Looking at the refractive index of glass, it's around $1.6$.
Then the speed of light $x$ through light should be given by $$ 1.6 = \frac{3.0\times10^8}{x}, $$ so $x$ is about $2\times10^8~\mathrm{m}~\mathrm{s}^{-1}$
The frequency is kept constant, so the wavelength must adapt to suit the slower speed, giving a wavelength of $2/3$ the original.
Does this mean that when passing through glass, say red light (wavelength $650~\mathrm{nm}$) changes to indigo ($445~\mathrm{nm}$), as $650 \times 2/3 = 433~\mathrm{nm}$, or is my logic flawed somewhere?
Answer
What do you take to define "red" light: a wavelength of $650~\mathrm{nm}$ or a frequency of $460~\mathrm{THz}$? On the one hand, this borders on being an ill-defined question, but I suppose it can be massaged into something answerable.
I would argue that frequency is more fundamental to describing the light. After all, it is the frequency that is constant throughout all this, as you noted. When a photon strikes a receptor in your eye, it doesn't matter whether it did so after just passing through glass or through vacuum - the biochemical response is dictated by the frequency/energy of the photon. Thus it would be more appropriate to say red light stays red, but the wavelength corresponding to red shifts in glass.
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