**Core Concept**
The ophthalmic artery is a crucial branch of the internal carotid artery responsible for supplying blood to the eyeball, optic nerve, and surrounding structures. It arises from the internal carotid artery near the optic canal and enters the orbit through the optic canal.

**Why the Correct Answer is Right**
The ophthalmic artery supplies the eye through its various branches, including the central retinal artery, which runs along the optic nerve and supplies the retina. The ophthalmic artery also gives rise to the anterior ciliary arteries, which supply the iris, ciliary body, and choroid. Additionally, the ophthalmic artery provides branches to the lacrimal gland, extraocular muscles, and the conjunctiva. The ophthalmic artery's supply is essential for maintaining the function and integrity of the eye.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the ophthalmic artery is not a branch of the external carotid artery. The external carotid artery primarily supplies blood to the face and scalp.
* **Option B:** This option is incorrect because the posterior ciliary arteries are actually branches of the short posterior ciliary artery, which in turn arises from the ophthalmic artery. However, they do not arise directly from the ophthalmic artery.
* **Option C:** This option is incorrect because the central retinal artery is a branch of the ophthalmic artery, not the posterior ciliary artery. The central retinal artery runs along the optic nerve and supplies the retina.

**Clinical Pearl / High-Yield Fact**
The ophthalmic artery is a critical structure in ophthalmology, and its branches supply the eye with essential blood flow. Knowledge of the ophthalmic artery's anatomy and branches is crucial for diagnosing and managing eye-related conditions.

**Correct Answer:**