How Does the Sagnac Effect Cause Interference Patterns in a Rotating System?

[n0_3sc]

I'm having trouble understanding the Sagnac Effect.
So far all I know is that a ring cavity is formed where 2 beams travel in opposite directions. My question is:
Why do the 2 beams form an interference pattern if the entire cavity is rotating at some angular velocity?

 

[Gokul43201]

This is easier to see when you have an external light source, in which case, even thinking non-relativistically, you can see that the beams traveling in opposite directions travel through different path lengths before meeting at the detector. (This is similar to what Michelson and Morley were hoping to see).

For the case where the source is also part of the rotating setup, this requires a more careful explanation. It might be better to just refer you to a good source. I can't think of one at the moment, but I will, in a bit.

 

[n0_3sc]

if you had an external light source, is this rotating as well? if not wouldn't that mean that all the mirrors in the cavity would have to be beam splitters?
Thanks for the help.