Step 1: DISCLAIMER AND HEALTH AND SAFETY
as always I'm not responsible for anything that happens to you or your possesions, should you choose to try this experiment.
Step 2: Materials
1. a dark room, with a mirror. (preferibly on the wall. doesn't have to be light tight. you should be able to just barely see. I found my bathroom to be perfect)
2. your eyes.
3. A powerful photographic flash. Note: a tiny little camera flash isn't going to work. I had to use one of my mom's professional camera-mount flashes to get this to work, and even then, it had to be set to the highest power level for it to be bright enough. you can try it with a regular flash, but if you want real results, you'll need a professional grade flash.
Step 3: The Experiment
make sure the flash is fully charged, and then set the flash off! STAY MOTIONLESS! because your eyes are acclimated to the darkness, and they just received an intense amount of light in such a short time, you'll literally loose your sight temporarily. about 1 second after setting the flash off, turn you body 90 degrees left or right of the mirror, and then stare into space...
Step 4: The Result
my guess is that, when you set the flash off, you see yourself in the mirror for a fraction of a second, and then you go blind, as your eyes try to re-acclimate. when you turn, because your eyes aren't acclimated, your brain defaults to the image you saw in the mirror because of the property our eyes have called persistance of vision.