What does 'gave her an academic air' mean in the following sentence:
He opened the door without knocking, and there she was alone at her desk, absorbed, serious, with the new eyeglasses that gave her an academic air.
The part "academic air" means resemblance to an academic (i.e. someone whose profession is related to higher learning).
You might wonder why the sentence uses the expression " gave a (blank) air". I think it comes from a common expression in French. In French, the expression "has the air of X" means "seems like X".
So the part of the sentence"gave her an academic air" means "made her look like a professor".
Wearing glasses reputedly increases other people's first impressions of the wearer's IQ by about 10 points. In popular culture too, they are strongly associated with studious or nerdy individuals, especially children and teenagers (hence the academic air).
The glasses serve to validate her status as an "academic" by giving the impression of such upon another (he, in this case).