1998 Ford Escort Alternator light

My Alt light started to come on very faintly at first. I checked the battery and it needed to be charged which lead me to beleive that the Alt was bad. I took it in to have it checked and confirmed that it wasn't charging. I replaced the Alt. Now when the car is idleing light is off. The faster the car goes with foot on gas pedal the brighter the light gets and then goes off when foot is removed from gas pedal. What else should I be looking for to correct this problem. I presently have a new battery, and Alternator.