pupil (n.2)
"center of the eye," early 15c. (in English in Latin form from late 14c.), from Old French pupille (14c.), from Latin pupilla, originally "little girl-doll," diminutive of pupa "girl; doll" (see pupil (n.1)), so called from the tiny image one sees of oneself reflected in the eye of another. Greek used the same word, kore (literally "girl;" see Kore), to mean both "doll" and "pupil of the eye;" and compare obsolete baby "small image of oneself in another's pupil" (1590s), source of 17c. colloquial expression to look babies "stare lovingly into another's eyes."
Self-knowledge can be obtained only by looking into the mind and virtue of the soul, which is the diviner part of a man, as we see our own image in another's eye. [Plato, "Alcibiades," I.133]
pupil (n.1)
"student," late 14c., originally "orphan child, ward," from Old French pupille (14c.) and directly from Latin pupillus (fem. pupilla) "orphan child, ward, minor," diminutive of pupus "boy" (fem. pupa "girl"), probably related to puer "child," probably from a suffixed form of PIE root *pau- (1) "few, little." Meaning "disciple, student" first recorded 1560s. Related: Pupillary.