In my world, I have ''classic'' knights but with helmets that have transparent visors which are strong enough to protect from arrows.
So which material available in medieval times could withstand an arrow shot to the face while being transparent to allow for better vision?
Or is there any such modern meterial which could be replicated with medieval technology?
This is not possible, medieval glass was primitive and expensive, it was not very clear to see through and would shatter into sharp shards when struck.
We were only able to change the dangerous shattering with the addition of plastics which involved a whole new level of technology.
The closest thing would be a wire mesh that in theory could block attacks while still allowing you to see out through it. Making the wire mesh strong enough to be useful would still be challenging though.
Medieval technology might not allow for direct "arrow-proof-glass", but what about periscope helmet?
Since arrows travel in approximately straight lines and cannot follow curves and bends, a helmet with an indirect visor, using mirrors, could prove useful. This idea basically comes from existing inventions like periscope glasses, periscope rifles/cameras and trench periscopes.
Proper silvered-glass mirrors did not exist yet, but simple glass mirrors did exist.
Example of a WW1 trench periscope, imagine a tiny version of this mounted on a helmet. There will not be a direct line in which an arrow can hit a knight directly in the eye.
But there are some disadvantages:
Side note: Bascinet helmets have incredible small eye-slits, I know they are not made from glass and are far from perfect when it comes to vision, but maybe worth checking out?
There are 2 naturally occurring materials which can - under the right circumstances - possess both the toughness and transparency to be viable: Moissanite (a.k.a. Silicon Carbide) and Corundum (a.k.a. Ruby and Sapphire). Unfortunately, this hardness makes them hard to work to a suitable thickness/shape - they at 9 and 9.5 on the Mohs scale (for comparison, Diamond is 10 and Quartz, mentioned by nzaman, is 7), and finding large enough examples to use would both be very hard and absurdly expensive.
So, handwaving time! * Jazz Hands *
If you accept the theory that the Baghdad Battery is a pre-medieval Galvanic Cell, then you open up the possibilty of creating artificial Sapphire via the Verneuil process, using Oxyhydrogen produced by electrolysis of water.
This allows you to have a heavily ahead-of-their-time alchemist-cum-jeweller who is creating artificial sheets of Sapphire, and then shaping them (with grit from previous attempts?) to form inserts that slot into the eyes slits on a metal helmet. They can also sell the offcuts to make money, since you probably only need a pair of 1" by 2" (by 0.5"?) lenses per helmet
The best you could do is quartz crystal, but that would shatter if hit directly. But then with a properly designed visor, your eye slits need not be big enough to be a feasible target for arrows, but then you wouldn't need a glass visor in the first place.
Polished horn is pretty rugged and flexible. Some forms are translucent to clear. Reinforce that with a mesh or something akin and you bring new meaning to a horned helm.
A bigger concern to me is getting enough air. An open face or mesh is less protective but has no such difficulty. Vigorous activity requires masses of air. If you don't account for that required exchange, people will run away from them and then counterattack when the shock troopers all have the vapours. That's just embarrassing.
(Terribly curious why you want this detail, I must confess.)
In contrast to other answers, I suggest that it is entirely possible to construct a visor such as you want - just not very practical.
As has been noted, medieval glass wasn't very transparent. If you can get some bright lad to come up with a technique for producing clear glass, the the solution is straightforward: make the glass thick. Enclose it in a housing of steel of even moderate thickness, and an arrow strike won't penetrate it. Put it this way: glass is nothing more than quartz, for all intents and purposes - in other words, rock. Punching a hole in a half-inch of rock is simply not something an arrow is going to do. In addition, unless the arrow strikes perpendicular to the face of the glass plate it's going to want to skip off. Modern bullet-proof materials are intended to handle bullets, and bullets have a great deal more energy and (importantly) brisance than arrows.
That doesn't mean that the result would be entirely practical. A single arrow strike in the visor would probably do enough damage to the surface to render the wearer effectively blind, and the long-term effects of being effectively blind on a battlefield would not seem to be much better than getting an arrow in the face. To handle this problem requires something like optical sapphire, and that is not in the cards for the time period you want.
Your knights could use some sort of lacquer- or resin-based visors. While not quite as durable or thin as metal, a curved shape could be enough to repel arrow glances, and any direct hits would likely just get stuck.
These visors would likely be fairly thick, and while transparent, would probably be both dimmer and distort images a little. There would also be the problem that such a visor would accumulate damage, making seeing harder.
Medieval glass may not have been very transparent, but there are many examples of Roman glass that were. It would probably not be beyond the means for a medieval knight to acquire Roman glass artifacts, or pieces of them, and reuse the glass. Glassblowers could rework it with steel wire, to make a reinforced glass. It probably still wouldn't be a good idea, and would be quite heavy. But it's a starting point.
Mediaeval glass could be made transparent enough for this purpose. To toughen the glass, they would need to heat the lenses to red heat and then blast both faces with air until cool. They would certainly know that quenching in oil or water makes glass resistant to breakage if it survived the thermal shock. So with the technology available at the time it would have been certainly possible. The lenses could also have been laminated, as already proposed, with resins, mica, etc.
