Final answer:
The convergence and accommodation reflexes are controlled by the oculomotor nerve (CN III), coordinating eye movement for convergence and lens shape for focusing.
Step-by-step explanation:
The cranial nerves responsible for convergence and accommodation reflexes are crucial in adjusting the visual focus to view nearby objects. The medial rectus muscles, which allow the eyes to converge, are controlled by somatic motor fibers of the oculomotor nerve (CN III).
Accommodation, the change in the shape of the lens, is managed by parasympathetic fibers of the same cranial nerve. Together, these actions form the accommodation-convergence reflex, which maintains focus on objects as they draw near.