Color of Light: Frequency vs Wavelength.

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So today I was thinking that color is connected with a given wavelength (for example red light in air is about 600nm) but after some research online I found out that color depends on the frequency and when light travels through various optical media (like air, glass etc) speed and wavelength change according to ƒ= v/λ so that the frequency f remains the same for all media. That's why it will remain red throughout all media.
So I found that red color for example may have many wavelength values depending on which medium it propagates. So if a red laser beam travels through air and then it goes through water, the speed and wavelength will change and the wavelength of the red laser in air is 600 nm but in water the wavelength of the same frequency gets about 460nm which corresponds to blue in air.
So I guess color is connected to a specific wavelength(like we are taught) but ONLY in air media(n=1), and universally frequency remains the same through all media, which is what defines what color we will perceive.
Unfortunately, it's confusing that certain wavelengths are associated with certain colors perceptually but these values apply only in air.
I would like to read any comments on the topic.

I used this page as source:

http://www.tedmontgomery.com/bblovrvw/emails/lightfrequency.html
 
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You got it right, pretty much.
Why are you confused, then?

The color is a perception concept, not a physical attribute. But it depends on the frequency of the light, but not in a 1 to 1 relationship. You can get same perception with more than one frequency.

And if you wish to associate color with a wavelengths, it should be the wavelength in the eye receptor and not in any other medium. So if you are in water and look at red light, the wavelength through water will indeed reduced but the wavelength in the medium of your eye will be the same as when you receive that red light from air (or glass, or anything else).

It is just more convenient to identify light by wavelength in air. Not just for perception. The wavelength of a laser for example, is given as the value in air.
 
thanks for the reply ,

yes you can get perceptually,say white light, with combining two or more 'narrow band'/monochromatic frequencies ( like with the early LED lights)

And I agree with the eye comment. The last medium before the receptors inside the eye will always be of the same n / Index Of Refraction so no matter what was 'before' that , a specific frequency will all end up being seen as the same color always.
 
You are right. What determines the color is essentially frequency.