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?
Answer
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.
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