**Core Concept**
Membranous conjunctivitis is a type of conjunctivitis characterized by the formation of a membrane on the conjunctiva, typically due to a viral or bacterial infection. This membrane is composed of a thickened layer of conjunctival epithelium and is often accompanied by inflammation and discharge.

**Why the Correct Answer is Right**
The correct answer is associated with the location of the membrane in membranous conjunctivitis. In this condition, the membrane is typically found on the underside of the upper eyelid, specifically on the tarsal conjunctiva. This is because the tarsal conjunctiva is a thin membrane that covers the tarsal plate, a bony structure that provides support to the eyelid.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because the membrane is not typically found on the cornea in membranous conjunctivitis.
**Option B:** Incorrect because the membrane is not typically found on the sclera in membranous conjunctivitis.
**Option C:** Incorrect because the membrane is not typically found on the meibomian glands in membranous conjunctivitis.

**Clinical Pearl / High-Yield Fact**
The membrane in membranous conjunctivitis is often associated with a foreign body sensation and can cause significant discomfort and vision impairment. It is essential to differentiate membranous conjunctivitis from other types of conjunctivitis, such as vernal conjunctivitis, which can also present with a similar membrane.

**Correct Answer:** C. Tarsal conjunctiva.