Color Theory - What does blue + yellow make?

[jaumzaum]

Hello!

PS. This is not a Homework question, I am asking about a concept.

I am a Physics teacher from Brazil and last week one of the biggest Engineer universities here applied its entrance exam. However, a lot of teachers (including me) don't agree with one of the answers. Can you guys help me?

The question is the following:
"Consider a double slit experiment in which a dichromatic light made from equal intensities of a 480 nm (blue) and 600 nm (yellow) is used. The distance between the slits is 2 mm and a screen is positioned 5m apart. Calculate the distance, from the center fringe, in with a green fringe is seen."

The answer they gave is that no green fringe will be seen.
I assumed they considered that blue + yellow generates white, but I really doubt that is the case. For humans to perceive a pure white color we have to mix a lot of monochromatic frequencies. Based on how our eyes perceive each wavelength and the sensitivity of our cones to red, blue and green, even an equal amount of red, blue and green color would probably give some whitish (but not purely white) color, like a whitish blue or a whitish green. I really doubt that if someone create a dichromatic LASER with equal intensities of 480 and 600 nm light the light would be white.

Based on the figure bellow we can estimate the sensitivity of the cones to the 480 nm light (R=0,15, G = 0,3, B = 0,3) and to the 600 nm light (R = 0,85, G = 0,35, B = 0). We are not seeing an equal amount of red, green and blue. I know that human perception is not linear, but I don't think this will make white.

Can anyone help me to figure out what is the outcoming color? Is there any simulator in which we can sum monochromatic colors by wavelength? Or any paper in this manner?

 

[tech99]

If green is not present in the light source it cannot be present in the image after passing through the slits.

 

[kuruman]

I think this is an interference problem, with color-mixing thrown into make it more interesting. If you send through a double-slit only blue light, you will get the familiar fringe pattern. If you send through only yellow light, you will also get the familiar fringe pattern but spaced farther apart. When you send through both colors with equal weights you will get interspersed blue and yellow fringes.

Now the separation between adjacent fringes is $\Delta y=\frac{\lambda}{d}~L$, where $L=5~\text{m}$ and $d=2\times 10^{-3}~\text{m}$. Note that the given wavelengths are in a 5 to 4 ratio, i.e. $5~\lambda_{\text{blue}}=4~\lambda_{\text{yellow}}$ which means that the fifth-order blue fringe will overlap the fourth-order yellow fringe (presumably on a white screen) and will appear to the eye as green.

Putting in the numbers gives $$\Delta y=\frac{4\times 600\times10^{-9}(\text{m})}{2\times 10^{-3}(\text{m})}\times5(\text{m})=0.006~\text{m}=6~\text{mm}.$$Of course, this is the first occurrence of the green-looking fringe. There will be another overlap at twice that distance and so on.

 

[tech99]

Blue and Yellow are complementary colours, lying opposite each other on Maxwell's Colour Triangle and on a line passing through the centre. All colours obtained by mixing varying proportions of Yellow and Blue lie along this line and we never obtain Green. At the centre we obtain White.
Please remember that colour mixing creates psychoperceptual colours, not physical ones.

 

[DaveE]

There are simulators of human color perception out there, google can help find them. Here's one paper about that (which I chose mostly at random).

But I think delving into the biology of human perception isn't really the point of a physics test. Frankly it's a complicated mess with the spectral response of 3 photorectors, etc. I like @kuruman's approach; where do the fringes overlap?

 

[jaumzaum]

There are simulators of human color perception out there, google can help find them. Here's one paper about that (which I chose mostly at random).

But I think delving into the biology of human perception isn't really the point of a physics test. Frankly it's a complicated mess with the spectral response of 3 photorectors, etc. I like @kuruman's approach; where do the fringes overlap?

@kuruman approach was also my approach and the approach of a lot of teachers. We also got 6 mm, which gave letter B as the answer. The problem is that the official answer is E (no green fringe will be seen), which led me to think they considered @tech99 approach. This is the most important Engineer entrance exam from Brazil (it's like MIT in United States), that's why this is creating a lot of polemic.

@tech99 you told that yellow and blue could never make green, can you explain me why would that be the case? I presume you are considering the line coming from the blue vertex to the center of the other side (yellow). In that case, we would never see green. But who said the blue vertex is 480 nm and the center of the other side is 600 nm? 480 nm can be other point near the blue vertex and 600 nm could be other point near the midside. In my perception the line joining these two could pass near the green vertex and be perceived as some type of green. That's why I thought a simulator would be the best way to confirm this.

Also, as the question is asking about where the green fringe will be seen, I presume they are considering the psychoperceptual colors.

@DaveE I tried to search in the internet for this type of simulator (where I could input the wavelenght of 2 monochromatic lights and get the outcome) but with no success, do you know where I could find them?

 

[DaveE]

I tried to search in the internet for this type of simulator (where I could input the wavelenght of 2 monochromatic lights and get the outcome) but with no success, do you know where I could find them?

No, sorry.

 

[sophiecentaur]

There are simulators of human colour perception out there,

The CIE chromaticity diagram is a plot of colours 'as they are perceived'. It is based on the eye's analysis curves and the Maths has eliminated the Luminance. Unlike the Colour Triangle, it uses and gives numbers when colour matching is involved and it works (additive mixing of course). If you plot two colours on the CIE chart then the resulting perceived colour will lie on the line joining the two points at the 'centre of mass' of the weighted levels of the two colours (considered to be Primaries for experiment but they don't have to be R,G or B).
People are sometimes pretty dismissive of the CIE chart but it's pretty damn good where colour TV is concerned and it will work a treat for this problem.
Assuming the two light sources are spectral then they will lie on the curved (spectral) portion of the chart. Depending on the levels of each, the result will lie somewhere on the line joining the points.
I should point out that spectral colours can only be synthesised from single frequency (line) sources ; the Yellow cannot come from a combination of Red and green sources. (Close, maybe but no cigar.)
To get a green line from the two slit interference pattern, you choose where the 'green' that you want is, on the spectrum. Draw a line from the 'White' reference point (somewhere in the centre) and then work out what proportions of the two primaries to give a resultant where you want it.
This link shows the sort of thing I'm talking about. If you look at a line joining 480 nm (blue) and 600 nm (yellow), it passes through or below the white in the centre so 'they' are right because no combination of the chosen B and Y can give any Green. A very pale blue / cyan source, mixed with a very orange red could give a very de-saturated green - I would have copied the diagram but only a screenshot seems to work. Here's an alternative image:

 

[kuruman]

To @jaumzaum: My first thought when I saw this question was that there are no green fringes because two waves of different wavelengths emitted by separate monochromatic sources are not coherent and cannot form fringes with one another. If passed together through a double-slit setup, they will form two separate interference patterns. However, the question remains, "what happens at the points on the screen where two fringe maxima of different wavelengths overlap?"

The answer to that question is that if you placed a diffraction grating at those points, you would not see a single green line but two resolved lines, one blue and one yellow. I guess that is the path of reasoning that the author of the question intended the solvers to follow.

It looks like the author set up a trap by providing (a) two wavelengths with an integer ratio and (b) the answer that is consistent with that ratio. This consideration made me move away from my initial thought of "no green line" for reasons explained above to "maybe this problem is about overlapping fringe maxima." It turns out it wasn't. As @sophiecentaur pointed out, the perceived color from the overlapping fringes would not be green by any stretch of the imagination.

 

[tech99]

As "Green" is a primary colour, so far as I know it cannot be created by colour mixing. Notwithstanding Dr Land's work, that is.

 

[sophiecentaur]

It looks like the author set up a trap by providing (a) two wavelengths with an integer ratio and (b) the answer that is consistent with that ratio.

The ratio of the wavelengths is irrelevant. There are two separate interference patterns which the eye detects through different filters and certainly incoherently. The resultant perceived colour at any given angle will be due to the relative levels of each interference pattern. No combination of those source 'primaries' can produce a 'green' - just a desaturated colour on the 'minus green' side of white on the diagram.

As "Green" is a primary colour, so far as I know it cannot be created by colour mixing. Notwithstanding Dr Land's work, that is.

A colour near 'spectral Green' can be used as a suitable primary colour because its position on the CIE chart gives it a good coverage of possible resultant colours when used in conjunction with two other suitable chosen primaries. (i.e. within a nice big triangle or 'gamut').
It is true that a spectral 'primary' can't be synthesised with two other colours (or even spectral wavelengths) because a chord across the curve is the closest you can get.
Most of what can be read about mixing colours is from people who want to fabricate colours from practical light sources (worse still, from pigments and filters). The colour triangle is a handy, arm waving way to describe things but it doesn't carry with it a rigorous (quantitative) treatment of the eye sensitivity curves. The CIE chart was derived from measurements of human colour vision - always a good place to start.
The Land theory can't really be argued with but afaics is more complicated than necessary for reproducing most scenes well enough. Perfection can be the enemy of the good, in this case.

 

[jaumzaum]

Thank you all guys!

 

[Drakkith]

The question is the following:
"Consider a double slit experiment in which a dichromatic light made from equal intensities of a 480 nm (blue) and 600 nm (yellow) is used. The distance between the slits is 2 mm and a screen is positioned 5m apart. Calculate the distance, from the center fringe, in with a green fringe is seen."

Good thing my father didn't take this test. He's color blind. Yellow and green are practically identical colors to him. Actually everything from green towards red is almost identical, and he can barely tell the difference between traffic lights and parking lot lights.

What a poorly chosen question. It has nothing to do with engineering and everything to do with color theory.

 

[sophiecentaur]

What a poorly chosen question. It has nothing to do with engineering and everything to do with color theory.

Not sure about "poorly chosen". talk to any TV systems Engineer and the colour theory is way up in design priorities.
If the students had not been told about the CIE coordinates and additive colour mixing then the question was 'unfair' but its purpose could have been to show how inadequate a simple colour triangle is as a model.

 

[Drakkith]

Not sure about "poorly chosen". talk to any TV systems Engineer and the colour theory is way up in design priorities.

Perhaps. I just find it an odd question to be on an entrance exam. But now that I think about it I've actually never taken an entrance exam, so I don't know what's on them.

 

[jaumzaum]

It was an odd question because it was the first time they make a question about color theory. But once in a while there are some odd questions in this entrance exam. One time they asked to describe the industrial process of extracting Magnesium from sea water. Last year they made a question about the Triple Slit Experiment. In 2014 there was a question about General Relativity (eventhough only Special Relativity is in the notice). In 2015 about peculiarities of the tartaric acid. In 2013 about peculiarities of AgF, AgCl, AgBr and AgI.

This was probably the one question that the people that were admitted got wrong.

 

[sophiecentaur]

Perhaps. I just find it an odd question to be on an entrance exam. But now that I think about it I've actually never taken an entrance exam, so I don't know what's on them.

A very valid point. It could be answered approximately by simple colour mixing ideas but even basic colour vision is a bit specialised because it’s generally seriously misunderstood. Maybe the setter was over optimistic.

 

[hutchphd]

I think that much of this discussion has not made the distinction between pigment mixing (subtractive) and source color mixing (additive).
The original question is too clever by half and of course one will not see green light from an additive combination of yellow light and blue light. It will look basically white.
But if you mix yellow paint with blue paint it is definitively green. Rather than recapitulate color theory here I recommend :https://colourware.org/2018/05/18/why-yellow-and-blue-dont-make-green/

 

[sophiecentaur]

Too simple. In the original situation, with two spectral colours, “of course” pretty well applies (but you would need to specify the reference white.
If you take a bluish light and mix it with a reddish light, the result could easily be a greenish white.? (A very desaturated green but no one specified a saturation for the ‘green’. The quantities are important here and the triangle won’t give a proper answer.

 

[jaumzaum]

@hutchphd Using @sophiecentaur diagram, blue + yellow can make green (491nm + 569nm 4:6 ratio):

 

[hutchphd]

The line you draw above is from blue-green to yellow-green and a very washed out and unsaturated "green" results. If you go from 460nm (deep blue) to 570nm(vivid yellow) there is really no green result.
There is no unique way to quantify color. The physiology depends upon the sensitivity of the cones (the tristimulus curves) and the response of the cones is not linear in brightness. This color gamut is a pretty good estimator. One can mimic the eye better by explicitly looking at the illumination, filtration (or reflection) and convolutiong this with the cone sensitivity. But there are always surprising color metamers.

 

[sophiecentaur]

There is no unique way to quantify color.

That's very true. It's actually very lucky (hardly a Scientific description, I know) that the tristimulus system works so well for TV. Ninety years of work have really done a good job. The quality of colour TV (camera to display, omitting the analogue coding) has been pretty fair since the sixties. Shame about NTSC but they had to get in there first, I guess.
It shows how much we are 'on the edge' when it comes to colour printing and filtering. The basic CMY of colour film and even Technicolour (three camera) systems have always produced dodgy results which the cinematographers have had to work round by picking scenes, lighting and costumes to get 'nice' pictures but fidelity has always been a problem.
Colour printing also has its problems with a large number of inks / dyes needed to get what's required. Basically, it's a bucket of this, a cup of that and a pinch of something else to get the right Red for the Coke ads.