pupil (n.)
The pupil of the eye is the dark opening in the middle of the iris. The word is the Latin pupilla, a little doll, a diminutive of pupa, girl or doll.12
It is named after what you see in it. Stand close enough to someone and there is a tiny figure of you in their eye, about doll-sized. Greek did the same thing with korē, girl, which meant both the doll and the pupil.1
The schoolchild comes from the same Latin root by another road. Pupillus and pupilla also meant an orphan or a minor in someone’s care, and the English pupil began as that legal sense before it meant anyone being taught.12
The doctor checked his pupils.