When we're say about 100 km above Earth's ground and look down to it and see the Amazonian region as green, is this green color a sort of "average" of greens from trees from that forest or is the "green" color of some trees only?

I'm trying to think of the problem with Maxwell's equations and their solutions at the above the ground point. To keep things simple, let's assume that there are several different kinds of trees and each kind of tree has leaves that have a single well definite green shade, i.e. its EM waves have a well definite single frequency. At a distance of about 100 km from the ground, we see the sum of such plane waves with different shades of green and the eye or brain interprets this sum as a sort of average green shade, i.e. it could even be a green shade that no tree has.

But I am told on IRC that I can't think of plane waves (I don't know why). I'm told that it's probably a matter of contrast and resolution of the eye.

Any clarification would be great.

Edit: My question is not about how the brain/eye interpret a mix of green colors (or a sum of waves of well definite frequencies). I am already aware of it. My question is whether it is correct to assume that the observer sees a sum of plane waves, each with a well definite frequency (following the above assumptions/simplifications). The eye would thereafter receive such light and the brain would interpret this sum of different waves of different wavelength as a sort of green shade which may not necessarily correspond to any green color of any tree in the forest.

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    $\begingroup$ Lots of people have the intuition that, since mixing colors together only ever gives you a single new color, superposing light waves of different frequencies will give you a new wave with a single frequency. This is totally untrue, it doesn't make any sense whatsoever in the math. The trees emit different greens independently, your eye takes in all these frequencies, and your brain shows you a single color. $\endgroup$ – knzhou Jul 3 '16 at 4:09
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    $\begingroup$ ^ note that I'm only using the word 'color' here to denote perception of light, and 'frequency' to denote the actual Fourier components. $\endgroup$ – knzhou Jul 3 '16 at 4:10
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    $\begingroup$ If it feels unintuitive, think of an analogy with music. You stand far away from an ensemble of instruments, some of which are playing C, and some of which are playing G. Does that mean you hear E? No! And light waves superpose just like sound waves, so the same is true for them. $\endgroup$ – knzhou Jul 3 '16 at 4:11
  • $\begingroup$ @knzhou it does not sound counter intuitive at all, because this is what I "deduced" and wrote as "we see the sum of such plane waves with different shades of green and the eye or brain interprets this sum as a sort of average green shade, i.e. it could even be a green shade that no tree has.". So, I was aware of this. $\endgroup$ – AccidentalBismuthTransform Jul 3 '16 at 14:40
  • $\begingroup$ If you already know all this, I don't see what the question is. $\endgroup$ – knzhou Jul 3 '16 at 17:13

The light waves propagate directly and the flux of photons reduces at a rate of 1/r^2 from the canopy top. This means that fewer of the photons reach your retina or CCD of a camera while in orbit.

It seems to be a more uniform color of green simply because that is the majority wavelength being reflected by the plants. As knzhou pointed out, light is absolute, and des not divide and recombine to form a new frequency over distance.

For instance, there could be little green, blue and red spots on the suns surface and if we were very close we might be able to see them, but over long distances that fidelity is lost and the sun looks almost pure white from orbit.

  • $\begingroup$ I don't see how this clarify my original post. I am well aware of what you wrote in your 1st paragraph as well as the last sentence of your second paragraph; and I fail to see how the 3rd paragrah shed light on my question. $\endgroup$ – AccidentalBismuthTransform Jul 3 '16 at 14:42

I think your question is about the perception of colour - ie how your brain responds to the mixture of light which stimulates the retina. This cannot be explained by the superposition of waves using Maxwell's equations. It is more a matter of physiology (biology) than physics [1].

Colour is not a property of the physical world. It is our subjective response to the different frequencies of light which stimulate the retina. Different combinations of stimuli result in different 'colours'. While the individual colours in the visible spectrum can be identified with different frequencies of light, the eye/brain can "see" many more colours which are not found in the visible spectrum of light.

Not everyone has exactly the same colour-response to the same combination of frequencies - even allowing for colour-blindness. The colour recorded by digital cameras or photographic film can likewise be different from what is seen with the naked eye.

Contrast and resolution are important factors in determining whether the eye can distinguish adjacent patches of different colour. The smaller the angle they subtend, or the closer the two colours are in the Colour Triangle [2], the harder to recognise them as two separate regions of distinct colour.

When your eye is unable to resolve the individual patches of different colours in an object, then the brain does, as you suggest, interpret some kind of an average colour. You see this effect in an Art Gallery in pointillist paintings. Up close the painting is nothing but a confusing forest of distinct blobs of paint of different colours. When you are far enough away your brain 'averages out' the differences and interprets a single colour (as well as distinct features, such as human faces and expressions).

You get a similar effect in Maxwell's Colour Wheel. When a wheel painted in a combination of colours is spun so fast that you cannot focus on any one colour, your brain interprets a single colour approaching white.

[1] https://en.wikipedia.org/wiki/Color_vision
[2] http://hyperphysics.phy-astr.gsu.edu/hbase/vision/colper.html

In response to your comments below :

I must say that I agree with the "renowned person on IRC" : I do not understand what point you are trying to make about the "sum of plane waves". It does not seem to have any significance for the problem you describe in the 1st paragraph of your question.

The individual leaves in the Amazon forest are not each a distinct pure shade of green with a definite frequency in the EM spectrum. Most of these greens are mixtures of many different frequencies corresponding to pure yellows and blues from the EM spectrum, as well as greens and perhaps reds also. See the Colour Triangle in [2] which explains that

While we know that the spectral colors can be one-to-one correlated with light wavelength, the perception of light with multiple wavelengths is more complicated. It is found that many different combinations of light wavelengths can produce the same perception of color.

The superposition of waves of definite frequencies does not create new colours in the light which enters the eye. The different shades of green which we "see" are created in the brain. Mixing light is not the same as mixing paints of different colours.

It seems to me that you really want somebody to tell you that you are right and the "renowned person" was wrong about a distinction which you are trying to make. I am not sure that I understand what that distinction is, but it seems to me either wrong or insignificant.

  • $\begingroup$ Unfortunately no, my question is not about how the brain interprets a mix of colors (I am somewhat aware of it). I'll edit my original post to make it more clear because apparently people focus on this exclusively. $\endgroup$ – AccidentalBismuthTransform Jul 4 '16 at 13:06
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    $\begingroup$ Sorry, I still don't see any difference between your Edit and the question which I have answered. What point are you trying to make about the "assumption that the observer sees a sum of plane waves, each with a well definite frequency (following the above assumptions/simplifications)"? Of course that light can be thought of as a superposition of waves of different frequencies which refract/diffract to form an image on the retina (the wave model). But detection in the retina occurs as individual photons (the particle model). The model you use must be appropriate for the phenomenon. $\endgroup$ – sammy gerbil Jul 4 '16 at 17:39
  • $\begingroup$ "Of course that light can be thought of as a superposition of waves of different frequencies..." --> This is exactly what I am looking for. I wanted a confirmation that I was right thinking of the problem by thinking about the light that enters the eye has a sum of plane waves. Because a well renowned person on IRC told me I was in the wrong direction and that he didn't understand at all why I was bothering with the "sum of waves". Feel free to edit your answer to include "Yes, of course, you can think of the light that the observer sees as a sum of plane waves, each with a $\endgroup$ – AccidentalBismuthTransform Jul 4 '16 at 17:45
  • $\begingroup$ different frequency. The result being a wave without a well definite frequency that the brain interprets as a shade of green, which may not even correspond to the color of any tree". Or something like that. This is what I am looking for. $\endgroup$ – AccidentalBismuthTransform Jul 4 '16 at 17:45

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