Sun light is dispersed by water droplets in the atmosphere and they are observed as arches due to the way in which the light refracts. The way in which we experience rainbows and colors in general may be unique to the way we process information, but photons and the spectrum in which they exist do react to the physical world in an objective, formulaic way, including dispersing at different wavelengths.
an arch of colors formed in the sky in certain circumstances, caused by the refraction and dispersion of the sun's light by rain or other water droplets in the atmosphere.
That exists ergo rainbows exist objectively.
If the definition of a rainbow was something multicolored and solid going through the sky then they would not exist because there is nothing solid there.
The term EXIST means something that is in existence. As long as you can see it, feel it, touch it. Or react to it in any other way it exist. If it did not exist. We would not have pictures of it. Or have so much information on how to even create one.
The phenomena which we call a rainbow, a colored arch formed in the sky under certain circumstances is not an objective phenomena.
Color is a phenomena of the mind. The phenomenon which we call Light is a very thin range of frequencies in the Electromagnetic Spectrum, and these range of frequencies can oscillate differently, our brain is capable of identifying between these changes in oscillation, and that mental differentiation of said oscillations is what we experience as color.
So since the colored arch is not independent of consciousness or sentience, it is not objective. The phenomenon which becomes the rainbow is, but not the phenomenon of the rainbow itself (the colored arch).
The other night I was at the movies, watching a giant monster attacking New York City. There were lots of other people in the theater and they all saw and heard the monster. So are monsters real?
No! It was just an optical illusion created by light from a projector, reflecting back at me off a screen. But what else is a rainbow? Light from the sun (the projector), is reflected off raindrops (the screen). Due to the refractive qualities of water, we can't see the entire spectrum of light from one position. Raindrops at one angle would reflect the full spectrum, but from our position, only the red would be visible. Raindrops at a different angle would reflect the orange. Etc etc. Yes, the sun is real, as is the light coming from it. The raindrops are also real, as well as the light being reflected to us. But the other rainbow is just an optical illusion, as real as the monster in the movie theater. Objectively, it does not exist.
When you see a rainbow, and you are moving, even if you are able to move as fast as possible, the rainbow seems to move along with you.
The end of the rainbow is never attainable as the rainbow only exists in one place, and that is in your head.
Sure, rain exists, the sun exists and you exist, but the rainbow only exists as a reaction of all of these 3 things together.