She studies part of the eye (5)

I believe the answer is:

pupil

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'part of the eye' is the definition.
('pupil' is part of 'eye')

I can't explain the remainder of the clue.

(Other definitions for pupil that I've seen before include "part of my anatomy" , "Learner at educational institution" , "Centre of iris, in the eye" , "One in the eye or in place of learning" , "Learner in the eye?" .)

I've seen this clue in the Sydney Morning Herald.

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