Snell's law and what determines color of light

Question

White light is dispersed by a prism into the colors of the visible spectrum with wavelengths ranging from violet 380 to red 750 nanometers. By Snell’s law, the refractive index $n_{21}=n_2/n_1=sin⁡θ_1/sin⁡θ_2 =v_1/v_2= λ_1/λ_2$ . For example, the refractive index $n_{21}$ of water is 1.3 and glass is 1.5. Light moves slower in glass than in water because its wavelength has shortened more.

There is a discussion of whether the light color is determined by frequency or wavelength. We see rainbow in a glass prism because it reflects, part of the light is scattered, by glass back to air. So, its wavelength has not really changed because it changed from $λ_1$ in air to $λ_2$ in glass back to $λ_1$ in air. But if we could observe it inside the glass, what color would we see?

The wavelength spectrum inside, $λ_2 (=λ_1/1.5)$, is shifted towards blue [253 nm, 500 nm]. If the light color our retina and brain detect is based on wavelength (wave-like $λ = \frac{h}{p}$), we would not be able to see red, orange, and yellow. Even if the medium is water, we lose red and orange colors because it is shifted to [292 nm, 577 nm]. On the other hand, if light color is based on frequency ν (particle-like $E=hν$ or Photoelectric effect), the observer inside the medium would be able to see the same spectrum as the one outside because there is no frequency change. Is this argument plausible?

Answer 1

On one hand, you see light when light stimulates a rod or cone in the retina. I don't know the photochemistry. But I presume a photon promotes an electron to an excited state. This implies the photon must have a suitable energy. Since $E = h\nu$, it must have a suitable frequency.

On the other hand, all colors happen in the mind. Light has a mix of wavelengths/frequencies, but it doesn't have color until someone sees it. You see light that enters the eye and strikes the retina. All light that you see is in the same medium, the aqueous humor of the eye. So it doesn't matter that light has a different wavelength in other media.

Note that wavelength/frequency play a role in the color you see, but so to other things like surrounding colors. See What is Gray, from a physics POV? for an example.

Answer 2

Color as perceived by an eye is based on frequency. The light wave causes electrical oscillation within the retinal cells. These oscillations have frequency to copy from the light, but the oscillations do not copy wavelength.
Frequency during refraction does not change. Wavelength changes because the AVERAGE speed changes. The light speed between molecules remains the same. The frequency controls the likelihood that a specific molecule will absorb the light (one photon at a time), hold the light and then release it after a very short time, or not interact at all. Holding for a short time delays the signal. In a simplified model, this is like driving at 60mph with occasional stoplights. Longer stoplights increases time required to travel the road. More stoplights also lengthens the time. Although driving speed is actually 60mph, you might travel a distance of only 50 miles in one hour. The average speed is 50mph.