**Core Concept**
The facial nerve, also known as the seventh cranial nerve (CN VII), is a mixed nerve that has both motor and sensory functions. It is responsible for controlling the muscles of facial expression, taste sensation from the anterior two-thirds of the tongue, and the parasympathetic innervation of several organs in the head and neck.

**Why the Correct Answer is Right**
The greater petrosal nerve is the first branch of the facial nerve, arising from the geniculate ganglion. It is a preganglionic parasympathetic nerve that conveys fibers from the facial nerve to the pterygopalatine ganglion, where they synapse with postganglionic neurons that ultimately innervate the lacrimal gland and the mucous membranes of the nasal cavity and palate. The greater petrosal nerve is responsible for promoting tear production and mucous secretion.

**Why Each Wrong Option is Incorrect**
**Option A:** The nerve to the stapedius muscle is the second branch of the facial nerve, arising from the facial nerve distal to the geniculate ganglion. It is a motor nerve that innervates the stapedius muscle in the middle ear.
**Option B:** The chorda tympani nerve is the third branch of the facial nerve, also arising from the facial nerve distal to the geniculate ganglion. It is a mixed nerve that conveys taste fibers from the anterior two-thirds of the tongue and parasympathetic fibers that innervate the submandibular and sublingual glands.
**Option D:** The lesser petrosal nerve is not a branch of the facial nerve but rather a branch of the glossopharyngeal nerve (CN IX) that conveys preganglionic parasympathetic fibers to the otic ganglion, where they synapse with postganglionic neurons that innervate the parotid gland.

**Clinical Pearl / High-Yield Fact**
The greater petrosal nerve is an important branch of the facial nerve that plays a critical role in the parasympathetic innervation of several organs in the head and neck. Damage to this nerve can result in decreased tear production and mucous secretion, leading to symptoms such as dry eye and nasal congestion.

✓ Correct Answer: C. Greater petrosal nerve