In the play Measure for Measure Vincentio, the Duke of Vienna, leaves his city in the charge of a judge while he goes on a "diplomatic mission". It transpires that he has not, in fact, left the city at all but has disguised himself as a monk and remained to spy on the actions of his courtiers.
However, it has always bothered me that during the course of the play, the disguised Duke interacts with several characters who know him well. It seems to be stretching the bounds of credulity to believe that they would not recognize him in his relatively thin disguise. Yet none do.
This motif, of a disguised character interacting with people close to them without being recognized, recurs in other literature of the period.
Is this something audiences in Shakespeare's day would simply have accepted? If so, why? And if not, why was/is it not viewed as a problem with the narrative of the play?