Does light change color on its way through a window? 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?
 A: I've had the same question some time ago, and discussed it with some friends.
First of all: yes, this question is fairly ill-defined, since you only observe color through your eyes, meaning the lightbeam will always be travelling through the eye-fluid when it strikes your photoreceptors, so it's kind of hard to define precisely define the color of light in any other context than when travelling through your eye.
That being said, it turns out what your eyes percieve are the excitations of molecules in your photoreceptors, i.e., the frequency (energy) of the light. Hence, should one try to "translate" the light from the interior of the glass to what your eyes would see, the color would be identical.
A: Do not try to characterize light by it's colour. Colour is something that is defined only in vacuum! Light is characterized by it's wavelength or frequency, one is enough. You additionally have to have the knowledge of the refractive index though. So you are right about how the wavelength is changing but the frequency stays constant.  
To the question what we will see as an observer: We would see red light. Because when the light quits the glass, the wavelength will experience the reverse change than as when it entered. You would see the exact same light that entered the glass which was described by you as red.  
An interesting question though is what would we see if we were able to put our eyes INTO the glass, so that the light is not transformed back to it's initial state. Well then SamRoelants pointed out what we would see.
A: 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.
