Check connectionstrings.com:
Database mirroring
If you connect with ADO.NET or the SQL Native Client to a database that is being mirrored, your application can take advantage of the drivers ability to automatically redirect connections when a database mirroring failover occurs. You must specify the initial principal server and database in the connection string and the failover partner server.
Data Source=myServerAddress;Failover Partner=myMirrorServerAddress;Initial
Catalog=myDataBase;Integrated Security=True;
There is ofcourse many other ways to write the connection string using database mirroring, this is just one example pointing out the failover functionality. You can combine this with the other connection strings options available.