Science Questions

What determines actual shape of rainbow?

Sun, 2nd Aug 2009

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Rosemary Gant asked:

What determines actual shape of rainbow? I watched one the other night and it was almost flat along the horizon


Dave -   Okay.  The rainbow is actually always the same shape.  Itís always a circle.  The way a rainbow is formed is that when the light goes into a raindrop, it kind of reflects around the back and as it goes in and goes out, it refracts.  It bends because light goes slower in water than it does in air.  Different colours refract slightly different amounts, so the light comes out of the raindrop in different directions depending on its colour. A raindrop is circularly symmetric so the refraction means that you get a cone of different colours of light coming out of the drop.

Lunar Rainbow So, if you look at the raindrop from certain different directions, it looks different colours.  If you have a whole sky full of raindrops at different angles you see different colours depending on the direction you are looking in.

You get a circular rainbow exactly opposite the sun. If the sun is high in the sky, you just see the top of the circle and the rainbow looks flat. If the sun is low, you can see a full semicircle, and if you are in a plane you can see a full circular rainbow.

Chris -   That makes sense and when you see a second rainbow thatís presumably where itís gone into the raindrop bounced off the front of the raindrop, gone to the back again and come out front.  So, there are two journeys and thatís why you get a second rainbow around the first?

Dave -   Itís doing more exciting things inside the raindrop.


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Rosemarie Gant asked the Naked Scientists: Hi Chris One thing I was wondering as I drove home through the storms last night: what is it that sets the curve of a rainbow?† I've previously thought that rainbows have sometimes smoother curves than others.† But last night I saw the most extreme example I have seen: the rainbow was practically flat along the horizon with just the tiniest bit of sky showing in the centre.† So I thought I'd ask :-) Best wishes, Rosie. What do you think? Rosemarie, Sat, 11th Jul 2009

All rainbows have the same curvature: that of a circle.
The position of the sun determines how much of the circle is seen:
the closer the sun is to the horizon the higher/bigger the rainbow.

BTW what you have seen may not have been a rainbow ... RD, Sat, 11th Jul 2009

You can get some funny shaped rainbows by spraying a fine mist in different patterns i.e. by sticking your finger over the end of a hose-pipe.  These are 'artificial' though, of course. LeeE, Sat, 11th Jul 2009

Does the shape of the water particles affect the appearance of the rainbow? Herman Melville, Sat, 11th Jul 2009
RD, Sat, 11th Jul 2009

It's not the shape of the water particles; they're all spherical.  No, it's the shape of the mist/spray; with a bit of practice you can make a 'U' shaped spray, for example, and with special nozzles you can make different shaped ones. LeeE, Sun, 12th Jul 2009

The bigger the drops are the more they deviate from spherical ... RD, Sun, 12th Jul 2009

The bigger the drops are the more they deviate from spherical ...

Umm... I'm talking about a mist, not raindrops from a shower. LeeE, Mon, 13th Jul 2009

I think that is all wrong, I'm afraid.
Whatever shape you make your 'mist' you will only get light from the appropriate angle of cone if the droplets are all spherical. If the mist doesn't cover the whole arc then you'll only get a partial bow.

The angle in all the classic explanatory diagrams will not be appropriate if the section of the drops is not a circle. So a bow which is formed by passing through the flattened drops of very heavy rain - like I got last Tuesday in Chichester Harbour - will not have the same curvature all the way round. I suspect that, as the vertical section through a flat drop will be a bit 'bone shaped', the scattering angle will be greater than for a circular section, making the bow a bit flatter at the top.
That picture on the other thread is very impressive too, showing the possibility of multiple 'fringes. Gawd knows what paths the light has to take inside the drops to produce them.Does it imply that there is only partial reflection or that there are ripples inside the drops?
EXPERT PLEASE???? lyner, Mon, 13th Jul 2009

Well I'm just going by what I've observed while messing around, sticking my finger/thumb over the end of a hose pipe. LeeE, Tue, 14th Jul 2009

Look at one of the many diagrams showing how it works.  Here is one.
Jeez, that's a URL and a half.
The light reflects off the inner surface of a sphere twice and emerges, having been bent through an angle of around 140 degrees and the various wavelengths are bent a bit differently (dispersion) . For a single drop, you see light of only one colour - that's the only wavelength which gives you the correct angle - other wavelengths go in different directions so you see different colours from other drops. If you had only one drop. you would see different colours from it as you moved your head - just  the same effect that you get when you look at the Sun's light catching a water drop hanging from a leaf.
This is true for all directions. So you will see light of a particular colour arriving as if  from a circular source.  It's a virtual image, of course, and appears at infinity. That is, without other stronger clues, such as the  fact that you may see it despite the garage wall being only a few metres away. Under those conditions the brain steps in and tells you that it must be nearer than the wall, despite what your eyes' focusing information tells it.   I think you need to do your experiment again and check what you 'really' see.  People have claimed all sorts of things about the appearances of rainbows but we can pretty well rely on ray optics to tell you what is actually going on. That doesn't detract from the pleasure of seeing them, though.             
The Sun's light can be assumed to be arriving on the scene as parallel rays and the size of the drops does not affect the geometry, as long as they're spherical. lyner, Tue, 14th Jul 2009

I'm not disputing the mechanism of the optics, which I do understand, and what you've said is perfectly true for a uniform mist.  The only point I was trying to make is that by making a non-uniform shaped mist you can get some strange shaped rainbows.  I don't need to perform the 'experiment' again (I was washing a car using a hose without a nozzle and used my finger/thumb to make a jet in an effort to dislodge some crud from beneath the wheel arches) as I was so intrigued by the effect that I was distracted for a good five minutes, trying different spray shapes and orientations to see how the appearance and shape of the rainbows changed. LeeE, Wed, 15th Jul 2009

Thatsounds fun Lee.. I will try it sometime.. something kids may find great fun also... Karen W., Wed, 15th Jul 2009

If the artificial mist doesn't cover the whole of the region needed for a bow, then the bow may not be its full length or thickness. BUT the green 'stripe' (i.e. one wavelength) cannot be anything other than circular. For it not to be would be like saying that a pair of compasses, bolted together at a certain angle, could produce anything other than a circular arc.  The mist shape is not relevant to the direction from which a certain colour arrives at your eye. Each drop does its own thing and produces light of a certain colour in a certain direction. Drops in line  with / behind that drop will also send green in your direction. Green can't come from any direction but the one which is dictated by the optics of each spherical drop.
Like I said before, what we see is often not what is actually there. Paul Daniels has proved this on many occasions.
Possible explanations for non-circular appearance might just be that  you viewed one part of the bow with one eye and the other part with the other eye but the eyes are so close together that, at a distance of even just a few metres, the angle difference would only be small. Also, if the spray is coming our of the nozzle at high speed, the drops may not be spherical.  (That's my favorite one). Once they have slowed down and drift downwards, they would definitely be pretty much spherical.
I shall observe when spraying the garden on the next sunny day. lyner, Wed, 15th Jul 2009

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