Did you buy one of the new Macbook Airs or Macbook Pros that were released a few weeks ago and now you're wondering, "What do I do with the new Magsafe 2 port when I'm connected to my Apple Cinema Display??"
For those that don't know, Apple released the new Macbook lineup with a redesigned Magsafe port (called Magsafe 2) which is thinner and wider than the old port, presumably to accomodate the new thin design of the Macbook Pro with Retina Display that is much thinner as a whole than previous Macbooks.
That's cool and all, but now the new Macbooks (Airs included) aren't compatible with your old Magsafe adapters (including the one built into your Cinema Display), and that's not really cool.
So what's a brother to do?!?
Simple: buy a Magsafe to Magsafe 2 Converter. I know, I know, "One more thing I have to buy??" Yes, but it will solve your problem, and it's only $9.99 (plus shipping).
Actually, it's kinda tough to find on Apple's website because you instinctively want to search with the term "adapter" which only brings up the actual Magsafe Adapters. They are calling it a "Converter."
For your convenience, here's a link: http://store.apple.com/us/product/MD504ZM/A?n=notebook_power_adapters&fnode=MTY1NDEwMQ