhaps we should reduce it to one raindrop, as natural rainbows are a mess of parallax, angles, a 3D refraction screen, and a non-point source of light.

You cannot reduce it to one raindrop. This will miss out on the entire argumentation of there being essentially parallel rays of light coming from different raindrops, thereby creating the virtual image at infinity.

From anorlunda's image, It is my vote, that the "rainbow image" should be located at the surface of the south pole of the raindrop, where the light finally exits.

Again, it is not a matter of popular vote. What you are saying is essentially equivalent to saying that the image of something seen in a mirror is where the light exits the mirror glass. This is not the case - the virtual image in the mirror is not even in the mirror, it is the same distance from the mirror surface as the actual object is and there may very well be other actual physical objects in this place - but the image is virtual and that therefore does not matter whatsoever.

 

[spareine]

If we are both looking at the letters "PF" on a sheet of paper then we would agree' it's the same "PF" but what if we are looking at a hologram that shows a P in one direction and an F in the other? We are looking at the 'same' hologram but seeing different letters. You may see a blue ray from one raindrop while I see a red ray from the same drop.

Optics is about images and apertures (openings or windows that restrict the field of view). In your hologram example, the plate is the aperture and the virtual image is behind it. A moving observer might see, depending on his position, the entire image or a part of it, like its left side or right side. In the case of a rainbow, the rain curtain is the aperture. The image is far behind it. A traveling observer might see, depending on his position, the entire rainbow, or its right side or left side.
The traveler would say that the left side and right side are parts of the same rainbow. Everybody is extremely familiar with the effect of a window on the field of view.

 

[sophiecentaur]

the virtual image is behind it.

Not necessarily. (See page 17 of this link.)

In the case of a rainbow, the rain curtain is the aperture.

The aperture is more like the individual droplet, or at least those in or near the 42° cone. The image is so diffuse that an aperture of many metres is not needed in order to see just one of the rainbow colours..

 

[spareine]

Sometimes, like in OmCheeto's photo in #48, individual rain drops are visible. In that case the aperture is a multi-pinhole screen. In most rainbow photos the camera doesn't resolve individual droplets, and the rain curtain can be treated as a uniform window. The distinction doesn't really matter, in both cases the virtual image is seen through an aperture.

 

[sophiecentaur]

Everything we see is "through an aperture". I don't see how that's really relevant. You seem to be suggesting that small or large regions of drops would produce a different looking rainbow. I doubt that. The net result of a lot of random scatterers would not show any detailed diffraction pattern.
A camera often works with a small f Number and the depth of focus can be pretty small. Most rainbow pitures are focussed on a distant landscape, for aesthetic reasons but I must try to see whether I can get a good photo of a raindrops at 42° and see if the coloured bit occupies a region within a drop. I guess it would be easier to get hold of a small glass sphere and do my own, non 42° trick. Small water frops must be approaching the diffraction limit, which complicates things further.

 

[Orodruin]

Everything we see is "through an aperture". I don't see how that's really relevant. You seem to be suggesting that small or large regions of drops would produce a different looking rainbow. I doubt that.

You are misunderstanding his post. His point is that you cannot see a rainbow at 42 degrees if there are no raindrops in that direction, just as you cannot see an object behind a wall if there is no window in the object's direction. There is nothing strange going on here.

 

[spareine]

And may be this helps: each raindrop of the rain curtain is represented by a single pinhole in the screen.

 

[sophiecentaur]

just as you cannot see an object behind a wall if there is no window in the object's direction.

A nearer parallel could be the limited field of view through a small mirror.

each raindrop of the rain curtain is represented by a single pinhole in the screen.

Yes. That, again, is fairly obvious at this stage in the discussion. In fact I really don't see where the last few posts have been going. A straightforward rainbow was explained to me when I was 15 years old or less and the whole class got the whole thing except the position of the image (not discussed ). Non-standard rainbows have been dealt with.
There are many images that work similarly to how a rainbow works. The result of smearing a lens or a window is due to an array of separate elements. A starburst lens filter is another example. In some cases, there is a real image and in some cases it will be virtual.

 

[Orodruin]

A nearer parallel could be the limited field of view through a small mirror.

Only if you put a lot of other mirrors arranged with their surfaces parallel to the first small mirror such that you never really lose sight of the object.

Edit: I just realized I have the mathematics skills to actually compute the angle of the rainbow caustic ... I wonder why I never thought about that in the 17 years since I learned calculus ... Anyway, it is a neat little exercise in geometry and calculus I can recommend to anyone who has not tried it yet. It also shows why there is no rainbow from the light exiting the raindrops without an internal reflection in between.

 

[Buckleymanor]

I will have to think about this some more.
Perhaps someone should start a survey: Where is the image of the rainbow?
To make it simpler, perhaps we should reduce it to one raindrop, as natural rainbows are a mess of parallax, angles, a 3D refraction screen, and a non-point source of light.
I was thinking about someone's comment; "No two people see the same rainbow". This got me thinking, and I came up with the question; "At what distance, do each of our eyes not see different rainbows"? Perhaps we should shut one eye when talking about rainbows. That would cut the confusion in half, at least for me.

From anorlunda's image, It is my vote, that the "rainbow image" should be located at the surface of the south pole of the raindrop, where the light finally exits.

I'm fairly certain that the water hose "water shape & flow selection device" was set on "mist", so the globs of water would have been nearly spherical.
Likewise with my "Hippies & Rainbows" image. Everyone was standing under a "mister", as it was somewhat hot that day.

The picture of my 90° intersecting rainbows was caused by a reflecting source.

The second bow being created by the sun reflecting off of the convex back window on one of my cars.

So according to anorlunda; "I think you mean "reflection" rainbow, not "reflected""
It is an example of a natural, and a reflection rainbow, captured in a single image.

Sorry about the late reply computer down.
The comment about no two people see the same rainbow is interesting in as much as that no one person sees the same rainbow or is it that we all see the same rainbow effect but from a different perspective.
I don't know if you have ever walked along the see shore with the sun shining low in the sky.You get a bright band of sunshine reflecting off the see from the horizon up towards your feet, as you walk along the bright band follows.So like the rainbow you can deduce that the bright band actually covers the whole of the see depending on which position the individual observer or observers are placed.Some one further up the beach would see a bright band just like you do but if you looked back towards him you would not see his band just the same as he would not see yours.

 

[sophiecentaur]

The comment about no two people see the same rainbow is interesting

Yes, it is interesting; more so because the form of the rainbow is exactly the same for everyone. This contrasts with the different view that two people have of most other things they may both be observing. We say that we all see the same Moon but the views from different parts of the Earth is measurably different. This conversation says more about People than about the Physics of the situation.

 

[Orodruin]

Yes, it is interesting; more so because the form of the rainbow is exactly the same for everyone.

But this is precisely what you expect for an object at infinity! So why have you (seemingly) been arguing that the rainbow (as a virtual object) is not at infinity?

 

[sophiecentaur]

I can put the image of a microscope sample at infinity. Can anyone else see that? What has the image distance got to do with it?
I really don't know where you are going with this.
We can all see the same image on TV and the image is a few metres away.?

 

[Orodruin]

I can put the image of a microscope sample at infinity. Can anyone else see that?

This has to do with the aperture, not the location of the virtual object. Just like seeing the rainbow is dependent on the aperture in the form of the raindrops. The rainbow itself as a virtual object is not at the raindrops, but at infinity. There is a family of rays which are parallel, corresponding to an image at infinity, whether you see it or not depends on the aperture.

I really don't know where you are going with this.

I am only trying to understand how you can have the view that the rainbow as a virtual image is at the raindrops at the same time as you consider it to not change depending on the observer - a typical property of an image at infinity.

 

[sophiecentaur]

how you can have the view that the rainbow as a virtual image is at the raindrops

I don't have that view. Where did I say that? Was it because of my comments about seeing a rainbow 'in front of' a field of grass? I would argue that I do and I assume most people do, also (due to the stories of pots of gold etc.) Where we place an image (mentally) need have nothing to do with the optics of the situation because our brains don't just use optics when we build up a scene in our minds. We 'see' a rainbow in a field because out brain tells us that we could not actually be seeing 'through' solid Earth and grass. We perceive the rainbow moving across the field as we walk. Interestingly, it is quite the opposite when we see an image in a mirror because we are quite prepared to believe there's a whole roomfull of stuff in that solid brick wall.
I think we would not be having any of this discussion is we could be totally objective about what enters out eyes. If you want to discus just the Physics of the Rainbow then that's ok but the thread would need to have been terminated way back.

 

[Orodruin]

I don't have that view. Where did I say that? Was it because of my comments about seeing a rainbow 'in front of' a field of grass?

Perhaps, I just got that impression over the course of the thread.

I think we would not be having any of this discussion is we could be totally objective about what enters out eyes. If you want to discus just the Physics of the Rainbow then that's ok but the thread would need to have been terminated way back.

Of course we cannot be objective, our brain plays tricks on us all the time, which is why I have always focused on the physics aspect. If you have been talking about the perception all the time this would explain why we talk around each other.