Final answer:
The first branch of the internal carotid artery is the ophthalmic artery, which supplies blood to the eyes.
Step-by-step explanation:
The first branch of the internal carotid artery is the ophthalmic artery. This vital artery penetrates the cranium via the carotid canal and then goes through the carotid foramen, emerging into the skull through the foramen lacerum. On entering the base of the brain, the internal carotid artery gives rise to several branches, including the anterior cerebral artery, which supplies the frontal lobe, and the middle cerebral artery, which supplies the temporal and parietal lobes. The ophthalmic artery is the third major branch and is responsible for providing blood to the eyes.
It is interesting to note that the signaling from the baroreceptors and chemoreceptors in the carotid sinus of the internal carotid artery is essential for cardiovascular homeostasis.