The answer is the first one: Optic, responsible for vision.
Explanation for each option:
Optic, responsible for vision: This is correct. The second cranial nerve is the optic nerve, which is responsible for transmitting visual information from the retina to the brain.
Facial, responsible for facial expressions and taste: This is incorrect. The facial nerve is the seventh cranial nerve and is responsible for controlling the muscles of facial expression and conveying taste sensations from the anterior two-thirds of the tongue.
Olfactory, responsible for smell: This is incorrect. The olfactory nerve is the first cranial nerve and is responsible for the sense of smell.
Trochlear, responsible for eye movement: This is incorrect. The trochlear nerve is the fourth cranial nerve and is responsible for controlling the superior oblique muscle, which is involved in eye movement.
Vestibulocochlear, responsible for hearing and balance: This is incorrect. The vestibulocochlear nerve is the eighth cranial nerve and is responsible for hearing and balance.
Summary:
The second cranial nerve is the optic nerve, and its primary function is vision.