The underlying physics of this is really the underlying physiology. The different cells in the retina are sensitive to different colors of light, and when we see a color it is because of the comparison between the responses of those different cells in the retina. So a simple way to describe that is that the two sources of light have to be close enough together that they look like one point of light to us, and then the color we see is the color of that light. In other words, it's determined by the resolution of our vision.

The resolution of our vision is partly determined by the density of receptors in the retina, but it's also determined by how well we can focus. If you have red and green LEDs right next to each other, some meters away, and you can still see them as two separate leds you could make them merge into one yellow light by either taking off your glasses if you need glasses to see them, or putting on glasses that are wrong for you, to make the view blurry. Or you could simply walk further away from them until you only see one point of light, and that you will see it as yellow.

A common place to see this effect is on a large, but not very high resolution television screen. If you get up very close to it you can see the individual pixels, and for many display technologies, you will see them as individual red, green, and blue pixels, rather than as a full range of colors including yellow. If you don't have an appropriate display where you can see that, you can use a magnifying glass with a higher resolution display, even a phone.

I was going to say, an LCD (or other computer/TV) display screen is the classic example of where colours in close proximity (RGB sub-pixels) are perceived as the compound colour.

Basically I second kilotesla's answer, but will add some additional clarification and related ideas.

The "resolution" of the human eye is highest in the very central few degrees of vision, the "fovea", which is populated with "cone" cells which are colour-sensitive. The rest of the visual field is mostly populated by rod cells, which are only brightness-sensitive - but are sensitive to lower light-levels. See https://www.cis.rit.edu/people/faculty/montag/vandplite/pages/chap_9/ch9p1.html#:~:text=Rods%20are%20responsible%20for%20vision,is%20populated%20exclusively%20by%20cones.

Empirically (presumably in the fovea) the human visual system has a higher "resolution" for brightness or "luminance" than for colour - this has been exploited for decades in the way analogue colour television or JPEG images are encoded - with the colour being coded ("sub-sampled") at a lower resolution than the brightness (to reduce the information), with little visual perceptual loss.

Empirically the black-and-white resolution of the eye is of the order of 300dpi at about 14 inches for someone with good vision who can focus properly, in high-ambient light levels. You could probably find a reference to the definition of "20/20 vision" and get a comparable angle subtended. In very low light levels, the effective resolving power will be lower.

Combining those two observations, I would expect the colour resolution to be something like 80-150dpi at 14 inches. This is equivalent to a subtended angle of around 1/(100*14) radians, so (180/pi)/(100*14) = 0.04 degrees, give or take.

If the coloured lines or stripes are closer than that sort of subtended angle, the colours are likely to merge into one - they will not be "resolved". The merging will work a bit better where the pattern is alternating (like in a TV or computer screen), rather than just a single source of each colour - in the latter case you may still perceive a coloured "fringe" on each side, even when you can't properly resolve the two colours.

In the early days of LCD computer screens, in the early 2000's, when they were only 1024x768 resolution, and before the days of sub-pixel font rendering, if you had white text on a black background, where the letters were only 1 pixel wide, the text often appeared to have some chromatic aberration, an orange-tinge on the left of the letters and a bluey tinge on the right, just because of the subpixel layout. As displays became higher resolution, and font often rendered more than 1 pixel wide, and/or they used more-clever sub-pixel rendering techniques (such as Microsoft's ClearType) these effects largely became consigned to history.
See also https://en.wikipedia.org/wiki/Subpixel_rendering#:~:text=Subpixel%20rendering%20is%20a%20way,the%20screen%20type's%20physical%20properties.

Don't take my word for it... you could print a piece of paper with fine alternating black and white lines and establish at what distance the lines cease to be resolved and "go shimmery" and then merge into grey - to get a gauge of your own personal black and white resolution.
If you can find an old Trinitron cathode-ray tube (this uses RGB lines of phosphor) - which is lower resolution than modern displays, you could try the same thing - look closely, then move back until the colours merge. If you can determine the pitch of the stripes and the distance, you can work out the subtended-angle when the colours merge.

Perhaps more easily, you could create a graphic of red/green/blue stripes on your computer (make each line several pixels wide) then see how far away you need to be for the lines to merge and it looks white.

The results are likely to be slightly different (fuse at a slightly closer distance) if you match the luminance of the coloured stripes (have blue at full brightness, red somewhat less, and green lower still), making probably a bluey-lilac colour when merged.

If you do some Google searches (other search engines are available) relating to measuring the resolving power of optical systems, contrast ratio etc, this will get you a sense of the underlying physics, which is then largely applicable to the eye - for the purposes of the question.

(I'm a physicist/electronics engineer, who has also spent several years of my professional life in optics, imaging systems, colour-reproduction and display-screen technology.)

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So I'm confused. If the fovea is responsible for highest resolution, and the fovea is packed full of cones which are color sensitive, how do we have more resolution with rods (black/white)?

My understanding was that rods are more sensitive to low light. That's why in the dark we have trouble discerning color. Also, our vision tends to be a bit less focused in the dark (more difficulty discerning details) because we're not getting much activation in the fovea, where our central vision is. In bright light, however, the cones will register the blue, green, red, far red wave lengths.

So we're sorta talking about two different "kinds" of light I guess?....white light/ambient light when it's daylight or you're in a lit room and then light in the form of the wave length being reflected off objects (like green curtains, say).

So wouldn't our color vision have higher resolution than our black/white vision, but that our color vision only works when the background intensity reaches a certain threshold. And our black/white vision has less resolution, but works in dimmer environments?

I'm no eye expert, but I spent a year working in a lab that was growing retinal organoids during a CIRM internship (super cool), it's been a few years so I could be remembering incorrectly, or perhaps understood incorrectly from the very beginning!

In response to hmartin430, my expertise is really in the use and application of CIE colour matching and display screen technologies, rather than the actual structure of the human eye.

My understanding too is that the rods are sensitive to low light (and saturate at higher light levels).

If we just consider the cones in the fovea, that comprises three types of cone: L,M,S (long, medium, short wavelength), which are very loosely red,green,blue. They are actually much broader bandwidth, with highly overlapping wavelength sensitivities than true RGB. The CIE colour matching functions (and resulting "chromaticity" coordinates) X,Y,Z are mathematically related to the L,M,S cone spectral sensitivities but are not quite the same thing (it's a long story...). The XYZ colour-matching functions are 'mathematically fudged' slightly such that the Y-coordinate represents luma (brightness) as well as (sort of) "green".

Grappling slightly for a consistent solution to all these things, I believe the answer is that in the fovea there is a highest density of M-cones, fewer L-cones, and fewer S-cones still. This means that our "luma" resolution is highest, red-green resolution is somewhat lower lower, and blue-yellow resolution the lowest. (In practice you need to match the luma (brightness) of the coloured test-stimuli to really demonstrate this effect, otherwise if "yellow" is much brighter than your "blue" it may be resolved in luma even if it isn't really resolved in chroma).

Again from a technological perspective, the Bayer colour filter array pattern used in the vast majority of electronic colour-camera sensors has twice as many green pixels as blue and red, which again maps to approaching human-eye properties to get the "best" visual image from finite technical resources.https://en.wikipedia.org/wiki/Bayer_filter

Ah, so I think my issue might be that I have a lay person's understanding of brightness? I suppose I was thinking as brightness solely as the amplitude of waves. So like, low amplitude is only gonna excite the rods? High amplitude will allow the excitation of cones and at that point frequency will determine which cones are excited? It's been about 15 years since my last physics class, and it was a struggle lol. Definitely not my strength.

>low amplitude is only gonna excite the rods? High amplitude will allow the excitation of cones and at that point frequency will determine which cones are excited?

Yes, and yes, if that helps. Of course, the rods' response is not independent of frequency, but since there's only one type, you have no way to distinguish colors using them.

The simple answer is it depends how for you are from the source. If you look at big event screens the size of the led pixels and the distance between them is huge by comparison to a mobile phone.

This is probably measurable and more to do with biology and neurology of light perception than the physics. Although arguably everything is physics at some point.

Nice, all this make sense and these answers were pretty close to describing in some detail what I was trying to look more into. Thank you!

I was also naively hoping for an undeniable elegant and satisfying practical demonstration of two different coloured lines kissing and boom, new colour, without fakery. I suppose things like the psychological aspect of colour perception will also get in the way to make it that level of satisfying. I haven't tried the computer graphic idea yet, but I'll give it a shot.

It's important to understand that colour sensation is entirely psychophysical. The colours we sense are a product of the construction of our eyes and nervous systems - they don't really exist outside the context of a human observer (or an observer with the same visual architecture).

A spectrometer can easily tell the difference between (light of wavelength 580nm) and (mix of light with wavelengths 480nm and 650nm). There is a physical difference. But human vision cannot tell the difference - our brains sense both these as "yellow". Which one is really yellow? Neither. "Yellow" has no physical reality outside a human brain - it's our label for a sensation that we have.

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Yes.

See metamerism

This is also why paint-matching can be a huge problem. You can get two paints that look the same colour under one lightsource (eg. daylight) but are visibly different under a different source (e.g. fluorescent, or sodium streetlights)