Final answer:
The parasympathetic fibers that control pupillary constriction travel through the oculomotor nerve (CN 3) and innervate the smooth muscle of the iris to constrict pupils in the eyes.
Step-by-step explanation:
In the parasympathetic division of the autonomic nervous system, the preganglionic fibers that control pupillary constriction travel through the third cranial nerve, also known as the oculomotor nerve (CN 3). The parasympathetic fibers within CN 3 terminate in the ciliary ganglion, which is located in the posterior orbit. From there, the postganglionic parasympathetic fibers project to the smooth muscle of the iris to control pupillary size.
This means that when the parasympathetic system is activated, it stimulates the circular iris muscles to constrict the pupils in the eyes. This pupillary constriction reduces the amount of light entering the eyes.
For example, in response to a bright light, the sensory input from the optic nerve triggers the parasympathetic motor output of the oculomotor nerve. The preganglionic parasympathetic fibers stimulate the ciliary ganglion, which in turn activates the circular fibers of the iris to constrict the pupils and decrease the amount of light reaching the retina.