Color Mixing I: Red + Green = Yellow

To show that three types of receptors cannot resolve all possible colors, we consider, for example, three spectral (monochromatic) colors:

• Red:
  
  $$L_r(\lambda)=\delta(\lambda-\lambda_r)$$
  
  
  where $\lambda_r=615$ nm;
• Yellow:
  
  $$L_y(\lambda)=\delta(\lambda-\lambda_y)$$
  
  
  where $\lambda_y=565$ nm;
• Green:
  
  $$L_g(\lambda)=\delta(\lambda-\lambda_g)$$
  
  
  where $\lambda_g=490$ nm;

As shown in the figure, the responses of the L and M (red and green) cones to color $L_y(\lambda)=\delta(\lambda-\lambda_y)$ are the same as their responses to the mixed color

$$L_{rg}(\lambda)=L_r(\lambda)+L_g(\lambda) =\delta(\lambda-\lambda_r)+\delta(\lambda-\lambda_g)$$

as

$$r_i=\int S_i(\lambda) L_y(\lambda) d\lambda =\int S_i(\lambda) L_{rg}(\lambda) d\lambda \;\;\;\;(i=L, M)$$

So colors $L_y(\lambda)$ and $L_{rg}(\lambda)$ cannot be distinguished by our visual system. That is why ``red plus green is yellow''.