Last rsync (version 3.0.9) was:
$ rsync -av --delete /home/. /auto/passport/home/. | tee -a ~/backup.log
...
sent 1001882570 bytes received 106527 bytes 1775002.83 bytes/sec
total size is 527398084971 speedup is 526.3

It took 10 minutes to scan the 500 MB partition (ext4). From the other posts, I guess the duration time is due to the number of files that is scanned by rsync.

What will happen if the laptop hard disk fail? Let's say the laptop harddisk is disk0 in the RAID-1 configuration. The external hard disk is disk1. The degraded RAID-1 is due to the presence of disk0, and the absence of disk1. If disk0 fails for some reason, can I put a new "empty" disk0 in the laptop and mirror disk1 to disk0? I am not sure how to do that with mdadm.

I used to do that: a scan using the find command to find modified directories, then using --exclude directives from rsync, I backup only the unchanged directories. At that time, I was also evaluating the size of the sub-directories to backup only less than 1 GB for each part. But the find search was still too long for my taste. At the end, the gain in time was very limited (if not longer than a full rsync).

Well, all my research work from the last 20 years, that makes some data, and you never know which data you need when you travel. So, when I change laptop, I copy all my data from the old disk to the new disk. That's why also I want to backup only the diff, and not spend my time scanning the disk to find these differences (which can be spread all over the disk).

OK. But you still scan the whole disk with a find command.