Spectrophobia is a kind of specific phobia

Specific phobia

A specific phobia is a generic term for any kind of anxiety disorder that amounts to an unreasonable or irrational fear related to exposure to specific objects or situations...

involving a morbid fear of mirrors and one's own reflections.
Catoptrophobia ( form the word catoptric meaning using a mirror to focus light; from Greek word katoptrikos ) is the fear of mirrors. This phobia is distinct from Eisoptrophobia, which is the fear of your own reflection.

Causes

Generally, an individual that deals with Spectrophobia has been traumatized in an event where they believe they have seen or heard apparitions or ghosts. The individual could also become traumatized by horror films, television shows, or by nightmares.
This fear could be the result of a trauma involving mirrors. It could also be the result of the person’s superstitious fear of being watched through the mirror. It may be that the sufferer has low self-esteem related to their physical appearance and avoids seeing his or her own reflection, and therefore avoids mirrors ( that is not to say that the individual is necessarily afraid of their own reflection, just ashamed of it ). Hollywood movies relating the supernatural world with mirrors could be the cause of this fear in younger children especially.

Fear

Sufferers of catoptrophobia can fear the breaking of a mirror bringing extreme bad luck. They can fear the thought of something coming out of the mirror or seeing something inside the mirror besides their own reflection when looking directly at it. Others fear that it is a link to the supernatural world or a gateway into another world.

Treatment

As with most phobias this fear could be cured with therapy and / or medication. Relaxation techniques or support groups could also be effective.