Turns out Ronald Reagan wasn't so crazy when purposed to build lasers that would shoot down Soviet missiles aimed at the U.S.Lockheed and Martin released a video of their High Energy Laser (HEL) called ADAM. In this video you will see a missile get launched and with in a second or two the ADAM finds, locks on, and blows up the missile.

 

Here is Lockheed and Martins video:

Here is a video of Reagan's SDI project (Star Wars):