I have seen the X-Men films, but have not really been a fan of the comic books.
I have always wondered if Cyclops just bandaged his eyes permanently growing up, and how he came to realise that ruby controls his "optic portals to another dimension".
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Origin 1: Scott Summers suffers traumatic brain injury as a child when he and his brother, Alex, parachute from a plane that is crashing. He uses his mutant power to break his fall and is injured. His mutant power later manifests randomly when he gets older and after causing an accident and nearly getting mobbed to death, he escapes, blind (powers were sporadic) but eventually he cannot even open his eyes.
He is rescued and becomes a ward of Charles Xavier. He is also the first of the X-men. It was Charles who figures out the resonance with ruby-quartz and creates a visor and later sunglasses to control Scott's power. Part of Xavier's genius (along with Moira McTaggart) was learning and understanding about mutant abilities.
In Origin 2: Everything starts the same but this time when he is put into an orphanage he is studied by the doctor Nathan Matthews (Mister Sinister) attempting to learn about his mutation. When Scott's power manifests after having severe headaches (and blowing the roof off the place) Matthews develops the ruby glasses he will use for the rest of his life.
Marvel has always hinted at giving Scott some level of control but never commits to it for very long, possibly because it is the visor and the lack of control which makes the underlying psychology of the character so compelling. Cyclops is a man whose power and responsibility to the Mutant Movement is something that requires precision and vision, both which are part of the use of his visor to control his power.
After becoming one of the Phoenix Five, Scott's optic blast's energy output was increased enough to stagger the demon-god Dormammu.
It also became more uncontrollable and Scott would go back to wearing his visor to control his power once more. His blast would display its more powerful state by having curved energy displays.
It's been a while since I've read the comics, and lord knows it's probably been retconned a few times, but he did have ruby quartz glasses as a teenager, which you see briefly during X-men Origins: Wolverine. It truth, it's not his glasses that control his mutant ability, as it neutralizes it. Everytime he blasts somebody with his optical beam, he is actually adjusting a small bar that opens up his visor to let a beam pass. It is mentioned in the comics that Cyclops is a master at accuracy; that he could even unlock a locked keyhole for a door with precision. He can change the opening for his visor to a very fine-tuned laser-like beam, to a full-on blast. I don't know just how powerful a full-on blast of his happens to be, but it has been suggested and noted the Scott Summers is top-tiered in terms of power.