Final answer:
A lesion of the right trochlear nucleus will cause weakness in the left superior oblique muscle. The right trochlear nucleus innervates the muscle that controls the movement of the left eye, leading to deficits in eye movement such as difficulty looking downwards.
Step-by-step explanation:
A lesion of the right trochlear nucleus will cause weakness in the left superior oblique muscle, which is innervated by the trochlear nerve (cranial nerve IV). The trochlear nerve is unique because it innervates a muscle on the contralateral side from its nucleus. Therefore, a lesion in the right trochlear nucleus affects the muscle that moves the left eye.
The trochlear nerve is responsible for the movement of the eye downwards and outwards through the action of the superior oblique muscle. Damage to this nerve or its nucleus can lead to double vision and difficulty with eye movements, especially when the affected individual tries to look down, such as when going down stairs.
In comparison to the oculomotor nerve, which is discussed in the information provided, the oculomotor nerve (cranial nerve III) innervates most of the eye muscles and is involved in pupil constriction through the Edinger-Westphal nucleus. Damage to the oculomotor nerve would result in different symptoms, such as ptosis (drooping of the eyelid), dilation of the pupil, and eye turning outward and downward as well as potential loss of the pupillary light reflex, depending on the extent and location of the damage.