פירוש על עבודה זרה 57:10

The mirror shouldn’t be necessary in the public domain—everyone can see what is going on there. But in the private domain it is hard to see how a murderous barber would be stopped by a mirror. The answer tells us a bit about the history of mirrors. Only important people seem to have had them, and therefore, a Jew who has a mirror will look important enough for the non-Jew to be afraid to kill him.