How does interferometry work!? I can't figure out how two small mirrors, a mile apart, could have the light gathering power of a mile wide mirror. If you could refer me to a good book or web site I would appreciate it
You're right, and interferometer does not have the light gathering power of a single mirror filling the whole space it spans, light gathering power only has to do with physically how big a mirror is.
Where interferometry has an advantage is in resolution (or resolving power). This is how small size objects the telescope can distinguish and this has to do with the biggest dimension of the telescope. So by putting two small mirrors far apart and combining the signal in the right way you can have the resolving power that a single telescope filling the space between them would have.
I'm not sure how basic an introduction you are interested in getting, but here is one suggestion on the ALMA observatory. This assumes some knowledge, but you might not need that for every part.
This page was last updated July 18, 2015.