Final answer:
Parasympathetic fibers that control pupillary size and lens shape modification travel through the oculomotor nerve (CN III) and release acetylcholine that affects the iris muscles.
Step-by-step explanation:
The parasympathetic fibers that innervate the muscles to modify the shape of the lens and control pupillary size travel through the oculomotor nerve, which is cranial nerve III. These fibers originate in the Edinger-Westphal nucleus in the midbrain, and after synapsing in the ciliary ganglion, the postganglionic fibers project to the smooth muscle of the iris.
The neurotransmitter released by the postganglionic parasympathetic neuron is acetylcholine, which stimulates the circular muscles of the iris, causing the pupils to constrict in response to bright light, thereby reducing the amount of light that hits the retina.
The parasympathetic fibers travel through the oculomotor nerve (CN III) to innervate the circular iris muscles in order to modify the shape of the lens, making them rounder. This helps with accommodation, which is the process of adjusting the lens to focus on objects at different distances.