Not a rule, I think, Mario, though the adjective 'new' should modify what you want it to modify, and here it is obviously 'pair', since the speaker already had an old pair, which was worn out or was an old prescription. The reason I say no rule, however, is that there is some variation in these pairs. You can have only one shoe from a pair of shoes, for instance, but you cannot have only one glass from a pair of glasses.
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