Tom- I've combined your two questions, the more specific and more general forms.
If you're at rest with respect to the medium, the speed of light in it will be c/n regardless of the source. Note, however, that n is different for different frequencies of light.
If you're moving with respect to the medium, then you'll see a different speed. I believe that this effect was first inferred by Fresnel in the early 19th century and confirmed by an experiment by Fizeau in 1851.
Mike W..
(published on 04/22/2013)