Why do we see a different color when we mix two colors?

Question

The compounds responsible for a color do not change when they are mixed with another material. The same compounds are there after mixing. However, when we mix colors such as blue and yellow we see green.

BUT we are able to tell where a color starts and ends in pictures. For example, if we hold a yellow piece of paper up to the sky, we can tell that the paper is yellow and the sky is blue. We can distinguish where the paper ends. And where the sky starts. We do not see a green outline near the paper.

I believe that how we perceive colors may explain this. But I am not sure how. Is it because how the brain integrates information. Or is it because of how the cones cannot register two signals at the same time. Why do we see green instead of a blue and yellow?

Answer 1

I am not sure if this is entirely correct, its just a scientific guess. But it might actually play some role in this phenomenon. This is actually the physics part part of answer rather than the biology part.

Rayleigh criterion for angular resolution is the minimum angle which two bodies should subtend on an object so that they can be viewed as distinct bodies by that object.

Suppose there are 2 bodies, (right now) with same color of wavelength $\lambda$. Now, they are viewed from a lens of aperture $d$. Thus, from Rayleigh's equation, the minimum angle which these bodies should subtend with each other on the lens is given by:

$\theta = 1.22 \lambda/d$

Now I'm not sure if this is correct, but if the 2 bodies have different colors, of wavelengths $\lambda_1$ and $\lambda_2$ then the equation becomes:

$\theta = 1.22\times (\lambda_2 - \lambda_1)/d$

$\theta = 1.22 \times \Delta\lambda/d$

Now, putting values in this equation:

$\lambda_2 = 597 nm$

$\lambda_1 = 492 nm$

$d = 5 mm = 5 \times 10^{-3} m$

Answer comes out as:

$\theta = \underline{1.22 \times 105 \times 10^{-9}}$
$\hspace{15mm}5 \times 10^{-3}$

$\theta = 2.56 \times 10^{-5} rad = 1.4 6\times 10^{-3\circ}$

So, if these 2 bodies subtend an angle less than $2.56\times10^{-5}$ radian, then they will appear as a single object with green color.

Now, solving it by a common formula:

$\theta = a/l$

$l = a/\theta$

$l = \underline{\hspace{7mm}10^{-2}\hspace{7mm}}$
$\hspace{8mm}2.56 \times 10^{-5}$

$l = 390.625 m$

It means if yould hold two 5 cm x 2 cm papers together (i.e. total 10 cm²), one with blue color and the other with yellow color, then you would see a single paper of green color if you keep these papers $\approx$391 m away (if my calculations are correct ;).

This, in part, explains that it is not the fault of only our eyes, but of light and physical laws too.

References:

1. Angular resolution

2. Wavelengths of different colors

3. Resolving power of imaging instruments