How could there be successful archers, some even riding on horses, with out needing glasses? Something like 4 billion people today need a prescription of some kind- what was the case in history? Did lots of people still need glasses but those that had good eyesight become the archers? Or were people just less blind back then? (It’s very possible I’m being dumb and there was some kind of ancient eye wear but it’s never depicted in ancient artwork that I have seen)
I disagree with /u/BarbariansProf 's assertion that there's no reason to think that eyesight problems were less prevalent in the ancient world. In fact, it has been well documented that the prevalence of myopia (nearsightedness) has steadily increased in frequency over the past several decades.
A pretty strong paper from Nature showed a distinct correlation between time spent outdoors in childhood and myopia. In fact, the American Academy of Ophthalmology recommends outdoor time in children to help prevent myopia.
Other studies have showed increased links of visual impairment associated with things like prematurity etc. Recall in the ancient world, it was pretty unlikely for a premature infant to survive, unlike today where we have improved infant survival rates drastically.
All in all, these point towards the conclusion that there would be significantly less risk factors present in the people of the ancient world to develop common visual impairments that affect many today.
There's no reason to think that the prevalence of eyesight problems was significantly different in the ancient world than it is today, People in antiquity may well have been less likely to have eyesight problems than people today, but having less than perfect eyesight was nevertheless not much of a problem for archers.
In war, archers and other missile-launching soldiers like slingers, javelineers, and stone-throwers rarely needed to hit such a small target at such a distance that they would have suffered from having imperfect eyesight. On the battlefield, missile weapons were typically deployed against large masses of opposing troops. As long as an archer could see where the enemy was grouped, even just as a dark blur across the field, they could see well enough to do their job. There was rarely any need for an archer to be able to distinguish an individudal at a distance.
Keep in mind also that arrows launched from a bow do not travel nearly as fast as a bullet fired from a modern firearm. Soldiers under arrow attack, unless it was from very close by, had time to see the arrows coming and to move, scatter, or take cover in response, so in most cases, there was no point in an archer trying to aim at an individual far away.
Edit: See samcobra's comment below and the linked article for better information about the effects of environment on eyesight. I appreciate the additional information and have amended my comment accordingly.