Time machine oddity

I''ve just connected an external drive to the Air for the first time. As I was hoping, it immediately gave me the option to use the drive as the time machine backup. It now claims to be doing this. However, the mounted drive does not appear on my desktop........ Is this normal for a new 2011 Air?

 

Thanks for the quick response

Thank you thank you thank you. Must have been one of the things my White Macbook (supplied with leopard, upgraded to Snow Leopard then Lion) did by default.