I have to be on the computer for work for most of my day. is there an eye exercise that i can do very quickly to alleviate the strain?

Yes: Looking off into the distance may relax the ciliary muscles, which can spasm during extensive computer use. A study in japan also indicated that warm compresses applied to the eyelids for a few minutes also reduced computer-related fatigue. Low blink rates during computer use can result in dry eyes, so application of artifical tears may also be helpful.

Adjust computer dist: Taking a "vision" break every 30 minutes by staring off at a distance helps. So does changing the distance the monitor is from you every so often. Be sure to use artificial tears regularly if you feel a burning sensation. Most importantly, change what you are focusing on regularly (screen, desk, looking out the window, etc.).