I get double vision after being on the computer for so long. Is this normal?

No. You are probably straining your eyes too much. Appropriate computer glasses may help this. Regardless, this is a reason to see your eye doctor as the underlying cause may be much more serious.
It may be normal. Some people get double vision when they are fatigued. Not only can the person be fatigued, but the eyes can be as well. Staring at a computer for hours can cause a fatigue or eye "strain" that can cause double viison. Usually, double vision that goes away when you concentrate may be normal, but you should have your eyes examined to be sure.