Why put glasses on a catatonic patient?

Why put glasses on a catatonic patient? Well, the fact that the patient was admitted to hospital wearing the glasses might give you a clue. The glasses were only put back on because they accidentally fell off. They were her glasses and therefore you can safely assume that they were prescribed for her.

As far as the catatonic aspect goes, how do you know if, whether, or how much, sight that kind of patient has? The sight may well be perfect but the patient just can't communicate what they see. That was one of the main thrusts behind Dr. Sayer's theory - he "knew" that these people were alive inside, which was why he wanted to try and "awaken" them. They hadn't reacted to other stimuli, but the act of catching the tennis ball convinced him that there was something there.

It's possible that they left the glasses on a patient just because they arrived at the hospital like that, however like you say it would be pointless because the staff believed these people had no brain functions whatsoever, as is said by John Heard.

Let me tell you what I think: they just wrote a woman with glasses into the movie (a fictionalized version BASED on real events) so that they could use the glasses as a prop in certain scenes. It's a movie, not a documentary.

Same as you do with someone who doesn't speak your language, a mentally challenged person, a child who can't give consistent answers, a deaf/mute, etc.

You use a retinoscope, which shines a light through the pupil onto the retina. You're looking for a specific shape of the light; you add a quarter diopter at a time of either plus lenses for farsightedness, or minus lenses for nearsightedness, then you work out the direction and strength of any astigmatic correction needed.

That's also how you get started if someone comes in with no glasses or medical records from which to find a starting point.

If possible, you refine it with patient input whenever possible, but if you're good at your job you can get them very close to their best corrected visual acuity.