Light and Redshift in material?

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I have been reading in astrophysics that when light escapes a massive object its being slowed down by its gravity, but since it can't be slowed down its being redshifted. now in our high school 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.