Does the frequency of light change when it travels across an interface between two media? What happens to the light wavelength and the light velocity at the interface?
I've gotten different answers some say all three change and some say frequency is constant or some say that the wavelength is constant...
What's the right answer?
Frequency is constant. If it were otherwise, you would have more (or fewer) wave crests hitting the interface per unit time than leaving it, which would lead to some sort of pileup that gets worse and worse as time progresses. Another way to think about it is the atoms/electrons/electric field lines/whatever at the interface respond immediately to their neighbors (the wave is essentially continuous), even if those neighbors are in a different medium.
Wavelength can change, and it does so in such a way that $f \lambda = c/n$ at all locations. Here $f$ is the frequency, $\lambda$ is the wavelength, $c$ is the speed of light in vacuum, and $n$ is the index of refraction. As you can see, going from air ($n \approx 1$) to glass (say $n = 1.4$) will result in the wavelength of optical light to decrease by a factor of $1.4$. Also note that in general $n$ can depend on $f$, leading to colors dispersing as in rainbows and chromatic aberration.
Does the frequency of light change when it travels across an interface between two media? What happens to the light wavelength and the light velocity at the interface?
When an EM wave passes through any medium other than air, it's frequency (number of oscillations per second) still remains the same. Only the distance between individual crests (or troughs) shorten out and thereby a decrease in the wavelength. And hence, it travels less distance at a given period of time (and hence $c_{medium}<c_{vacuum}$). As Chris said, This is probably determined by the refractive index (a relative parameter) of the medium. The color of light still remains the same, since its energy $h\nu$ still hasn't changed. There's another interesting answer for: "Why doesn't color change with wavelength?"
