Final answer:
The oculomotor nerve (cranial nerve III) controls the contraction of the circular smooth muscle of the iris, resulting in constriction of the pupil(option c).
Step-by-step explanation:
The cranial nerve that controls the contraction of the circular smooth muscle of the iris is the c) oculomotor nerve (cranial nerve III).
According to the information provided, the parasympathetic fibers within the oculomotor nerve terminate in the ciliary ganglion, located in the posterior orbit. The postganglionic parasympathetic fibers then project to the smooth muscle of the iris to control pupillary size. When the parasympathetic fibers release acetylcholine onto the circular fibers of the iris, it causes constriction of the pupil.