When light enters a medium (ie. something that isn't free space) it "slows down." (For you relativity buffs, yes it still travels at c. But it takes time for it to be absorbed, then re-emitted from atom to atom so its net speed is less than c.) The overall effect of this is something called the "index of refraction" of the material, usually denoted as the unitless constant n > 1. The speed of light in a material of index of refraction n is:
The problem with what you are asking is that every point on the wavefront you initially described undergoes this speed change when at the point where the wavefront hits the new medium. New wavelets are generated at all points along the boundary. The description of the effect is called "Huygen's Principle."
It is easier to see what happens with linear wavefronts, as opposed to circular ones. When the line wavefronts hit the new boundary a new line wavefront is generated (as a result of Huygen's Principle). A similar effect occurs for circular wavefronts, they produce new circular wavefronts. (In general the radius of the new circular fronts is different from the one in the source medium, and the center is also changed.)
I haven't found a good internet source to help you with this, but the new propagation speed of light can be found if you know the index of refraction of the material, and you can trace the center of the new circular fronts by "winding time" backward in your equation. (I don't have the equation at my fingertips, and don't have my source for this with me. But it should be relatively easy for you to write the equations out.)