>Sure you can. There are only so many eye charts in use. It's possible to memorize them.
No, you can't. Sure, you can memorize the optometrists' eye charts now, but that's because they're not expecting anyone to try to cheat, and just use some printed charts. Why would they expect someone with ill intentions? You're paying them to help you see optimally.
However, at the DMV, they absolutely can test you properly, because their machines (at least the last one I used a couple years ago) can change all the letters around however they want, and presumably every test is different (within the maximum number of combinations, which is surely too high to memorize). They're actually expecting people to try to cheat there, so they don't just use a single printed wall chart, they have a special device you stick your head in.