Why does light diffract into only seven colours?

[Vanadium 50]

Coal? You had coal? When I was a kid your so-called coal was still dinosaurs.

 

[DaveC426913]

Loogxury.

 

[louis_slicka]

Hi all thanks for the detailed and varied replies to my very flawed question! I realized as soon as I posted that there are an almost infinite variations on the basic seven colours. It's like asking how long is a piece of string

 

[hutchphd]

We have managed to play with that piece of string for quite a while! Good fun for all..

 

[hilbert2]

I think the distinction between "night vision" (which is Near Infrared (NIR) often actively illuminated usually silicon detected devices) and thermal imaging FIR devices needs to be emphasized here. Only the thermal imaging devices will see the glowing enemy combatant in the dark field but these are very different from usual silicon optics or eyeballs.
I once had to explain this to a client who had already spent a fair sum of money trying to develop a silicon CCD-based imaging thermometer. Lack of understanding can be expensive, and I felt like the Grinch as I invoiced him for my services.

A good point. You'd have to detect wave lengths over 1 micrometer to have temperature differences near room temperature be visible, and the chemical properties of surfaces would also affect the appearance at the same time.

 

[sysprog]

One of the 64 colors in the big Crayola crayon box was a pinkish color called 'Flesh'. I asked my Dad (who as an attorney and law professor did a lot of civil rights work) wasn't that a bit racist? $-$ my 'negro' friends didn't have close to that skin color $-$ Dad told me (I was maybe age 7) to not worry about it $-$ that was for grown people like him and Mom to deal with $-$ I should just keep on being my friends' friend.
:;

 

[Vanadium 50]

It is now "peach".

And no human being ever had skin that color.

 

[DaveC426913]

It is now "peach".

And no human being ever had skin that color.

Well true, but Macaroni and Cheese was never that colour either...
Nor Outer Space, that colour...

http://www.jennyscrayoncollection.com/2017/10/complete-list-of-current-crayola-crayon.html

 

[sophiecentaur]

Well true, but Macaroni and Cheese was never that colou

The colour named Indigo is often placed well inside the CIE graph, rather than on the spectral locus. It's a pretty dodgy part of our colour perception range around there.

 

[Anachronist]

Fun fact: not all colors are found in the rainbow. There's no magenta, and no cyan.

No, actually there is cyan in all rainbows, as well as white light split by a prism. But there is no magenta.

 

[sophiecentaur]

No, actually there is cyan in all rainbows

The problem with that statement is that Cyan is a mix of blue and green primaries (It can also be considered as -Red but that system is based on primaries. Primaries are not spectral wavelengths and can only add together to produce resulting colours on a straight line on the CIE chart. That means it cannot actually lay on the (very much curved) Spectral locus. A rainbow is not actually a very pure spectrum; it's very de-saturated because there's a lot of white in there. Basically, a rainbow is not a very good example of the spectrum of sunlight. The colours can often look impressive and vivid but nothing like as good as what you get in a dark room with a prism.

 

[DaveC426913]

The problem with that statement is that Cyan is a mix of blue and green primaries.

Maybe on a monitor, but there's a frequency of light between blue and green that correlates with cyan (at least, allowing for saturation, as you say).

The problem with magenta is that there is no single frequency, since magenta is a perceived mix of red and blue. If you took the frequency between red and blue, you'd get a green.

 

[sophiecentaur]

Maybe on a monitor, but there's a frequency of light between blue and green that correlates with cyan (at least, allowing for saturation, as you say).

The problem with magenta is that there is no single frequency, since magenta is a perceived mix of red and blue. If you took the frequency between red and blue, you'd get a green.

Yeah I can’t really disagree. I was being mischievous but no colour you can make with primaries is actually spectral. Lowering the saturation involves adding a third primary.

nothing is real with colours.

 

[MysticWizard]

https://en.wikipedia.org/wiki/Color_wheel

 

[Baluncore]

After all we have only three distinct eye pigments and yet I swear there are seven colors when I look at the rainbow.

There are a couple of ways to demonstrate why it might be seven.

We detect three different colours. Red, Green & Violet, that we sometimes call Blue.
That gives us a three bit binary number with 2³ = 8 possible combinatorial states.
But black is zero, so only 2³ - 1 = 7 colours remain.
If we are colour blind to one colour we see 2² - 1 = 3 colours.
If we had an extra detection pigment we would see 2⁴ - 1 = 15 colours.

But the rainbow is different because photons are ordered by wavelength, so in the rainbow detected Red cannot be adjacent to and mixed with Violet. Our Red and Green detectors are significantly overlapped which makes it all the more complicated. Anyhow, in the rainbow we see;
Red = Red.
Orange = Red, with a touch of green. (R+G with R>G).
Yellow = Green, with a touch of red. (R+G with R<G).
Green = Green.
Blue = Green, with a touch of violet.
Indigo = Violet, with a touch of green.
Violet = Violet.
So that gives us seven named and identifiable colours in a rainbow.

I am not surprised that most people agree on the presence and the spelling of 7 colours, even if some misspell the word colour.

 

[hutchphd]

So that gives us seven named and identifiable colours in a rainbow.

Very interesting. I was wandering down those same (3-bit) channels myself while staring at the CIE chart of colors (please note the compactness of the absent silent "u")
In particular the results of the various pigment deficiencies seem congruent with this idea. But it is not clear exactly how these spectra are rendered. For instance
https://www.researchgate.net/figure/Top-color-spectrum-as-seen-with-normal-vision-Next-6-rows-the-three-main-types-of_fig2_342092723

 

[Baluncore]

Very interesting.

Is gold an orthogonal colour ?
Apparently it can be found at the end(s) of a rainbow, perpendicular to the colours.

 

[Merlin3189]

There are a couple of ways to demonstrate why it might be seven.

We detect three different colours. Red, Green & Violet, that we sometimes call Blue.
That gives us a three bit binary number with 2³ = 8 possible combinatorial states.
But black is zero, so only 2³ - 1 = 7 colours remain.
If we are colour blind to one colour we see 2² - 1 = 3 colours.
If we had an extra detection pigment we would see 2⁴ - 1 = 15 colours.

If 000 is black, would not 111 be white, leaving 6 colours ? Which is what most people see.

I suspect a protanope might still see six colours in a rainbow, as do normal people, but not necessarily the same ones.
That is based on the notion that 7±2 is the number of categories we can recognise. If asked to discriminate between small sections of the rainbow, I think everyone could divide it into many more than 7.

 

[Baluncore]

If 000 is black, would not 111 be white, leaving 6 colours ?

Yes. But the physiological cone detectors get weighed and balanced dynamically by the brain, so white is coloured. We then use rod detected brightness to determine the difference between dark and light.
https://en.wikipedia.org/wiki/Color_vision#Non-spectral_colors

https://en.wikipedia.org/wiki/Color_vision#/media/File:Cone-fundamentals-with-srgb-spectrum.svg
If you scan across the resolved spectrum in that image, and classify situations based on the three cone detectors, you can look for clearly differentiated colours. But then all colour balances are variable, based on the background and recent bleaching of the three different cone detectors.

Maybe it comes down to how many colours a child needs to recognise and name correctly, before the family can communicate and survive to pass on the language with the names for the different colours.

 

[JeffJo]

Late to the party, I know. But in skimming the thread I didn't see the right answer, and did see much that is wrong. (And speaks poorly of Newton.)

First, Newton separated the colors of the spectrum (not the rainbow) into seven categories of color (not discrete colors).

• The rainbow has different colors. The spectrum's are all single wavelengths of light, and the rainbow's are composites of one tight group of wavelengths that is very bright, and less dim contributions from all the others toward the red end of the spectrum. In fact, the rainbow continues all the way to its center as gray.

• He chose seven categories of color, not seven discrete colors.
• "Blue" in Newton's day was more like sky-blue; that is, the ninth and tenth bands in that picture.
• What you probably think of a "true" blue, as opposed to cyan or sky blue, is what he called Indigo. It is the color of indigo dyes, as made popular by "blue jeans" which get their classic color from that dye.
• The relationship to music, and the planets, was a more a result of his categorization, than a driving force.

The story goes that Newton had poor eyesight. So he asked a friend to draw divisions between the colors produced by his spectrum. Friend chose five categories: Red, Yellow, Green, (sky?) Blue, and Violet. What Newton noticed was that two of these categories (Red and Blue) covered roughly a 50% a wider extent along the spectrum than the other three (Yellow, Green, and Violet). He also knew that in the Pentatonic Minor Scale (he used D minor: D, F, G, A, C, D+), two of the intervals (D to F and A to C) covered a 50% wider pitch range than the other three (F to G, G to A, and C to D+). And wouldn't you know it, the ordering was the same as the colors! There also is a link to the planets, but I'm not sure what that was.

So Newton added two categories, orange and indigo, to what Friend had drawn. (And yes, he ended up with a Dorian scale, not the Minor scale). Here's his representation:

 

[sysprog]

The 'visible light spectrum' is the entire range; the individual frequencies are termed 'spectral colors'; subranges within the spectrum are called 'spectra'.

 

[hutchphd]

First, Newton separated the colors of the spectrum (not the rainbow) into seven categories of color (not discrete colors).

• The rainbow has different colors. The spectrum's are all single wavelengths of light, and the rainbow's are composites of one tight group of wavelengths that is very bright, and less dim contributions from all the others toward the red end of the spectrum. In fact, the rainbow continues all the way to its center as gray.

Please provide a reference for this claim. It does not comport with my understanding of either light or Newton.

 

[Anachronist]

As others have noted, "indigo" generally isn't used nowadays. Instead of the 7-color spectrum ROYGBIV, I'd remove "I" (indigo) and add "C" (cyan) for ROYGCBV. Still seven.

It also makes more sense to break down the color categories into six groups, corresponding to each color receptor type in our eyes (red, green, blue) and the colors in between them (yellow=red+green, cyan=green+blue, magenta=blue+red). That's basically how we perceive colors. Violet or purple is basically magenta skewed a bit toward blue at lower luminance, and orange is basically yellow skewed toward the red.

 

[JeffJo]

Please provide a reference for this claim. It does not comport with my understanding of either light or Newton.

What part of the claim? There was a link to Newton's history, which is well known so I have to assume that isn't what you meant. So it must be the rainbows?

I showed you the picture of it. It came from here, one of the leading references on rainbows:
https://www.atoptics.co.uk/rainbows/primcol.htm

Or you can follow the math at:
http://www.trishock.com/academic/rainbows.shtml

Here's my graph of the equations in that reference, for red light:

Consider a great circle of the drop. The horizontal axis considers all of the light that hits the drop along that great circle, as a function of the distance each ray would have passed from the center of the drop if it had not been there. So the energy density along this line is constant. The blue lines, if I recall correctly, show how much deflects within a 0.1 degree range. As this range approaches zero, the deflected energy density within the range approaches infinity. Like this:

In the color bars I showed, the bright areas show the diameter of the sun.

 

[JeffJo]

As others have noted, "indigo" generally isn't used nowadays. Instead of the 7-color spectrum ROYGBIV, I'd remove "I" (indigo) and add "C" (cyan) for ROYGCBV. Still seven.

Those are pretty much the categories Newton used. But what you call Cyan, he called Blue. What you call Blue, he called Indigo (as in "blue jeans" which are indigo). Only the border between them is unclear.

It also makes more sense to break down the color categories into six groups, corresponding to each color receptor type in our eyes (red, green, blue) and the colors in between them (yellow=red+green, cyan=green+blue, magenta=blue+red). That's basically how we perceive colors. Violet or purple is basically magenta skewed a bit toward blue at lower luminance, and orange is basically yellow skewed toward the red.

That is indeed one way. It wasn't what Newton did.

 

[sophiecentaur]

It also makes more sense to break down the color categories into six groups, corresponding to each color receptor type in our eyes (red, green, blue) and the colors in between them (yellow=red+green, cyan=green+blue, magenta=blue+red).

When trying to 'regularise' colour, it's easy to paint oneself into a corner. Of your six colours, one (magenta) is not a spectral colour and you don't get it by choosing one section of the spectrum. The only 'magic number' involved is the three analysis curves that (so the tristimulus colour theory says) are used to give the gamut of colours we perceive. But there are no hard boundaries and those analysis curves all cover pretty much the whole of the visible spectrum. It's wide band analysis that allows three 'signals' to be obtained for all those colours in the CIE chromaticity chart.

I have no idea what is so attractive about choosing to quantify the colours - except to allow kids to learn, by rote, some names for the colours of the rainbow. Nothing that we perceive is quantised to why to quantise colour?

 

[Baluncore]

Nothing that we perceive is quantised to why to quantise colour?

Because red berries are poisonous and we needed to communicate or die.
For a while there, we also needed to read resistor colour codes.

 

[sophiecentaur]

Because red berries are poisonous and we needed to communicate or die.

Berries come in a whole continuum of 'reds' which we have always needed to distinguish between. Also, the colour of another human's face can extends over a whole range of reds, pinks, light and dark browns and will be used to assess the other guy's health and emotional state. Look in your garden and you will see leaves with yellows, greens and blues (and browns).
If the millions of colours used by colour TV were not necessary, we would use single bit chrominance values.

 

[hutchphd]

I showed you the picture of it. It came from here, one of the leading references on rainbows:

Thanks. A few comments about the physics.
Any spectrometer will have an overlap between wavelengths because of the finite width entrance slit. For a rainbow this "slit" is the half-degree angle subtended by the sun projected by the internal reflection and the curved refractive surfaces. But the raindrop is still just a (slightly bizarre focussing) prism. I like the characterization of the resulting cusp anomalies as bright edge discs however.
As to effect on color perception one needs to always remember that the eye is very logarithmic in response

 

[DaveC426913]

I have no idea what is so attractive about choosing to quantify the colours - except to allow kids to learn, by rote, some names for the colours of the rainbow. Nothing that we perceive is quantised to why to quantise colour?

OK. Here's a million dollars to paint my 100 storey skyscraper DaveC Blue^(C).
Millions of consumers all over the world recognize my brand and trademarked colours, so get it right.

Annnnd go!

What? You want a sample of DaveC Blue^(C) to be sure you've got it right? OK, here you go:

 

[sophiecentaur]

As to effect on color perception one needs to always remember that the eye is very logarithmic in response

. . . and that the colours we see in a rainbow are highly desaturated.

Millions of consumers all over the world recognize my brand and trademarked colours, so get it right.

Hence PANTONE came into being. Not cheap but it's a standard that gives a pretty good match between identical colours on different materials and surface textures.

 

[JeffJo]

But the raindrop is still just a (slightly bizarre focussing) prism.

No, it isn't; at least, not how it gets depicted. And rainbows aren't a prism-like effect. Nor did Newton characterize them.

On a sunny day, when sunlight shines though a window onto the opposite wall:

1. Close the shade, and poke a pinhole in it large enough for a beam of light to hit the wall, making a white dot.
2. Hold a triangular prism in the beam with its axis vertical, and at an angle where a spectrum (the visiblespectrum, if you need to be that pedantic) is projected to the side of where the white dot was.
   1. It is a horizontal line of varying colors, the same width as the dot. Red is closest to the spot where the white dot was, and violet is farthest.
   2. The ray of white light is separated into individual rays of colored light.
3. Widen the pinhole into a vertical slit.
   1. The line stretches vertically into a rectangle, with the colors varying horizontally but not vertically. You can think of it as having mant lines, like in 2.1, stacked vertically.
   2. Or you can think of it as a knife-blade of white light being separated into knife-blades of colored light.
4. Rotate the prism so that its axis is horizontal.
   1. The spectrum lines from 2.1 are now vertical. But instead of being stacked next to each other, they are overlaid on top of each other, offset vertically.
   2. The exact result depends on many things. But in general, it will be red at one end, fading through pinks to white in the center. And violet at the other end, fading through lavenders to reach the center.
   3. Each ray of light in the slit does still undergo separation, but on the wall each re-combines with rays of other colors, that hit the prism at a different place.
5. Open the shade.
   1. Now the prism makes a smear of mostly-white light from the light deflected by the prism.

The line in 2.1 is essentially is Newton's famous prism experiment. The almost universal depiction of that experiment is a single ray separating into colors.

The smear in 5.1 is not Newton's famous experiment. But it is much closer to what causes a rainbow. The effect is not the result of a ray of white light separating into colors. It is the result of how many such rays recombine after separating individually.

They really needed a narrower beam to make the result "pop" here. But the white part of this reflection is the equivalent of the smear in 5.1. The brighter (well, they would be, with a narrower beam) edges are caused by the light being concentrated at the "rainbow angle." The separation of color bands is not caused by color separation, like you think of happening to a single ray in the prism experiment. It is caused by the reflection having different widths for different colors. The light in each band even comes from light that hits the drop at different places, making most of the diagrams you have seen wrong.

What most people were taught, as the cause of a rainbow, is grossly inaccurate at best. And negligently incorrect at worst. Any diagram that shows a single ray separating into colors is wrong. Not wrong as in "that doesn't happen," but wrong because one should ask "what about the ray that hits the drop just below that one?"

And any explanation that mentions Total Internal Reflection is blindly repeating what was taught to them. First year geometry students can show why TIR is impossible.

A better model - although it may be a bit abstract for some high schoolers - is to compare the incoming sunlight to a water wave hitting a floating beach ball. Upon exiting the drop after one reflection inside it, line of the wave will be bent into a shape that resembles a used staple. It will be brighter at the edge, where your eye is looking along the line of the bent shape instead of perpendicular to it.

All of the rays, not just one. The rays drawn in red are close to parallel when they exit:

The staple:

(From https://www.usna.edu/Users/oceano/raylee/RainbowBridge/Chapter_8.html). This effect was one of the first to confirm the wave nature of light. If all of the drops are the same size, we can observe fifferent patterns of constructive and destructive interference, for different colors, in the area that is usually white.

 

[sysprog]

Wow, @JeffJo, that's quite a digression/diatribe $-$ what is (simply put, please) your reason for asserting that a raindrop isn't a (spheroid) prism?

 

[JeffJo]

I didn't say it wasn't a light-deflecting device. I said the way the effect is formed is not due to what people think of as the prism effect.

 

[sysprog]

I didn't say it wasn't a light-deflecting device. I said the way the effect is formed is not due to what people think of as the prism effect.

In response to this remark:

But the raindrop is still just a (slightly bizarre focussing) prism.

Your opening sentence was:

No, it isn't; at least, not how it gets depicted.

@hutchphd did not say that a raindrop was a "light deflecting device"; he said that it was a "(slightly bizarre focussing)" prism.

If you don't think that a raindrop is a (spheroid) prism, please, in simple terms, say why not. If you think that it is a (spheroid) prism, but "not how it's depicted", then please explain, not why some other depiction is to be preferred, but what characteristics of the commonly used depictions of it as a (spheroid) prism (including plain photographs as well as accurate diagrams) are not consistent with correctly showing it to be a (spheroid) prism.

Also please explain, in simple terms, how the multicolored visual effect is "not due to what people think of as the prism effect". Isn't the multicolored visual effect produced by refraction? And isn't it refraction that produces what people think of as the prism effect?