Wavelength of light changing in a medium

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What would the colours of light produced by a diffraction grating look like if the grating were under water? (Or for an oil film between glass and water etc. etc.)

No, I was referring to the interference pattern, not to the perception of the colour, as I wrote before.
We know that

d⋅sin(α) = n⋅λ

and λ will be different so the pattern will be too. If, for a specific value of n, we measure α, we find a different λ. Let' say that the difference between the two lambdas is too small to be appreciated by the human eye even if the frequencies were different and you don't know if the difference in wavelength is due to a difference in the source's frequency or to a difference in the medium's refractive index, do you conclude that the colour is "roughly" the same just because it seems the same to you eyes? Your precise measurements tell you the wavelengths are different..
What I mean is that "colour perception" is a thing, a "precise definition of colour" is another and one could define it using wavelengths, as many textbooks do (even if I am not keen on it). So we need a definition...

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but when it leaves the sample is just a pack of information called spectra traveling directly to your retina

Yes and why was the OP referring to the medium between the photograph and the eye and not between the reflecting surface of that photograph and the eye? In theory, a lot of things are included in his generic question, even if what you say is certainly the most obvious.
For this reason I asked the OP for a better specification of its question.

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[sophiecentaur]

No, I was referring to the interference pattern, not to the perception of the colour, as I wrote before.

I think the emphasis of the thread have shifted here and there. If you illuminate a diffraction grating from all directions you may see 'colours' - a mixture of different wavelengths in different parts of the grating. That's what I meant, the same as when you see an oil film or reflections in a CD.
In this thread, the words colour and wavelength, have been used indiscriminately. Combinations of monochromatic and wide spectrum light are perceived as colour and colour is what we actually see. Interference patterns in nature produce colours. The mechanics of this are wavelength dependent. This is particularly relevant to the Lipmann system.