Physics of colors and our perception

[Vrbic]

The wavelength (wl) coming from a heating body (absolute black body) obeys Wien law. We can also find out this wavelength from the peak of the Planck's law. Planck's law describes a distribution of energy (per unit area, angle...) for different wls (or frequency,...). We say that body has some color if we determine wl of the peak of Planck's distribution. If you disagree let me know.
My question is:
Why we determine color from energy distribution, i.e., we look for the wavelength in which is radiated most energy? I would expect to do it from the "number of the photon" distribution and peak in this distribution, which is different than the distribution for energy. Because our eyes distinguish the amount (the number of photons), not the energy (or am I wrong?)

 

[.Scott]

My question is:
Why we determine color from energy distribution, i.e., we look for the wavelength in which is radiated most energy? I would expect to do it from the "number of the photon" distribution and peak in this distribution, which is different than the distribution for energy. Because our eyes distinguish the amount (the number of photons), not the energy (or am I wrong?)

Here is wikipedia's "normalized" response chart for the cones and receptors in the human eye. It is "normalized" in the sense that the peak response for each type of cone or rod is set to 100:

 

[BvU]

I liked https://chem.libretexts.org/LibreTexts/University_of_California_Davis/UCD_Chem_110A%3A_Physical_Chemistry_I/Chapters/01%3A_The_Dawn_of_the_Quantum_Theory/1.1%3A_Blackbody_Radiation_Cannot_Be_Explained_Classically but I fear neither of us actually answered the question "why do we take the color corresponding to the wavelength that has the highest energy ($Nh\nu$) instead of the wavelength with the highest $N$ ? "

Perhaps we should first establish that we actually do what the poster states ?

My view is that it makes little difference: the relative variation in $\nu$ over the range of relevance isn't shifting the peak all that much -- the eye senitivity distorts the spectrum as .scott indicates and it's all pretty subjective anyway.

Note that the peak in the spectral energy density (fig 1.1.3 in the link) as a function of $\lambda$ doesn't even coincide with the peak in idem as a a function of $\nu$, simply because $d\lambda\propto {\displaystyle{ d\nu\over \nu^2}}$ -- a nice exercise in itself.

 

[pinball1970]

The wavelength (wl) coming from a heating body (absolute black body) obeys Wien law. We can also find out this wavelength from the peak of the Planck's law. Planck's law describes a distribution of energy (per unit area, angle...) for different wls (or frequency,...). We say that body has some color if we determine wl of the peak of Planck's distribution. If you disagree let me know.
My question is:
Why we determine color from energy distribution, i.e., we look for the wavelength in which is radiated most energy? I would expect to do it from the "number of the photon" distribution and peak in this distribution, which is different than the distribution for energy. Because our eyes distinguish the amount (the number of photons), not the energy (or am I wrong?)

The colour is not the light/photon energy it is the interaction with cones in the retina as per Scotts post #2

Sometimes the wavelengths may relate to colour you would expect to see sometimes not.

 

[BvU]

Nice picture. What does it show ?

 

[pinball1970]

I took a measurement of yellow textile samples and that is the reflectance data for the measurement

The curves are quite flat with no real peak at 650nm it mainly flat with similar % near 700nm, the actual physical samples look like the below. You can make some good guesses on actual colour from RD but some curves do not look what yo

 

[pinball1970]

Apologies that post flipped out. Yes some curves appear to make sense but others have peaks where you would not expect.

 

[Vrbic]

Apologies that post flipped out. Yes some curves appear to make sense but others have peaks where you would not expect.

Thank you, very nice experiment, but I think blackbody radiation (sun) and reflection from some real object is a another story.
But also very interesting.

 

[Vrbic]

I liked https://chem.libretexts.org/LibreTexts/University_of_California_Davis/UCD_Chem_110A%3A_Physical_Chemistry_I/Chapters/01%3A_The_Dawn_of_the_Quantum_Theory/1.1%3A_Blackbody_Radiation_Cannot_Be_Explained_Classically but I fear neither of us actually answered the question "why do we take the color corresponding to the wavelength that has the highest energy ($Nh\nu$) instead of the wavelength with the highest $N$ ? "

Perhaps we dhould first establish that we actually do what the poster states ?

My view is that it makes little difference: the relative variation in $\nu$ over the range of relevance isn't shifting the peak all that much -- the eye senitivity distorts the spectrum as .scott indicates and it's all pretty subjective anyway.

Note that the peak in the spectral energy density (fig 1.1.3 in the link) as a function of $\lambda$ doesn't even coincide with the peak in idem as a a function of $\nu$, simply because $d\lambda\propto {\displaystyle{ d\nu\over \nu^2}}$ -- a nice exercise in itself.

Well, if I understand correctly, our eye is unable to distinguish small variance in a light beam. I see because the sun should be greenish from view above the atmosphere. And I can't see it.
On the other hand, do you agree with me, that in strictly way we should calculate the color from N (the number) distribution?
I've calculated it for both distributions (energy and number) for the sun (T=5700K) energy distribution gives maximum at wavelength 500 nm and the number distribution at 640 nm. It seems enough to me. But the curve is quite flat at the visible part.

 

[BvU]

Are we talking about the same distributions ? The 500 I can believe but the 640 looks way too red ...

 

[Vrbic]

Are we talking about the same distributions ? The 500 I can believe but the 640 looks way too red ...

I mean for these two distributions: http://hep.ph.liv.ac.uk/~hock/Teaching/StatisticalPhysics-Part5-Handout.pdf (the first I've found, distributions are for energy but as you wrote above, we can transform it), equations 59 for number of photons is maximum at 640 and for ordinary Planck (eq. 60) it is 500.

 

[BvU]

I'm puzzled and lost in luminous intensity, radiant intensity and the various distributions.
Link in post #3 fig 1.1.3 shows spectral energy density

Don't know what to do with the 640 -- 'apparently' the eye sees energy, not photons, but that's corny. Anyone ?

 

[sophiecentaur]

The colour is not the light/photon energy it is the interaction with cones in the retina as per Scotts post #2

Sometimes the wavelengths may relate to colour you would expect to see sometimes not.

Microsoft Word documents cannot be read by everyone and will not be read by some people if they are not from trusted sources. As you can produce Docx files, you can save them in PDF format and everyone can / will read them. The "P" stands for Portable.

others have peaks where you would not expect.

What peaks would you expect? Reflective surfaces can have virtually any wavelength response that you care to think of and many different responses can produce a matching 'colour' response in the observer. Trying to use perceived colour as a measure of anything is likely to cause problems - except in a taylor made experiment where colour matching has already been validated.

The colour is not the light/photon energy it is the interaction with cones in the retina as per Scotts post #2

Yes - I would add that it is the combination of the three sensor outputs that gives a particular colour sensation / match.
There are really two issues here, though.

Firstly, we can't equate colour and wavelength (only wavelength with colour - in that direction)

The perceived colour of a hot black body is due to the three sensors and that colour is extremely de-saturated so the photon energy variation over the whole spectrum will not have the same effect on perceived colour of a monochromatic source. I seriously doubt that the eye could perceive any difference between the perceived colour of a hot source and a monochromatic source with only approximately the same wavelength as the measured peak of the black body spectrum. (Colour resolution is hardly better than 1%)

 

[davenn]

Sometimes the wavelengths may relate to colour you would expect to see sometimes not.

Microsoft Word documents cannot be read by everyone and will not be read by some people if they are not from trusted sources. As you can produce Docx files, you can save them in PDF format and everyone can / will read them. The "P" stands for Portable.

indeed ... I took the risk and did what @pinball should have done ...
screen dumped from his PC screen to a graphics prog and saved as a xxx.jpg file, then uploaded

like this ...

cheers
Dave

 

[sophiecentaur]

indeed ... I took the risk and did what @pinball should have done ...
screen dumped from his PC screen to a graphics prog and saved as a xxx.jpg file, then uploaded

like this ...


cheers
Dave

I take it that you are implying that my method will produce poor resolution. Any screenshot will have a resolution that's no better than the original screen image and, as we'd expect, in your sample, the labels are illegible. The point about PDF coding from an original Document that's been produced by a 'legit' method for possible zooming or printing is that the resolution can be whatever you want. Look at any Data Sheet or Learned Paper and you can print it at full (300+dpi) res. In my experience, when saving a Word document in pdf form, you get a printable image, even with a pretty small pdf file.
Also, JPEG is not the best bit reduction method for 'line' images; it was developed for pictures and the artefacts are pretty dreadful when text is involved, however acceptable the rendering of a 'photograph'.
Do some experimenting yourself and you can compare the various forms of compression for the various forms of source file. Screen shot is probably the worst way to do it - in the same way that MS Paint was probably the worst way ever invented, to draw diagrams .

 

[davenn]

I take it that you are implying that my method will produce poor resolution.

no, not at all …. just a better way of displaying it, for a PDF file it still has to be opened after it's uploaded by anyone that wants to see the info

An image file is already there displayed for anyone to view when reading the thread

I used a jpg for that file from pinball mainly because it was a colour one
In fact if you have ever seen any of my circuit drawings ( mainly in the EE forum)
you will see they are all GIF files which are ideal for black on white "line" drawingsDave

 

[sophiecentaur]

no, not at all …. just a better way of displaying it, for a PDF file it still has to be opened after it's uploaded by anyone that wants to see the info

An image file is already there displayed for anyone to view when reading the thread

I used a jpg for that file from pinball mainly because it was a colour one
In fact if you have ever seen any of my circuit drawings ( mainly in the EE forum)
you will see they are all GIF files which are ideal for black on white "line" drawingsDave

That's good. We agree largely then. I think you would agree that screen shots are too low resolution for most purposes, though.
Directly viewable images are good and GIF is a good format.
But my point against proprietary software like Microsoft Word stands. Over the years, Microsoft (and Apple) have moved their stance on portability between their document producing software and it's always a surprise when you try to Import or Export a file with a new version, as to what other software they are prepared to talk. PDF is about as universal and timeless as you're likely to get. It's also good if you want to discourage plagiarism.

 

[pinball1970]

Apologies on the uploads- PDFs noted

 

[sophiecentaur]

Apologies on the uploads- PDFs noted

You just witnessed a typical PF technical deviation but we usually end up OK with things.