Final answer:
The pupillary sphincter muscle, controlled by the parasympathetic nervous system via the Edinger-Westphal nucleus, regulates the pupil size by constricting to limit light entry in response to bright conditions.
Step-by-step explanation:
The pupillary sphincter muscle controls the size of the pupil, making option 1, "Controls the size of the pupil", the correct answer to the question. The Edinger-Westphal nucleus gives rise to preganglionic parasympathetic fibers that travel through CN III (oculomotor nerve) to the ciliary ganglion, then postganglionic fibers project to the iris. When these postganglionic fibers release acetylcholine onto the circular fibers of the iris, the pupillary sphincter muscle contracts, resulting in the constriction of the pupil, which reduces the amount of light entering the eye. This is part of the pupillary light response, which is a homeostatic mechanism to protect the retina from excessive light and to improve the visual acuity depending on the light conditions.