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in reply to Re^2: How many colors does a rainbow have?
in thread How many colors does a rainbow have?

One cannot expect the naked eye (especially from a distance and through an imperfect picture) to see or not see specific colors or even all of the colors hidden in a rainbow.

I found this:

(PhD physicist responds) The eye perceives six colors in the rainbow. Red, orange, yellow, green, blue and violet. (some people include the violet color of Indigo as a separate color.) But there are also colors in the infrared and ultraviolet present as well. The rainbow is caused by diffuse refraction of sunlight in water droplets. The source of the light is the sun's photosphere. While each atom in the photosphere may emit light at one quantum frequency, the sun is so hot that doppler shifting of the light causes the lines to "fuzz out" so that you see essentially a continuous spectrum of light. The strictly correct answer, would then be, "an infinite number".

I also found Physics in the Arts By P.U.P.A Gilbert, Willy Haeberli - Page 27. I found that to be pretty interesting.

_ _ _ _ _ _ _ _ _ _
- Jim
Insert clever comment here...

• Comment on Re^3: How many colors does a rainbow have?

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I'm not a PhD but...
by why_bird (Pilgrim) on Feb 03, 2009 at 08:19 UTC
But there are also colors in the infrared and ultraviolet present as well.

Isn't this a contradiction? Colo[u]r being those frequencies of light visible to humans... and infra-red and ultra-violet not being among those...?

While each atom in the photosphere may emit light at one quantum frequency, the sun is so hot that doppler shifting of the light causes the lines to "fuzz out" so that you see essentially a continuous spectrum of light.

I might be wrong about this, but isn't the vast majority of the sun's radiation thermal, i.e. blackbody, i.e. continuous in the frequency domain? Yes, there are spectral lines caused by atomic de-excitation, and they are broadened by Doppler shifting due to the temperature of the gas in the sun (amongst other things) but this isn't what the majority of radiation emitted from the sun is.. is it?

Someone help me out here!
why_bird
........
Those are my principles. If you don't like them I have others.
-- Groucho Marx
.......
Isn't this a contradiction? Colo[u]r being those frequencies of light visible to humans...

All of these arguments depend on the definition of "color", and until we all agree on one, there will never be agreement on how many "colors" are in a rainbow.

isn't the vast majority of the sun's radiation thermal, i.e. blackbody

Well, obviously, essentially all of the sun's radiation is blackbody, in that none of it is reflected or transmitted. :-)

blackbody, i.e. continuous in the frequency domain

While blackbody radiation may be continuous theoretically, that doesn't mean that thermal radiators like the sun have continuous spectra in reality.

Brass tacks: Is the solar spectrum continuous or quantified? If the physics PhD says it's continuous, I'll believe him.

Yes, there are spectral lines ... but this isn't what the majority of radiation emitted from the sun is.. is it?

Is there any reason to suppose that the "smoothness" of the solar spectrum is qualitatively different from one part to another? No; In fact, it looks like the roughness is merely proportional to the intensity, across the spectrum. It also appears that whatever "fuzzing out" is happening, it is not enough to completely smooth out the spectrum. Far from it!

Between the mind which plans and the hands which build, there must be a mediator... and this mediator must be the heart.

Thanks for answering my post jdporter. You've let yourself in for it a bit though, as you've generated more questions :) If you or anyone else can help me understand this I'd be grateful. I realise it's hideously OT in terms of perl, so feel free to ignore me, but here goes(!)

Whilst I agree that without a definitive definition of 'colour' (or 'color' :P) we won't agree how many colours are in the rainbow, I am proposing that part of the definition of 'colour' should include 'wavelengths of light that humans can see'. By definition (at least any that I've ever seen) infra-red and ultra violet are outisde the visible spectrum. That's all :)

As to the rest of my post.. I am bad at expressing myself with physics! Let me try again.. for one it should have sounded more like a (series of?) question(s):

Firstly, am I right in thinking that a blackbody doesn't just require not to 'reflect or transmit' (I am not quite sure what you mean by this) any of it's radiation? It must also have a continuous spectrum which is dependent only on temperatue, and is determined by Planck's law? And it must be able to absorb and emit radiation at any (and all) wavelengths?

Given that the Sun is (approximately at least) a blackbody radiator, doesn't that mean that it's spectrum is continuous, and it (absorbs and) radiates EM waves at all frequencies? If the previous is correct, is the mechanism for the sun's radiation atomic exctitation/de-excitation? Or plasma recombination, I would've thought more likely.

If the main mode of EM emission by the sun is through atomic excitation/de-excitation, is that true of all black bodies? What other modes (if any) of photon emission are there from materials? (Thinking about it, the only other ones I know would be the acceleration of charged particles---relevant to a plasma? and annihiliation of matter-antimatter pairs---plausible in something pretty hot I would have thought). If so, how is it that a theoretical black body has a continuous spectrum, dependent only on temperature if the main mode of anything's EM emission is through de-excitation? Wouldn't you expect the spectrum to be concentrated around spectral lines?

It also appears that whatever "fuzzing out" is happening, it is not enough to completely smooth out the spectrum. Far from it!

My point is though, shouldn't it? If the main mode of EM emission from a black body is by atomic excitation/de-excitation, shouldn't black body theory take account of this, or use it as its starting point?

Thanks!
why_bird
........
Those are my principles. If you don't like them I have others.
-- Groucho Marx
.......
Colo[u]r being those frequencies of light visible to humans...

If you define colour in terms of what the human eye sees, there are only three of them, four if you count luminosity that's not in any of the three color categories, or throw in tetrochromacy; five if you count both. So yellow, for instance, is not a color if you define it this way. It's a combination of colours (specifically, red and green), or else it's a pigment that absorbs a certain color (blue).

And yeah, the output of the sun is pretty well continuous across the electromagnetic spectrum, so if you define colors as wavelengths of electromagnetic radiation then the cardinality of the set of all colours in the rainbow is aleph-sub-one, the same as the cardinality of the set of all real numbers. I suppose that means the number of colors in the rainbow is actually greater than infinity, if you define infinity in the usual gradeschool way (which comes out in math as aleph-sub-naught, the cardinality of the set of natural counting numbers).

If you define colour in terms of what the human eye sees, there are only three of them

I think you're misconstruing me! I am limiting colours to be 'things which humans can see' which doesn't correspond to 'the specific frequency ranges which stimulate only one cone type'. (And in fact the frequency ranges overlap so your definition becomes a bit more tricky than you make out)

I can see EM radiation with wavelength 570nm (yellow), so I would define it as a colour! I just happen to see it by stimulating more than one cone type at once.

so if you define colors as wavelengths of electromagnetic radiation then the cardinality of the set of all colours in the rainbow is aleph-sub-one

As tilly pointed out, you don't get mixtures of blue and red light in a rainbow, which we see as pink-purples (the line of purples on the CIE chromacity diagram.)

Update: In fact, you don't get any mixing in a rainbow (approximately, obv mist is not a perfect refractor and probably some other caveats like angle and distance), so it's like going around the edge of the chromacity diagram... so there's quite a few less than all possible colours/hues in a rainbow.. but still probably infinite (I'm not a mathematician either, so no fancy 'alehps' from me... :P). That's my current conjecture anyway!
........
Those are my principles. If you don't like them I have others.
-- Groucho Marx
.......
Infinite number?
by massa (Hermit) on Feb 03, 2009 at 16:10 UTC
Shouldn't wavelenghts be multiples of the Planck length?
[]s, HTH, Massa (κς,πμ,πλ)
I believe we would need a better theory of quantum gravity to confirm or deny such speculation.
Now I'm seriously curious - why should they?

So far I've never worked with energy scales where quantization of that order of magnitude would matter (10^-9 vs. 10^-35 meter), so I'm curious where that comes from.

IANAPhycisist. That said, I was under the impression that there were no wavelengths smaller than ℓP. This may or may not have anything to do with the subject in question and, to add full disclosure, I am not renowned for my mental sanity.
[]s, HTH, Massa (κς,πμ,πλ)