Mirrors are much older than vampires. Early mirrors have been dated back as far as 6,000 BC, and the modern idea of a vampire is quite young by comparison, most heavily influenced by the advent of Dracula.
Mirrors themselves carry a great deal of superstition, the most common myth being that breaking a mirror will result in seven years of bad luck. This ties to a curious belief from ancient Rome, in which it was thought it took seven years for a wounded soul to renew itself. Mirrors were long believed to be a reflection of the soul, rather than the physical body, so it became a natural assumption that the undead would bear no reflections.
Of course, not everyone plays by these rules. Anne Rice popularized the idea that a vampire should have a reflection, being that they have a physical body and we now have a more scientific understanding of mirrors. This wasn’t an original notion, of course, as many ancient vampires were believed to have reflections–and mirrors were used to repel them.
In China and in some parts of Africa, it’s believed that a mirror can repel evil. In some stories, this is due to the mirror portraying their true nature. It’s possible, then, that the idea of vampires having no reflection could permeate these cultures through a vampire’s abhorrence for mirrors. (After all, if a vampire is never near a mirror, does it still have a reflection? An age old quandary.)
Though the first mention of vampires lacking reflections takes place in Bram Stoker’s Dracula, it’s a logical step to take, regarding old beliefs about souls. The Slavic people of the middle ages believed a proper burial was required, or a person’s soul would be sullied or lost. If the body is up and walking after death, like with vampires, a proper burial would be impossible. If the belief at the time dictated a reflection was a vision of a person’s soul, it stands to reason vampires would be assumed to have no reflection.
Another popular belief is that vampires have no reflection because, through history, many fine mirrors were made with silver. Stories have long held silver as having powers and an association with purity: due to silver’s anti-microbial properties, it’s been used for cleansing in both medicine and mystic rituals. The purity is why it hurts corrupt creatures, such as vampires–and also contributes to why they don’t appear in photos, as film was developed with chemicals containing silver.
Then again, an old superstition claimed that a photograph would steal a person’s soul. If they didn’t have one to begin with, as it’s believed vampires don’t, why would they appear in photographs?