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Can we only see electromagnetic radiation that has certain range of frequencies and a certain range of wavelengths?

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The short answer is frequency. At the lowest level, photons of various energies interact with molecules in receptors in our eyes to produce a reaction. That interaction depends on the energy of the photon, which depends on the frequency ($E=h\nu$).

If you are considering light in a medium of refractive index $\neq 1$, then it is the frequency that determines the range of light you can see, not the wavelength. The wavelength of light changes with the medium it is moving through. The frequency doesn't, and it is the frequency that determines the colour seen by our eyes, or whether it is visible or not to us.

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    $\begingroup$ Might also be helpful to point out that the wavelength in the eye does not change either. A certain frequency wave will always correspond to a unique wavelength in the eye. But the answer that the interactions is fundamentally about the photon energy and therefore the frequency is the right one. $\endgroup$ – WetSavannaAnimal Sep 16 '17 at 14:06
  • $\begingroup$ This is—of course—correct, but because the wavelength that people generally quote for various bands is the vacuum wavelength it's not always worth insisting on the distinction. $\endgroup$ – dmckee Sep 16 '17 at 17:40

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