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According to the Dawes limit formula A=116/d where A is the maximum angle of resolution in arcsecs and d is the aperture diameter in millimetres.
Rearranging terms, d=116/A.
Assuming the components of alpha Centauri are separated by 20 arcsecs,
then d=116/20~=5.8 millimetres. As the pupil of the eye can dilate to 7mm at night for some, then it is theoretically possible under perfect seeing conditions but highly unlikely under normal conditions.
Of course, if she is seeing double for every star I would be suspicious!
Regards, Rob
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