Final answer:
The parasympathetic functions of the oculomotor nerve are to adjust lens shape for focusing and control pupil diameter for light regulation. This involves the Edinger-Westphal nucleus, ciliary ganglion, and the pupillary light response.
Step-by-step explanation:
The parasympathetic functions of the oculomotor nerve include the ability to adjust the shape of the lens for focusing (accommodation) and the diameter of the pupil to control the amount of light entering the eye (pupillary constriction). The parasympathetic nervous system is responsible for what is called the 'rest and digest' functions of the body. Specifically, the preganglionic parasympathetic fibers from the Edinger-Westphal nucleus within the oculomotor nerve innervate the ciliary ganglion in the posterior orbit from where the postganglionic fibers control the muscles responsible for constricting the pupil and changing the shape of the lens in the eye. These actions are part of a reflex known as the pupillary light response, which adjusts the pupil size in response to the amount of light that hits the retina.