Light and Redshift in material?

[Link]

I have been reading in astrophysics that when light escapes a massive object its being slowed down by its gravity, but since it cant be slowed down its being redshifted. now in our highschool physics books it says that light takes a diffrent path when its being slowed down when entering aother more dense medium like glass. Judging from this, is it possible to achieve redshift if the light passes through a very thick layer of glass?

[Janitor]

There is a Principle of Least Time in optics that you are probably thinking of when you say that "light takes a different path..." But if you have a light beam pointed straight at a flat piece of glass (i.e. the beam is perpendicular to the surface of the glass), the path the beam takes through the glass does not deviate from a straight line, so what you said about taking a differenent path is not quite universally true. Even in my example of the perpendicular beam of light, the light's speed is less than c inside the glass. That means that the product frequency * wavelength must be lower for the beam inside the glass than outside the glass. And I am thinking the frequency does not change, so that the wavelength is smaller inside the glass than outside the glass. That actually amounts to a blueshift, not a redshift.

Somebody will correct me if I am screwing up on this.