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Why do rainbows have their characteristic inverted arc shape ?

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Good question. I suppose rain drops are spheres and the sun shines downwards so the reflected and refracted light would be in a curve, shaped downwards too.

I think. Maybe.

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• 8 months later...

In fact, a rainbow is a circle, but we can’t see the full shape because the horizon cuts off the lower half.

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If you draw a line between the sun and you as observer and extend it in the direction away from the sun, the rainbow forms a circle with a point on that line as the centre. That is because the reflection you see occurs when the angle between the the line (you to sun) and (you to rainbow) has a particular value which varies slightly with wavelength. As stated above, this actually forms a complete circle, which I have actually seen once from the cockpit of an airplane.

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Rainbows are just one of a plethora of atmospheric optical effects, and some arch up or to the sides.

Les Cowley is an expert and here is his main page: >> Atmospheric Optics

Here's his rainbow page: >> Rainbows

Rainbows take many forms. Multiple bows, bows that cross, red bows, twinned bows, coloured fringes, dark bands, spokes and more. Rainbow pictures and explanations here.

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The number 42 is, in ‘The Hitchhiker’s Guide to the Galaxy’ by Douglas Adams, the answer to the ultimate question of life, the universe and everything, calculated by an enormous supercomputer called Deep Thought over a period of 7.5 million years. Unfortunately, no one knows what the question is, but I’m thinking rainbows:

42 degrees is the angle at the observer’s eye between the arc of a rainbow and the center of the circle it would make if not obscured by the land/sea. So if the rainbow is estimated to be say 1.5miles from the observer: Sine 42 degrees x 1.5 miles, or 0.67 x 1.5 miles giving a rainbow radius of 1mile. If it makes it any easier to guess the distance between the rainbow ends at the surface (often somewhere between the radius and diameter) simply double the radius to get the diameter, 2 miles in this example. Hmmm…I’ve just realised this has not answered the post question or find what the ultimate question was, sorry everyone.

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I loved that book. I don't see how the Earth could have been in the way of the intergalactic highway though, space is quite big. Go underneath!

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• 1 year later...

I am glad I found this thread before posting my question.  Now it is partly answered.  The rainbow is a sphere?  Or, someone said a circle but it must be a sphere.  No?  To start, this is what I had planned to post:

Have you ever wondered about this?  The rainbow's colors are in order according to what they make.  We have blue green yellow because blue and yellor make green.  We have yellow orange red because yellow and red make orange.

My assumption is that, in each case, the first and third are blending their colors to make the second.  All right.  We see a rainbow as sunlight is reflected through a water drop.  But we do not see the entire water drop.  The rainbow begins with violet, then blue.  The red that is needed is at the other end.  So, how do the red and blue manage to meld and form violet?  Is the rainbow a sphere which we see (as we do the moon) only half of?  Where do the red and blue meet?

As regards my question, what I've read above says to me that there is no "other end".  The red almost meets the blue, having melded colors to form violet first.  Am I right so far?

Now I am left with this.  We have our three primary colors and our three secondary colors: SPSPSP.  That is six colors and we manage to see more than half of them in the front half of that sphere.  Only one pair do not appear to meet.  They seem to take up the entire back half of the sphere to blend their colors.  Or, are we seeing more than half the sphere?

Comment?

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I am glad I found this thread before posting my question.  Now it is partly answered.  The rainbow is a sphere?  Or, someone said a circle but it must be a sphere.  No?  To start, this is what I had planned to post:

Have you ever wondered about this?  The rainbow's colors are in order according to what they make.  We have blue green yellow because blue and yellor make green.  We have yellow orange red because yellow and red make orange.

My assumption is that, in each case, the first and third are blending their colors to make the second.  All right.  We see a rainbow as sunlight is reflected through a water drop.  But we do not see the entire water drop.  The rainbow begins with violet, then blue.  The red that is needed is at the other end.  So, how do the red and blue manage to meld and form violet?  Is the rainbow a sphere which we see (as we do the moon) only half of?  Where do the red and blue meet?

As regards my question, what I've read above says to me that there is no "other end".  The red almost meets the blue, having melded colors to form violet first.  Am I right so far?

Now I am left with this.  We have our three primary colors and our three secondary colors: SPSPSP.  That is six colors and we manage to see more than half of them in the front half of that sphere.  Only one pair do not appear to meet.  They seem to take up the entire back half of the sphere to blend their colors.  Or, are we seeing more than half the sphere?

Comment?

Be careful with this line of thinking. The colours we see are the result of the way our retinae handle light of different wavelengths. We have three different types of receptor, each of which has a maximum sensitivity to light of a different wavelength. The ideas we have about mixing colours are the result of the way these receptors and our brains work, and have nothing to do with the physics of light itself. A good example is the idea of mixing red and blue to get violet. In terms of physics, red light has the longest wavelength, blue is shorter and violet is shorter still. Violet light is NOT a mixture of red and blue light.

The separation of colours in a rainbow is because the refractive index of water is greater for shorter wavelengths of visible light than for longer ones. So the violet light is bent through a bigger angle than the red (this is why violet appears on the inside of the rainbow) and the wavelengths corresponding to other colours somewhere in between. This phenomenon is called dispersion (and has some very interesting chemical physics behind it which I won't bore you with. :) )

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Be careful with this line of thinking. The colours we see are the result of the way our retinae handle light of different wavelengths. We have three different types of receptor, each of which has a maximum sensitivity to light of a different wavelength. The ideas we have about mixing colours are the result of the way these receptors and our brains work, and have nothing to do with the physics of light itself. A good example is the idea of mixing red and blue to get violet. In terms of physics, red light has the longest wavelength, blue is shorter and violet is shorter still. Violet light is NOT a mixture of red and blue light.

The separation of colours in a rainbow is because the refractive index of water is greater for shorter wavelengths of visible light than for longer ones. So the violet light is bent through a bigger angle than the red (this is why violet appears on the inside of the rainbow) and the wavelengths corresponding to other colours somewhere in between. This phenomenon is called dispersion (and has some very interesting chemical physics behind it which I won't bore you with. :) )

(quote)  violet light is NOT a mixture of red and blue light.

:-)  Exactly the thought that finally dawned on me last night.  First, a question.  Where in the spectrum are the colors that we humans cannot see?  After the red?   I think so.  That would put quite a gap of unknown colors between red and blue.  And from in there - along with the visible blue - maybe comes the violet?

Now I have an unscientific theory - unscientific meaning I cannot test and prove it.  The visible red and some unseen color forms purple.  Purple is a very different color.  I once knew an art teacher who was constantly saying "there is no such color as purple".  Well, we know there is.  That strong, bold, rich, deep mix of red and (what?).  We can see it?  We're just  not allowed to wear it unless we are rich or royal.  :-)

Your paragraph 2:   I forgot my geometry.  Sorry about that.   That said, a recently-read article kept talking about observing the rainbow through a rain drop.  That can't be exactly accurate, can it?  The rain drop would have to be terribly large.  We need one large, spherical prism of water.  No?

Thank you.  I'll be interested in your idea of where purple came from.  It does exist.  I have an art pencil that makes a beautiful purple.  Of course, how makers of paints and leads do it is another story.

Edited by hazelm
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(quote)  violet light is NOT a mixture of red and blue light.

:-)  Exactly the thought that finally dawned on me last night.  First, a question.  Where in the spectrum are the colors that we humans cannot see?  After the red?   I think so.  That would put quite a gap of unknown colors between red and blue.  And from in there - along with the visible blue - maybe comes the violet?

Now I have an unscientific theory - unscientific meaning I cannot test and prove it.  The visible red and some unseen color forms purple.  Purple is a very different color.  I once knew an art teacher who was constantly saying "there is no such color as purple".  Well, we know there is.  That strong, bold, rich, deep mix of red and (what?).  We can see it?  We're just  not allowed to wear it unless we are rich or royal.  :-)

Your paragraph 2:   I forgot my geometry.  Sorry about that.   That said, a recently-read article kept talking about observing the rainbow through a rain drop.  That can't be exactly accurate, can it?  The rain drop would have to be terribly large.  We need one large, spherical prism of water.  No?

Thank you.  I'll be interested in your idea of where purple came from.  It does exist.  I have an art pencil that makes a beautiful purple.  Of course, how makers of paints and leads do it is another story.

Hazel the table in this article shown you the visible spectrum and the huge range of wavelengths of electromagnetic radiation that we cannot see.

Purple colour is a sensation perceived by our eyes. It may not correspond to a particular wavelength of light in physics, because our eyes do not scan the spectrum the way a spectrometer does. We do a kind of interpolation from the signals of three receptors which have maximum sensitivity to different parts of the visible spectrum. The result is that your eyes can be "tricked" by a mixture of red and blue into seeing a single colour called magenta, when in fact two different wavelengths of light are present. More here: https://en.wikipedia.org/wiki/Color_mixing

The explanation of how it works in the human eye and brain is fairly complicated. There is a description here: https://en.wikipedia.org/wiki/Color_vision

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Thank you, exchem.     That is ?????  Green is not a primary color.  But there it is.

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Thank you, exchem.     That is ?????  Green is not a primary color.  But there it is.

In the conventional additive colour system, which is how we perceive coloured light (and is NOT the physics of light), green is a primary colour.

The three are red, green and blue.

This is not to be confused with the subtractive system for pigments (paint, crayons) in which the three primary colours are cyan, yellow and magenta - often referred to slightly incorrectly as blue, yellow and red. This is explained in the second of the links I included my previous post.

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In the conventional additive colour system, which is how we perceive coloured light (and is NOT the physics of light), green is a primary colour.

The three are red, green and blue.

This is not to be confused with the subtractive system for pigments (paint, crayons) in which the three primary colours are cyan, yellow and magenta - often referred to slightly incorrectly as blue, yellow and red. This is explained in the second of the links I included my previous post.

They just keep changing things to keep us alert.  :-)

I have often wondered if we all see the same color in the same hue and tone.  Is your red my red or someone else's red.  I was assured once that it is but what proof.  Maybe some brain neuron shows the truth?  Who knows.

Take care.

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