The story goes like this: according to Snopes, mirrors held significance back in the day not just as a way to more accurately pinch your own zits into submission, but as a "portal to the soul." Vague? Yes, but ominous nonetheless. The idea was that damaging a mirror could also damage the spirit of the person reflected therein, with more in-depth superstitions claiming that the bruised essence of the victim would no longer be able to effectively ward off incoming threats of a supernatural nature.
As for the "seven years" part, that likely comes to us courtesy of ancient Romans, who held the belief that "life renewed itself every seven years." When a soul was damaged, it would take an entire life cycle to undo the harm.
Never fear, though, as there are a number of ways to combat your otherwise pessimistically cemented destiny. Traditionally, the seven year sentence can be commuted by throwing salt over your shoulder, burning the broken shards and burying them, or putting the fragmented mirror bits into a running river. You could also always just buy another mirror, but that's less about beating fate and more about making sure you look presentable.
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