Musculus Sphincter Pupillae is a complex term referring to the circular muscle that controls the size of the pupil in the eye. However, there are several synonyms for this medical term that are easier to understand and use in layman's terms. Some of the synonyms used are the pupillary sphincter muscle, iris sphincter muscle, and circular muscle of the iris. The pupillary sphincter muscle is responsible for controlling the amount of light that enters the eye by dilating or constricting the pupil. The iris sphincter muscle is a simple term that refers to the contraction of the pupillary sphincter muscle during the process. The circular muscle of the iris is another term used that refers to the same muscle and its functions.