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### Re^2: I'm not a PhD but...

by why_bird (Pilgrim)
 on Feb 04, 2009 at 15:39 UTC ( #741319=note: print w/replies, xml ) Need Help??

in reply to Re: I'm not a PhD but...
in thread How many colors does a rainbow have?

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
.......

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Re^3: I'm not a PhD but...
by BrowserUk (Patriarch) on Feb 04, 2009 at 16:22 UTC
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.)

It's way more complicated than that. What we see at any given point, at any given moment in time, in our mental image of a rainbow, is not the result of a single pure frequency stream of EM emanating from that point.

If that were the case, then everything we see would scintillate between shades of red, blue and green as we move our heads. Because if the stream of photons coming from that point source are accurately focused, they would only hit one cone at a time: say red. Then when you moved your head slightly, that point source would hit a different cone, say green. And so on.

You have to appreciate that the image we see is a complex, time-averaged (think:persistance of vision), sum of the frequency responses of photons hitting many cones of the three types, as that point source and/or our heads and bodies move. In the same way that ultrasound images are not instantaneous snapshots of the reflected waves from a single position of the tranducer, but rather a complex mapping of the responses from many points as the transducer is moved around in both 3D space, and over time.

So whilst there my not be any mixtures of 'red' and 'blue' frequencies in the spectrum at the source of the light, by the time it has been refracted through a billion drops of water, with some frequencies being attuenuated by the gasses in the air on the way to and from the raindrops; and by the water, and whatever contaminants it contains, of the raindrop itself. Add to that, any coincident (reflected, refracted and backgound light from other sources), photons that reach our eyes from the same direction, and what we "see" is an entirely different thing to what is there (in the rainbow), to begin with.

Even teh rainbow itself is an entirely nebulous entity. Consisting of only some small patr of the frequencies in the original light source that happen to refract in out direction. If air currents (wind, inversion layers etc.), cause the falling raindrops to change tragectory half way through their transition across the piece of sky where the angle is correct for the light to be refracted in our direction, then the frequency of the portion of the source that comes our way will change. Simple put, the rainbow will appear to ripple.

The term "colo(u)r" only makes sense in terms of our perception of what we see. And that perception is far from set in the frequencies of EM coming from any given point source. It is also influenced (a lot) by everything else we are seeing at the time. That is no more clearly demonstrated than by this famous optical illusion

Our perceptions have almost nothing to do with the frequencies of the EM spectrum. Hence my brother's yellowish coloured car looked almost purple under low-pressure sodium street lighting.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
If that were the case, then everything we see would scintillate between shades of red, blue and green as we move our heads. Because if the stream of photons coming from that point source are accurately focused, they would only hit one cone at a time: say red. Then when you moved your head slightly, that point source would hit a different cone, say green. And so on.

This assumes that only one cone will respond to a specific frequency. This is not true. As this diagram shows, the responses of the cones overlap, so you get a continuously varying mixture of colours as the wavelength varies.

As this diagram shows, the responses of the cones overlap,

I'm very aware of that as you'll see if you follow the 3rd link in this post.

This assumes that only one cone will respond to a specific frequency.

Okay. The "colors" through which each point would scintillate wouldn't be red, blue and green. But, assuming the light eminating from any given point source consisted of an unattentuated, pure frequency, then if what we percieve were in direct proportion to that pure frequency, then the points would scintillate as the focused light hit the three diferent types of cones. And the three colours through which they would scintillate would be the same for every source of that given frequency.

But that doesn't happen. In part because of the persistance of human vision which aggregates and averages the spectral responces of many individual cones of all three types over time. To quote from another link in that other post:

Any color on the CIE chromaticity diagram can be considered to be a mixture of the three CIE primaries, X,Y,Z. That mixture may be specified by three numbers X,Y,Z called tristimulus values.

The CIE primaries are not real colors, but convenient mathematical constructs.

Nevertheless, the tristimulus values X,Y,Z uniquely represent a perceivable hue, and different combinations of light wavelengths which gives the same set of tristimulus values will be indistinquishable in chromaticity to the human eye.

So, whilst there may be no adjacent bands of red and blue in the source spectrum, our perception of all hues (including "pure red" and "pure blue"), will have influences from the conal responses to incedental and coincident frequencies eminating from other sources over both space and time. Ie. We percieve pinks in a rainbow even though there are none there at the source.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

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