**Core Concept**
The transmission of pain sensations from the ethmoidal sinus involves the **trigeminal nerve**, which is responsible for conveying sensory information from the face, including pain, to the brain. The **ethmoidal sinus** is one of the paranasal sinuses located between the nasal cavity and the eye socket.

**Why the Correct Answer is Right**
The correct answer involves the **nasociliary branch** of the **ophthalmic division of the trigeminal nerve (V1)**, which carries sensory fibers from the ethmoidal sinus. This branch is specifically responsible for transmitting pain sensations from the ethmoidal sinus.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because it is not specifically associated with the transmission of pain from the ethmoidal sinus.
**Option B:** Incorrect as it is not directly related to the sensory innervation of the ethmoidal sinus.
**Option C:** Incorrect because, although it is a branch of the trigeminal nerve, it is not the specific branch responsible for the ethmoidal sinus.

**Clinical Pearl / High-Yield Fact**
It's crucial to remember that the trigeminal nerve has three main divisions (ophthalmic, maxillary, and mandibular), each responsible for different areas of the face, including the paranasal sinuses.

**Correct Answer:** D. Nasociliary branch of the ophthalmic division of the trigeminal nerve.