From Wikia, the explanation is slightly murky but better than nothing
The concept of using mirrors as an energy storage and transfer medium is frequently discussed in today's world of solar technology. In the episode "Duped", Artie describes the interaction of the disco ball and Lewis Carroll mirror as like the "shadows on a wall at Hiroshima." He is describing the common effect that resulted from the thermal rays of "Little Boy," the atomic bomb dropped on the city of Hiroshima, Japan. Pictures of the after effects show that when the bomb exploded, the rays encountered objects in their path, some human. The resulting collision of rays and objects left shadows on walls, steps, and roads much like photographs, displaying a shadowy imprint of the object encountered, sometimes human in shape.
And, from the mirror's Wikia entry:
What is known about the mirror's operation relates to interaction with other artifacts. When interacting with the Studio 54 Disco Ball, a process Artie calls "optical divagation" occurred. Artie further describes the process as "kind of like an optical flare after a photo flash." Although he later says he really doesn't know how the mirror works, he initially speculated that the blast from the disco ball "fritzed the mirror's primary reflective capacity and then it probably clipped part of Myka's psyche and fused it" in the mirror.