After glass mirrors were introduced, it was the Ancient Romans who intoduced the broken mirror as a sign of bad luck. They put an idea forward that a person's health changes in cycles of seven years. Therefore, if a person ever broke a mirror, that person would recieve seven years bad health and misfortune.
There is a theory that you can do penance to counteract the bad luck of a broken mirror. The rituals that are involved, include grinding the broken mirror to dust, to remove all possibility of any refection remaining. Some believe burying the broken mirror by the light of a full moon under a tree will also work. African slaves in the USA would place the broken pieces of mirror in the river that flowed south.