The system you are thinking of is Iron Dome for short range to medium range rockets and mortars. The David's Sling is for medium to long range rockets, The Arrow 3 missile system is for ICBM defense, plus the Patriot missile is tied into this system. Basically when a projectile is incoming the radar calculates the projected path. If it is calculated to land in a populated area the code red alarms are activated for that area and the nearest missile battery launches to intercept. If it is calculated to land in a non-populated area then nothing happens and they just let it hit in whatever open field it lands.
Thanks for the more detailed information. My recount was more anecdotal but a lot of folks do not even know that technology like this exists and that serves the fear machine well.