The frequency of a photon is a property of the photon, the amount of energy with which it was created.
Refraction preserves this property, or else the process of focusing light would change its color. To understand how, you need to look at how light passes through a “transparent” medium.
In a vacuum, it’s easy to be transparent. The photon moves along, unimpeded, because there aren’t any atoms to interact with. In water or glass, things are different. A photon interacts with the electrons around an atom. This interaction exchanges energy back and forth between the photon and the electron. It’s complicated, but in the end the photon (actually a new photon, but we’re ignoring photon serial numbers here) ends up with all the energy it started with. This allows the light to pass through without being absorbed†. Since it leaves with the energy it started with and the frequency depends on the amount of energy inside, the light remains the same color.
† Of course, some is absorbed because water and glass aren’t perfectly transparent like vacuum is. However an individual photon is either absorbed or not.
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