**Core Concept**
The vidian nerve is a vital structure in the autonomic nervous system that plays a crucial role in regulating the parasympathetic innervation of the nasal mucosa. It is formed by the fusion of the greater petrosal nerve and the deep petrosal nerve, which convey preganglionic parasympathetic fibers from the facial nerve and postganglionic sympathetic fibers from the superior cervical ganglion, respectively.

**Why the Correct Answer is Right**
The nerve of the pterygoid canal, also known as the vidian nerve, is formed by the combination of the greater petrosal nerve and the deep petrosal nerve. The greater petrosal nerve arises from the geniculate ganglion of the facial nerve and carries preganglionic parasympathetic fibers that synapse in the pterygopalatine ganglion. The deep petrosal nerve, on the other hand, originates from the superior cervical ganglion and conveys postganglionic sympathetic fibers. These two nerves merge to form the vidian nerve, which passes through the pterygoid canal and reaches the nasal mucosa, where it regulates the secretion of mucus and the vasomotor tone.

**Why Each Wrong Option is Incorrect**
**Option A:** The mandibular nerve is a branch of the trigeminal nerve (cranial nerve V) and is responsible for sensory innervation of the lower face, motor innervation of the muscles of mastication, and some special sensory functions. It is not related to the formation of the vidian nerve.
**Option B:** The deep petrosal nerve is a component of the vidian nerve, but it is not the correct answer because it is only one of the two nerves that merge to form the vidian nerve.
**Option D:** The lesser petrosal nerve is a branch of the glossopharyngeal nerve (cranial nerve IX) that carries preganglionic parasympathetic fibers to the otic ganglion, which innervates the parotid gland. It is not related to the formation of the vidian nerve.

**Clinical Pearl / High-Yield Fact**
The vidian nerve plays a crucial role in the regulation of nasal secretions and vasomotor tone, and its dysfunction can lead to conditions such as atrophic rhinitis or vasomotor rhinitis. It is also an important landmark in surgical procedures involving the pterygopalatine fossa.

**✓ Correct Answer: C. Nerve of pterygoid canal**