Why do traditional color wheels have yellow opposite to violet (purple), whereas graphics programs such as Adobe Photoshop have yellow opposite to blue?
Yellow opposite violet (purple):
Yellow opposite blue:
The traditional wheel is based on pigments. It's the mix of the primary colors that creates the secondary and tertiary colors in the wheel. That's your first picture.
The second picture is based on the RGB colors and are colors produced by light; they're not "mixed" together and technically don't work the same way as pigments. It might be better to call this wheel a spectrum than a color wheel. By definition they're not really complementary but opposite.
So in general, when people talk about complementary, they still refer to the traditional model: purple and yellow, orange and blue, red and green.
By the way, that "blue" from the RGB wheel is still very close to be a purple in CMYK; but in RGB, it's a blue. The violet on the traditional wheel is also a very pale violet... The wheel below is closer to the real traditional color wheel!
There are different color models which result in different opposites.
One is a subtractive color model (CMYK) -- the top image, where the opposite of yellow is purple. This is for real-world, tangible things like paint, ink, etc.
The other is a additive color model (RGB) -- the bottom image, where the opposite of yellow is blue. This is for light basically, screens, displays, bulbs, etc.
For more information see here: What is the difference between CMYK and RGB? Are there other color spaces I should know?
Becouse that is a color wheel intended for kids. And its roots are older than a modern understanding in color. Some traditional color paletes for painters also use it, again becouse it is a traditional (but arcaic) understanding of it.
The "modern popular understanding" of color comes with 2 inventions: offset color printing for photography, and color tv. Bofore that you could find textbooks saying that the rainbow has 7 colors.
Still, the quality of the pigments for CMYK printing is evolving to achive more consistent colors. Some years ago the combination of 100 magenta and 100 cyan turned into a more violet color. Now the pigments are better but still you don't achive "pure blue" becouse it is not a linear mathematical proportion.
There are some other color models like Lab that has a scale from yellow to blue and red to green. That aproach is more "organic perception model". But this color wheel is not that case.
Imagine how Painting (and painting materials) evolve (Not an acurate historical explanation, but it still works). At the beginning you had some charcoal to paint a cave. Later you had some earth dust with some deer fat and you had some ocre colors.
Years pass and you find some insects or snails to pure pigments from them.
You have some other pigments from combination from metals etc. The point is you had a limited palete of phisical pigments to use. (A timeline of pigments http://www.webexhibits.org/pigments/intro/history.html)
Time after, when you explain things to your students, there has being a traditional model to combine existent pigments. The models built back then were perceptual and experience based.
For example the Fuchsine (magenta) dye was invented in the XIX Century. It could not make part of a color wheel before that.
All that slow evolution makes that the color theory and color wheels need to evolve.
If you ask general population or a group of kids without any formal theorical understanding, they will say that the primary colors are yellow, blue and red... And the sky will be sky blue, not cyan, and the magenta will be a bright pink.
But again, the traditional color wheel is simply wrong.
The first one is called RYB model. And it is charted as HISTORICAL model... "RYB predates modern scientific color theory". https://en.wikipedia.org/wiki/RYB_color_model I totally agree with that description.
Purple is a very complicated color, because
These violets are true blue(pixel blue is 240 hue, these violets are ~236) by the way(just at 70% saturation).
Look to see how tricky it is to neutralize true Yellow(which is incredibly good at absorbing blue light, indicated by how non gray it is on paper compared to most colors) using naive overlaying.
I guess the people who made the diagram would prefer a reddish gray over a greenish gray, or maybe they thought the sienna-like color was good enough for gray, or maybe they found it easier to finish neutralizing it with ultramarine blue(a common neutralizing color), Grays in art can get pretty subjective.
Notice that there is no red, orange, yellow, blue, nor violet in it, Everything is cyan or green, maybe a tad of cyan-blue.
The intentions of the wheels are totally different. The computer RGB color wheel is created for presenting maximally colorful RGB combinations. It usually starts from red, then R+G mixed, G, G+B mixed, B, B+R mixed and back to R. When the transition is gradual and uniform along the circle, yellow must be the opposite of blue. B is 240 degrees after R and yellow is exactly in the half way from pure R to pure G.
In the next image we have the computer RGB color wheel and the proportions of its RGB numbers as color zone thicknesses of the inner ring.
Your traditional wheel tries to present some of the possible paint mixtures of yellow, red and blue (2 colors at a time) altough the colors are not paint, but computer RGB colors.
In the past generally and among painters even today yellow, red and blue are considered as basic hues which are as far from each other. When we leave between them the same amount (=120 degrees) space in a color wheel, we get this:
Of course the opposite of yellow is exactly in the middle of red and blue due the initial spacing decision.
I hope this at least removes some of the divine glamour of color presentations and proves they are human creations.
The traditional colour wheel, for all its faults, is right about the fact that colourant-mixing complementaries differ from additive complementaries near the yellow-blue axis. RGB "blue" and RGB "yellow" are additive complementaries, and in subtractive mixing of IDEAL colourants (reflecting wavelengths in an all-or-nothing fashion) would also be complementary.
And if you slot together two discs painted with these colours (say, ultramarine blue and a lemon yellow) and spin them quickly together they will neutralize each other, because you are in effect additively mixing the light reflected from the paints.
BUT if you mix the same paints together you get a mid-chroma green, not grey, because the sloping ends of the spectral reflectance curves of the two actual paints have some "green wavelengths" in common. To directly neutralize any given yellow paint requires a mixture of blue and violet paints.
Please see my Fig. 1.9 here: http://www.huevaluechroma.com/001.php