CN III parasympathetic fibers constrict the pupil and accommodate the lens for near vision. The parasympathetic fibers of CN III, also known as the oculomotor nerve, innervate the sphincter pupillae muscle in the iris, causing it to contract and constrict the pupil. This constriction allows less light to enter the eye, thus protecting the retina from excessive light exposure. Additionally, these fibers also innervate the ciliary muscle, which controls the shape of the lens. When the parasympathetic fibers are activated, they cause the ciliary muscle to contract, allowing the lens to become more rounded, which facilitates near vision.