So you have a RAID1 comprised of two 500GB drives. In a RAID1, each individual drive is an exact copy of every other drive in the array. (That's why a RAID1 is also called a mirror.) One of the great benefits of RAID1 is that as long as at least one drive in the array is good, your array remains alive and accessible.
So your question is moot. In the case of a single drive failure in a 2-drive RAID1, your array is still good (albeit in a "degraded" state), so you don't have to do anything special to recover your data. You should still be able to access the data as you would normally do.
That said, whenever a drive in a RAID array fails, you really do need to replace that drive with a good drive, and then "resync" the array, as soon as possible. Most RAID appliances I'm aware of automatically initiate a "resync" whenever a new drive has replaced a failed one. Furthermore, during a resync, the array should remain alive and accessible (although probably slower).