Final answer:
the type of theater wherein the spectators participate through the imagination while separated from the action is called invisible theater.
Step-by-step explanation:
The type of theater wherein spectators engage with the performance through their imagination while being physically separated from the action is referred to as proscenium arch theater, which is not mentioned explicitly in the provided reference texts. However, based on the descriptions given, the term that could be closest to the definition, although not perfect, is 'invisible theatre'. Invisible theatre involves actors performing in public spaces, presenting real-life scenarios without the audience knowing they are part of a performance. While not a complete match, it involves spectators being unaware and thus passively participating through observation alone.
Theatre is a performing art that utilizes the collective talent of actors, directors, designers, and more to provoke emotional responses and engage the audience's imagination. It can be observed from the provided information that the theater experience aims to create a believable world on stage, which calls for an audience's imaginative participation, albeit usually within a physical space designed for such experiences. When a performance is successful in engaging the audience, they are drawn into the narrative, momentarily setting aside the reality of watching a staged fiction.