Chances are you damaged the LCD, which contains the backlight. iPads are heavy and a drop from that height can inflict a lot of damage and the LCD is actually pretty fragile. The other possibility is that the backlight driver circuit was damaged but the first thing to try is a new LCD.
Unfortunately, replacement screens (the LCD and digitizer are fused together on the Air 2) are hugely [product|IF276-000-9|expensive] right now so I don't recommend you order one just to find out. Your best bet is to bring it to a shop that has one in stock so they can try it.