No, rainbows do not exist. Review my debate on debate.org. Colors only exist in our minds, therefore it's impossible for a arch of colors to exist in reality. Cameras capture light of different frequencies and create a image that transmits those same frequencies. It takes an eye and a mind to convert those light waves into color.
Most people make the mistake of believing we see reality with our eyes. Like our brains see the image captured on our retina. They are mistaken. The physiology of sight is more like a antenna and TV. Your antenna recieves radio waves and sends a signal to your TV via the RV cable. Your TV converts this signal and creates a picture. It does so using just 3 different colors, but using different combinations we can see all the colors.
Our eyes are light wave antennas. There are 3 types of cones on our retina and each responds to only a certain wavelength of light. When triggered, these cones send a electrical impulse along our optic nerve to the brains imaging centre. Here the brain converts these electrical impulses and creates a visual representation of our surroundings. It actually combines the impulses from both eyes and creates a 3 dimensional picture in our head about 30 times a second. What you see, is that picture.
It's impossible for us to be seeing the world with our eyes, because we would see everything upside down. Our brains turn the picture so things make sense to us. So yes, light waves exist, but light waves have no color. A rainbow is a arch of colors. It exists only in our head.