I've seen just rain rainbows, oil rainbows and wax rainbows but all of those share one property: If you convert a photo of a rainbow into black and white, you will see that the brightness difference in most of the colors seems to be unsignificant but yellow seems to be the lightest color of the spectrum.
Considering the fact that rainbow is just a dispersed reflected light, I would assume we should see it as a monolithic gray stripe, slightly lighter than the background. Why isn't it so?
Because the light intensity in Sunlight varies with wavelength, and this means when you split the sunlight into a rainbow the intensities of the bands in the sunlight vary with wavelength.
Sunlight is an approximately black body spectrum. This is well described in the answers to How is a blackbody spectrum formed in the Sun?, from which I've extracted this spectrum:
You can see that the intensity peaks in the yellow region, whioch is why in a rainbow the yellow band is the brightest.
Oversimplified, it takes more light to create the perception of yellow.
Yellow usually indicates the presence of both red light and green light in equal amounts, with a relative absence of some blue light. Another way of looking at it is that yellow is white that is missing a little blue.
Red light alone can create the perception of red. Same with green and blue acting alone. But the perception of yellow requires the perception of both red and green and often only a small drop in the perception of blue.
The reason behind this is that the human eye has no receptors dedicated to perceiving yellow light. We can only perceive red, green and blue directly. The other colors are a creation of our brains. This is how TV can generate a full range of colors from only those three primary colors. Yellow is red + green in balance. Orange is both red and green with more red than green.
There is one other way of creating the perception of yellow and that is with the wavelength of light where our receptors for red and green overlap in their sensitivity. Thus, this one color can stimulate both our receptors for red and green the same amount. This is how yellow laser light works. It is one monochromatic light source but our brain only knows that both our red and green receptors are stimulated by it.
