# Curvature of an Artificial Rainbow (created in Lab).

leoflindall
I have just created a rainbow artificially and the photo is attached. I didn't expect the bow to come out straight as it has. Does anyone have any idea why it is straight and not curved (or circular)?

I know rainbows are normally curved (or spherical) normally because the particles that the effect originates are in differant places in the sky to maintain the critical angle for the primary bow to be observed. So I am wondering if it is straight (or possibly very slightly curved) as the observer is much closer to the effect maybe?

Any thoughts or ideas would be greatly appreciated.

Many Thanks

Leo

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Without knowing any details of your setup, it's hard to say. The angle of a 'natural' rainbow is found by approximating the sun as a point source and the raindrop as spherical.

How did you make the rainbow?

leoflindall
Hi Andy,

The rainbow was made by producing water droplets in a enclosure. High intensity light was then shone through a lens setup with the aim of collimating it, although at this point It has just focused it and reduced the amount of divergance of the rays. I tried to upload a photo of the setup but the file was too large.

What I dont understand is that you would expect to observe the primary bow at around 42 degrees from the angle of the incident light, but (i appreciate it is hard to tell from the photo!) the rainbow is observed at an angle of 42 degress to the side (ie; in the x-plane). At first I though the effect had just been rotated through 90 degrees, but if that was the case the bow would have also been rotated. I can't see how the bow is produced in that orientation!

Any ideas?

Many Thanks

Leo

leoflindall
I just drew up a quick setup diagram, excuse the crudeness!

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yuiop
I know rainbows are normally curved (or spherical) normally because the particles that the effect originates are in differant places in the sky to maintain the critical angle for the primary bow to be observed. So I am wondering if it is straight (or possibly very slightly curved) as the observer is much closer to the effect maybe?
I do not think it is due to the proximity of the observer to the effect because as can be seen in this video the curved rainbow effect can be seen close up to a garden sprinkler with the sun as light source. Warning: Turn off your sound before playing the video or you may get brain damaged. (Apparently this never happened 20 years ago... LOL) :tongue:

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leoflindall
Hi yuiop,

Very amusing video, begs disbelief! I hadn't thought about a sprinkler, however what intrested me in that video (after the commentry of course!) was that the curvature seemed to be less than that of a bow produced in particles in the atmosphere. As my rainbow is another step down in magnitude. (the bow is around 2-3mm from the outer bounday of the red band to the inner bounaday) that maybe there is another stap down in cuvature, and mine is curved, but only slightly so. If I'm right I cant find any theory that would support this as i would expect the bow to be sperical around the anti solar point, unless the radius of the bow to the anti solar point was massive, and of a magnatude much greater than my setup would be able to produce.

Can't get my head round this one!

Hi Andy,

The rainbow was made by producing water droplets in a enclosure. High intensity light was then shone through a lens setup with the aim of collimating it, although at this point It has just focused it and reduced the amount of divergance of the rays. I tried to upload a photo of the setup but the file was too large.

What I dont understand is that you would expect to observe the primary bow at around 42 degrees from the angle of the incident light, but (i appreciate it is hard to tell from the photo!) the rainbow is observed at an angle of 42 degress to the side (ie; in the x-plane). At first I though the effect had just been rotated through 90 degrees, but if that was the case the bow would have also been rotated. I can't see how the bow is produced in that orientation!

Any ideas?

Many Thanks

Leo

I understand your setup better- thanks. Collimating the light should be close to a "solar simulator", but you were imaging the source onto the droplets?

The rainbow is formed at ~138-139 degrees from the incident light- the sun is *behind* you when you view the rainbow. The secondary bow is from 129-127 degrees. The rainbow is a caustic, and thus forms a cone with respect to the illumination; this may explain what you mean by "x-plane".

Or am I not understanding your setup?

leoflindall
I understand your setup better- thanks. Collimating the light should be close to a "solar simulator", but you were imaging the source onto the droplets?

The rainbow is formed at ~138-139 degrees from the incident light- the sun is *behind* you when you view the rainbow. The secondary bow is from 129-127 degrees. The rainbow is a caustic, and thus forms a cone with respect to the illumination; this may explain what you mean by "x-plane".

Excuse my use of x-plane, that wasnt really the best description!

I made an attempt to collimate the light using lens (the light source if just a flood light), but the len's where wrong but intrestingly caused the effect shown in the photo. I think maybe the divegance of the light at the edges of the lens may be very low allowing the rays to centre on the maximum of ~42 degrees (~138 degrees) as the effect is onlt seen in this region.

The photo is taken from the side of the light source, so as in nature the light source is behind me, and the angle between the incident ray and the scattered ray is 42 degrees. It is just as if the effect you would observe in nature has been rotated 90 degree but for one differance that I can't explain, which is that the orientation is the same as if it had not be rotated, I would have predicted that the bow would be 90 degrees rotated than what is shown in the photo.

The second thing that I dont Understand is that it seems strange is that is appears as strange, so I wonder if it is very slightly curved due to the closeness of light source and observer to the water droplets.

I have attached another diagram (even more crude than the last, I apoligise) which i hope will give you an idea of the path the rays is taking. The black rays represents what was observed, as in the photo, and the red ray shows what I predicted.

Thank You

Leo

yuiop
I have attached another diagram (even more crude than the last, I apoligise) which i hope will give you an idea of the path the rays is taking. The black rays represents what was observed, as in the photo, and the red ray shows what I predicted.
Oops, you seem to have forgotten to attach the diagram. It would be helpful to us if you show the actual location of the camera in the set up relative to the light source and the curtain of droplets. Is the curtain of droplets actually a right angles to a line passing from the light source and the centre of the collimating lens? One obvious difference is that the light source is much closer to the droplets than in nature and while the rays coming from the sun are essentially parallel, the rays from your source are presumably diverging (or converging?).

leoflindall
My apolgies! They are now attached. The camera is at ~1m from the droplets, the attached diagram should hopefully show where it is position, but it is next to at the light souce at the same height, just moved left by the amount dictaed by the 42 degree scattering angle.

Is the curtain of droplets actually a right angles to a line passing from the light source and the centre of the collimating lens?
.

The droplets are fallingslightly aways from perpindicular (~~95 degrees) as the light source is raised. (this was originally done as i was expecting to see the effect beneath the light source, so was to allow the scattered light to be reflected out of the set up and not hit the bace of the enclosure(see set up diagram in third post)). I think the diagram will also make this clearer.

One obvious difference is that the light source is much closer to the droplets than in nature and while the rays coming from the sun are essentially parallel, the rays from your source are presumably diverging (or converging?).

I attempted to collimate the light using the lens, although I used the worng lens to collimate it, i believe that it has collimated some of the light. I have attached naother diagram where i have marked the ray paths that where determined through inspection of the effect produced by the set up.

The photos of the set up are too big to upload, but i will try to upload them online and post the link.

Sorry for forgetting the attachments!

Leo

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yuiop
OK, the collimating lenses are obviously a problem, because the light rays are neither coming from a single point nor parallel making calculations difficult. I think one thing that might be happening is that your droplets are not spherical but actually more like short vertical cylinders. The horizontal cross section of each water cylinder is circular so you get the expected diffraction at 40 to 42 degrees horizontally but not vertically because the vertical cross section is not circular. You would need a high speed camera (or possibly a low speed camera and a fast flash) to try and find out the shape of your droplets. One thing I am curious about is that the photograph of the rainbow in the first post looks like it is approximately horizontal while I would expect it to look nearly vertical when viewed from the side of the source.

leoflindall
PHOTOS! I have uploader them to flickr. It's my first time using this site so please let me know if it doesn't work. INcluded are photos of setup, effect and droplet size. the link is;

http://www.flickr.com/photos/58973961@N04/

OK, the collimating lenses are obviously a problem, because the light rays are neither coming from a single point nor parallel making calculations difficult. I think one thing that might be happening is that your droplets are not spherical but actually more like short vertical cylinders. The horizontal cross section of each water cylinder is circular so you get the expected diffraction at 40 to 42 degrees horizontally but not vertically because the vertical cross section is not circular.

I agree, it was purley by accident that I discovered this lens configuration worked. I think that theres is a possibility that the droplets are cylindrical. If you look at the photos I have included a picture of the droplets produced by the system and it shows the particles as streak, however i think a lot of this is due to the exposure speed (1/500 s). I worked out the velocity of the particles and it was significantly lower than the terminal velocity or a raindrop so I wonder how much of each 'streak' could be taken up by the 'cylindricalness' of each droplet. Brian Lim (2006) wrote an extensive paper on the shape of the raindrop, and one of the conclusions draws was at the sizes of particles that have been produced the remain spherical, despite the forces on them from falling. Of course this doesn't allow for the fact that the droplets are being emitted under pressure from the sprinklers.

I wonder if the explanation for the bow being oriented as it is (assume x-plane in the direction of the incidnt light, y vertical and z depth) the light is incident on the droplet on the side of the central axis and refracted in the z-plane, then reflected in the y-plane, and then refracted again in the z- plane, which could account for the orientation of the bow. Not sure though, what do you think?

Regards

Leo

Buckleymanor
So I am wondering if it is straight (or possibly very slightly curved) as the observer is much closer to the effect maybe?

Any thoughts or ideas would be greatly appreciated.
My take on this is that the reason why it's only slightly curved or straight is because you have not got the round Sun behind you and only a point source.
If you stand with your back to the Sun and pinch the end of a garden hose so it sprays water in front of you.You should move your arm about a bit.You will not only produce a rainbow but also a rain circle if you persist a bit.The shape of the droplets don't have to be too consistent as just pinching the hosepipe makes the effect.
You can't get much closer than this and the raincircle appears to be about 8ft in diameter so I can't imagine the nearer to the bow having an effect that makes it only slightly curved or straight, it must be something to do with the light source.

leoflindall
My take on this is that the reason why it's only slightly curved or straight is because you have not got the round Sun behind you and only a point source.
If you stand with your back to the Sun and pinch the end of a garden hose so it sprays water in front of you.You should move your arm about a bit.You will not only produce a rainbow but also a rain circle if you persist a bit.The shape of the droplets don't have to be too consistent as just pinching the hosepipe makes the effect.
You can't get much closer than this and the raincircle appears to be about 8ft in diameter so I can't imagine the nearer to the bow having an effect that makes it only slightly curved or straight.

I think you have a point there! I had considered a hosepipe earlier but got the relative magnatude's of the curvature mixed up in my head. However the light source in significantly larger than the effect observed. The bow is ~2mm across, and the light source is ~10Cm before going through the lenses. I think this could be the reason why it isn't curved (kinda of the same thing but the other way around!), but I am trying to understand why that is.

Thank you for you help

Leo

neduet89
keep it up!

yuiop
I have plotted some rays paths in 3d program trying to duplicate your set up as near as possible, but I am unable to duplicate your results. The ray tracing gives a slightly curved rainbow that is nearly vertical rather than the straight nearly horizontal rainbow in your photo. I have attached the 3d construction if you are interested. The grey cylinder on the right is the light source and the small square on the left represents the back plane of a pin hole camera. The near vertical light blue plane represents the sheet of droplets from the spray bar. I have tried various angles for the water sheet from vertical to 45 degrees and various orientations of the light source relative to the sheet but get nothing close to your result. Obviously I must be making some assumptions that are not in agreement with your actual set up. Incidentally, it might be worth trying taking a photograph with a pin hole camera and this will remove any artefacts due the lenses and filters of your camera. All you have to do is remove the lens from your camera and cover it with aluminium foil and make a pin hole in it. The tricky part is getting the exposure time right and you will need a tripod to hold the camera steady for the long exposure. As I mentioned earlier, it might also be worth getting/borrowing a flash for your camera to freeze the droplets. This is much cheaper than getting a high speed camera.

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leoflindall
I have plotted some rays paths in 3d program trying to duplicate your set up as near as possible, but I am unable to duplicate your results

Thank you for the time, I appreciate it!

The near vertical light blue plane represents the sheet of droplets from the spray bar. I have tried various angles for the water sheet from vertical to 45 degrees and various orientations of the light source relative to the sheet but get nothing close to your result. Obviously I must be making some assumptions that are not in agreement with your actual set up.

What the program has predicted is what I would have expected, and as far I can see you have made any assumptions that are not the case, or at least significant enougth to alter the bow so significantly!

I have attached a very crude paint image od what i think might be going on, where the light is incident on the particle and is reflected in the x-plane, then reflected in the Z-plane and the refracted in the Z-plane. I think this would give the image observed, but as an explanation it's not sitting particularly well. And if it does explain the effect, I have no therotical rational to support the hyperthosis just that it is instramantal in explaining the observation!

Many Thanks

Leo

leoflindall
ATTACHEMENT!

Once again I fogot to attach the file! Here it is...

Leo

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yuiop
I have attached a very crude paint image od what i think might be going on, where the light is incident on the particle and is reflected in the x-plane, then reflected in the Z-plane and the refracted in the Z-plane. I think this would give the image observed, but as an explanation it's not sitting particularly well. And if it does explain the effect, I have no therotical rational to support the hyperthosis just that it is instramantal in explaining the observation!
I found a very good applet for tracing the various light paths through a raindrop here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=44 and that link has a couple of good videos too. Unfortunately, I am still not able to explain your observation adequately. Hopefully you will keep us informed if you make any additional observations in your experiment that shed any light (:tongue:) on this problem.

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