Yes.
> Do we see bands of color in a rainbow because of the physiology of eyes
Yes. You have different physical structures in your eyes that respond to different frequencies of electromagnetic radiation. When they are struck by a photon of the appropriate frequency, they are stimulated and send a signal to your brain.
> or the way the brain interprets the frequencies?
Yes. Your perception of color is entirely constructed within your head. Your brain receives a signal from your optic nerve and builds your “image” based on the information it receives. What this means for the individual person and their perception of reality is actually a long-standing philosophical question: Does the “red” I see look the same to you? In other words: If you could someone look inside someone else’s brain and see their “image” of the world, would the colors look the same as what you see?
> or are those bands of separate colors a product of unequal refraction?
Yes. The color banding occurs because different frequencies of light are refracted differently by raindrops. This is a smooth gradient across the visible spectrum, and it’s consistent for all frequencies. Red light is bent the least, violet light the most, and that’s why the colors of the rainbow always show up in the same order and proportion.
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