B Why does light diffract into only seven colours?

[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?

 

[sophiecentaur]

Isn't the multicolored visual effect produced by refraction?

It needs dispersion to produce a spectrum i.e. differential refraction.

Refraction / dispersion takes place at entry and exit. I seem to remember school experiments with glass prisms which showed that the greatest dispersion occurred with a symmetrical path through the prism ( i_in = r_out and i_out = r_in), on account of Snell's Law; or is that just rosy tinted prisms / specs?
The internal reflection is just an added complication which sends the light back towards an observer with their back to the Sun.

 

[hutchphd]

Thanks to @sophiecentaur and @sysprog for elucidating. The dispersion of color is caused by differential refraction of the frequencies of light at interfaces. For the raindrop the surfaces are curved and there can be several reflections internally, so the result is more complicated. But the physics is not fundamentally different.
Of course rainbows have more serendipity.

 

[DaveC426913]

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.

Ah, but in my example, I neither had - nor gave you - a PANTONE chip.
An even if I had, you'd still have to recreate it perfectly consistently in your 10,000 gallons of paint.

Granted, PANTONE is one way of doing it. But they couldn't have done it without first quantifying their own colours.

 

[phinds]

Ah, but in my example, I neither had - nor gave you - a PANTONE chip.
An even if I had, you'd still have to recreate it perfectly consistently in your 10,000 gallons of paint.

Which is actually quite doable, apparently, since part of each of the Pantone colors is a specification for the appropriate ink mix. That's the only way that magazines can reliably and consistently reproduce specific Pantone colors. Without that capability the Pantone colors would be useless and they make a lot of money because they aren't useless.

Their testing facility (for batch consistency) is very impressive.

I can't remember whether Pantone colors actually apply to paint (I think they are not). They were designed for printers ink used in magazines.

 

[JeffJo]

If you don't think that a raindrop is a (spheroid) prism, please, in simple terms, say why not.

From Wolfram's Mathworld: "A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure)."

• I don't want to be as pedantic as some of these responses. This was about color, and why you should say "spectrum" and not "rainbow," but I keep being asked to explain what a rainbow is when a demonstration of "not a spectrum" should have been enough.
• I agree that you can get your meaning across by calling it a prism, but only when that shares the important properties. Here, the important property is not that it deflects light of different colors, but how it deflects them differently. A sphere does it differently that the prism as Wolfram defines it.

So, a sphere is not a prism. A prism has flat faces that deflect all of the (parallel) light of a single color the same way. That way you can reduce the effect to one dimension; a single point of entry, or entry along a line where all the light deflects the same way. A curved surface produces deflections that vary across the surface in a way that has to be accounted for. In a prism, you need first-year geometry to see where the light goes. In a raindrop, you either have to plot it or use calculus.

If you think that it is a (spheroid) prism, but "not how it's depicted", then please explain,

Pick your favorite explanation of rainbows. Most are based on a diagram like these:

And compare it to:

In most rainbow explanations, it is clearly implied - and sometime stated - that the rainbow is caused by light from a single white ray separating into colors like what happens in that prism. Or that each color emerges with a single angle of deflection. Since both statementgs about rainbows are wrong, they never explain why they think red light comes out only that one angle. As I keep repeating, that is not the case, and how these angles differ explains why a rainbow is not a spectrum.

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?

All that light coming out at the same angle is what I called "the prism effect." See the diagrams above.

I tried to explain this "prism effect" is what happens in Newton's experiment, the one he used to characterize colors, and is supposed to be the subject of this discussion. But a rainbow is not caused by all of the light of a single color emerging at the same angle. As I have said several times. That's why a rainbow is different than a spectrum.

Refraction / dispersion takes place at entry and exit.

<Sigh.> Dispersion is not synonymous with refraction, or separation. It is caused by refraction, and may or may not involve separation. Depending on what you think is separating.

Dispersion means that the path traveled by light, which was once independent of wavelength, must be treated as a function of wavelength. And no, I don't have a reference that uses that exact definition. Ignore that I said it if you don't like it, as it really isn't that important to why a rainbow is different than a spectrum. I only mention it because it when we treat similar, but different, concepts as equivalent that issues like spectrum-or-rainbow arise.

The internal reflection is just an added complication which sends the light back towards an observer with their back to the Sun.

The internal reflection is what creates the minimum deflection that makes rainbows. (Not to be confused with the "maximum deviation" sometimes used with prisms as you vary the angle of incidence.)

 

[sysprog]

I keep being asked to explain what a rainbow is when a demonstration of "not a spectrum" should have been enough.

I didn't ask you to explain what a rainbow is. I did ask you to, if you don't think that a raindrop is a (spheroid) prism, please, in simple terms, say why not. Your answer was essentially that it's not a prism because it's not geometrically a polyhedral prism. That difference was acknowledged parenthetically, so your answer that merely elaborates on that already acknowledged difference is unresponsive.

[*]I agree that you can get your meaning across by calling it a prism, but only when that shares the important properties.

Then the term 'spheroidal prism' is adequate to get the meaning across, and to acknowledge differences in properties.

Here, the important property is not that it deflects light of different colors, but how it deflects them differently. A sphere does it differently that the prism as Wolfram defines it.

The difference between a spherical or spheroid prism, and a polyhedral 'proper' prism, is acknowledged by the use of the modifying adjective.

So, a sphere is not a prism.

The term 'spherical prism' or 'spheroid prism' means a spherical or spheroidal object which produces a prismatic optical effect. It's clearly not referential specifically to a polyhedral prism. It's easy enough to understand that.

As I keep repeating, that is not the case, and how these angles differ explains why a rainbow is not a spectrum.

The term 'rainbow' designates the physical phenomenon by which spectral colors are displayed; it's not as precise in separating them as a glass prism is, but that doesn't mean that people are wrong when they say that a rainbow manifests the spectrum of visible light, or when they say that a raindrop is a spheroidal prism that produces a circular spectrum. That's part of a reasonable explanation for why, from the ground, the rainbow looks like a multlcolored semicircular arch.

All that light coming out at the same angle is what I called "the prism effect."

Maybe so, but you made reference to "what people call the prism effect", and that isn't restricted to all the light (for a given spectral frequency) coming out at the same angle, as individual light frequencies would in an abstractly perfect prism $-$ the effect by which white light is separated visibly into its consituent frequencies is reasonably called the prism effect, because the prism is the model object for production of that effect.

 

[sophiecentaur]

I agree that you can get your meaning across by calling it a prism, but only when that shares the important properties. Here, the important property is not that it deflects light of different colors, but how it deflects them differently. A sphere does it differently that the prism as Wolfram defines it.

Actually, the same laws of reflection and refraction apply to any shape of surface because they relate to the Normal. The fact that a raindrop has a curve makes no difference to what goes on; lenses and curved mirrors are designed on the basis of Ray Optics, which breaks any surface into elemental facets.

When right angled prisms are used in optical instruments, care is taken to ensure the light strikes input and output faces Normally, with the specific intention of eliminating dispersion but that is only an example of different behaviour from a raindrop.

An appropriate (shallow) three sided prism can be used to incorporate internal reflection and dispersion on the way in and out. Much the same effect as in a raindrop and with the same angles involved..

 

[hutchphd]

<Sigh.> Dispersion is not synonymous with refraction, or separation. It is caused by refraction, and may or may not involve separation. Depending on what you think is separating.

As with many foolishly contentious arguments this one now wallows in a sea of semantic purity devoid of Physics. I will now take a short swim myself.
To disperse means to "distribute or spread over a wide area" and dispersion is the act of so doing.
The classic Newton sunlight-through-the-window-shade experiment causes a projection (real image) of this color-dispersed light while the rainbow provides a virtual image of the color-dispersed light. In each case the separartion is caused by the same physics: the frequency dependence of the speed of light. This is in contradistinction to a diffraction grating whch really is different.
Whether you wish to call this the "prism effect" is a matter of personal preference.

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.)

Thanks for joining the party, but it is getting late..

 

[Mondayman]

My old coworker was color blind. Manufactuers would send furniture with wrong labels on occasion, so if he happened to deal with it, the customer would receive the wrong coloured furniture. To make matters worse, it always happened to somebody who was from out of town.

 

[hutchphd]

At one of my happiest jobs, the other physicst was red green colorblind and this was occasionally startling. I vividly remember Rick wandering into my office with two "gelatin" filters, one magenta and one forest green, to ask me which was which! He could not see any difference!

 

[sysprog]

Refraction / dispersion takes place at entry and exit.

<Sigh.> Dispersion is not synonymous with refraction, or separation.

It is not reasonable to interpret that sentence from @sophiecentaur as saying that dispersion is synonymous with refraction.

 

[hutchphd]

Yes. As a semantic issue I always interpret "/" to be shorthand for "and/or" and so this is exactly correct.