ἐννενόηκας οὖν ὅτι τοῦ ἐμβλέποντος εἰς τὸν ὀφθαλμὸν τὸ πρόσωπον ἐμφαίνεται ἐν τῇ τοῦ καταντικρὺ ὄψει ὥσπερ ἐν κατόπτρῳ, ὃ δὴ καὶ
κόρην καλοῦμεν, εἴδωλον ὄν τι τοῦ ἐμβλέποντος;
I have enjoyed very much explaining the Greek and Latin roots of medical terminology this semester, and was delighted to learn a new bit of Greek vocabulary this week. I thought it was curious that the word κόρη appeared in medical terminology for the "pupil" of the eye. There is no lack of strange usage in this field, but I couldn't make the connection no matter how hard I stretched. The textbook only informed us that this particular root for "pupil" comes from the Greek word for "girl", without any sort of explanation. One of my students made the clever, but incorrect, suggestion that it was the "core" of the eye.
The answer was spelled out clearly for me in the third LSJ entry: "pupil of the eye, because a little image appears therein". This usage must derive from the previous entry, in which we learn that the word was also used of "dolls" and "small votive images". The most informative passage is the one I've cited above, placed in the mouth of Socrates by Plato in Alcibiades.1.133a, in which he says: "Have you considered that the face of someone observing the eye appears in the eyeball of the one opposite him just as in a mirror, and which we call a pupil, an image of the observer?" Socrates goes on to claim that, just as the eye must look into the eye to see itself, so must the soul look into the soul if it wishes to see itself, and other things like that.
The word κόρη is also used of: "the long sleeve reaching over the hand" (I'm not sure what this means yet, see X.HG.2.1.8); "the Attic drachma", because it had the head of Athena on it; as a synonym for ὑπέρεικον, or St. John's Wort (beats me: see Hp.ap.Gal.19.113); and, finally, in architectural language for "female figures as supports", or Caryatids.
The word pupil itself seems to come through Old French from Latin
pupilla, a diminutive form of
pupa, "girl", although according to Lewis's dictionary, it was the form
pupula that was used in Latin for the pupil of the eye. (I don't have the OLD at hand.) I imagine that this Latin usage is based on a Greek analogy.
For an English curiosity, see the obsolete term "baby" in OED for "small image of oneself in another's pupil", which manifested itself in a 17th c. expression "to look babies", meaning to stare lovingly into another's eyes. Fun.