Sight Recovery Time
Date: Winter 2013-2014
If you can blink faster than light would you see your eyes close? (If in front of a mirror)
You should be able to receive light reflected off your eyelids, even if you blink slower than or at the speed of light.
For example, if your eyes open 1 inch, and you are standing 10 inches away from the mirror, light reflected off your eyelids while they were closed has only gone 1 inch toward the mirror by the time your eyes are fully open. That light has to go another 9 inches toward the mirror, then another 10 back to your eyes, before you can "see" it. So your eyelids will be open in plenty of time.
The problem is, your eye can't see things that fast. There have been Air Force tests that show ability to see pictures flashed as short as 1/200th of a second, even if we call that 1 one thousandth of a second, that's a huge amount of time for light. In that 1/1000th of a second, standing 10 inches from the mirror, light could go from your face to the mirror and back to your face around 60,000 times, or you could have blinked with your light speed eyelids 600,000 times. The light from the one moment that your eye was closed, would get mixed in with light from nearly 600,000 other moments before and after when your eyelid was open, so unless your eyelid was super super bright, you probably wouldn't even notice any difference from the other 1/1000th second periods when your eye didn't close at all.
So it depends on what question you are asking. Can light reflected off your eyelids reflected off a mirror get to your eyes while they are open if you could blink fast enough? Yes, as long as you are far enough away from the mirror, you have plenty of time. Can you "see" or recognize that there was a period that your eyelids were closed, given that you blinked so fast? Probably not, unless you switched to some sort of bionic eye/camera, you probably couldn't isolate or identify that moment as being different from other moments that you are looking at your (unblinking) eye in the mirror.
P.S. There might be another question you are asking, that is, if you can blink fast enough, would you be able to close and open your eyes without any light reflecting off of it. I'm not a physicist, so I'll plead ignorant to any relativistic implications of faster than light eyelids, but using a physical world analogy, it seems that some light should reflect off. Imagine a highway with cars running at 60mph. Now imagine a Porsche at 120mph dragging a fence perpendicular to traffic flow across the highway and back. Unless the traffic is super light, there is very little chance that the Porsche can make it over and back without at least a few cars hitting the fence. (In this analogy, the cars would be light photons, and the fence would be your eyelid).
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Update: November 2011