A terminology limited to point objects is introduced to distinguish between finite and infinite, transparent and opaque mirrors. A basic image-producing operator is defined, and its properties are examined in detail. An operational form of the basic operator is derived, two general definitions are presented, and a formal expression for the images of a system of plane mirrors is written. Some simple systems are analyzed in detail to illustrate the applications of the theory. Finally, indication is given of possible directions for future development of the subject, and of its relationship to existing mathematical theories.

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