# Why do we need very small luminous intensity of UV to add to yellow to get white color?

We can get the sRGB white point color with $$(x,y)=(0.3127,0.329)$$ by adding two monochromatic lights: e.g. 360 nm and 566 nm. Calculation tells that we need luminous intensity $$Y(360\,\mathrm{nm})/Y_\Sigma=0.7\%$$ and $$Y(566\,\mathrm{nm})/Y_\Sigma=99.3\%$$. This is counter-intuitive, since this means that you only need to add almost invisible amount of UV light to greenish-yellow light to get white color. See this diagram:

And if we take equal luminous intensities, we'll get a color very close to (ultra)violet:

Note that we already are working in terms of luminosity, not raw power, so the fact that luminous efficacy of UV light is very small shouldn't get into the way. But apparently, it does...

To make sure that my results are correct, here're my calculations:

In CIE XYZ space, points of the two primaries with luminous intensities $$L_{360}=0.007$$ and $$L_{566}=0.993$$ (arbitrary units, since the space is linear) are$$^\dagger$$ $$P_{360}=\operatorname{XYZ}_{360}\frac{L_{360}}{Y_{360}}=(0.232,0.007,1.08),$$ $$P_{566}=\operatorname{XYZ}_{566}\frac{L_{566}}{Y_{566}}=(0.709,0.993,0.00264).$$ Adding them gives the point of mixture $$P_{\mathrm{mix}}=P_{360}+P_{566}=(0.941,1,1.11).$$ The chromaticity coordinates $$x,y$$ of the mixture are then calculated as $$p_{\mathrm{mix}}=\frac{(P_{\mathrm{mix}}^{(X)},P_{\mathrm{mix}}^{(Y)})}{P_{\mathrm{mix}}^{(X)}+P_{\mathrm{mix}}^{(Y)}+P_{\mathrm{mix}}^{(Z)}}=(0.31,0.33),$$ which is within ~1% from the sRGB white point.

The question: How can this be intuitively understood? Why is so small luminous intensity of the UV light needed to make up white when combined with greenish-yellow? Or, in other words, why do we need so much greenish-yellow light to overcome the violetness of the mixture?

$$^\dagger$$ Data correspond to CIE 1931 2° observer, taken from this website.

• Can you check your calculations? If you are correct it means the human eye perceives white with very little violet when mixed with yellow. The yellow already contains lot of green and red, the green is close to blue. – PhysicsDave Oct 7 '18 at 1:00
• @PhysicsDave I've put the results into the question. After double-checking I still think they are correct, albeit strange. – Ruslan Oct 7 '18 at 19:23
• rit.edu/science/calculating-relative-powers – PhysicsDave Oct 8 '18 at 0:50