Step 1: Understand what "allergy to tubercular bacilli" means in the eye.
This phrase points to a hypersensitivity reaction, meaning the eye reacts to tuberculoprotein (antigens from the TB bacillus) rather than the bacillus directly invading the eye tissue.
Step 2: Recall phlyctenular conjunctivitis.
Phlyctenular conjunctivitis (or keratoconjunctivitis) is a delayed type IV hypersensitivity reaction to bacterial antigens, most classically tuberculoprotein, though it can also follow staphylococcal disease. It shows up as small, tender, pink or grey nodules (phlyctens) at the limbus, with redness, photophobia, watering and lid spasm. It is the textbook example of an ocular allergic response to TB.
Step 3: Rule out Koeppe's nodules.
Koeppe's nodules are small white deposits at the pupillary margin of the iris, seen in granulomatous uveitis. They reflect direct granulomatous inflammation in the eye, not a hypersensitivity type reaction, and are not the classic allergic TB eye sign.
Step 4: Rule out posterior scleritis.
Posterior scleritis is a rare, painful inflammation of the sclera that can be linked to autoimmune disease or, less often, infection including TB, but it is not described as a hypersensitivity/allergic phenomenon and is far less common than phlyctenular disease.
Step 5: Rule out optic neuritis.
Optic neuritis can rarely complicate TB, usually from direct spread or drug toxicity (ethambutol), but again it is not the classic allergic manifestation.
Step 6: Final answer.
Phlyctenular conjunctivitis is the well known hypersensitivity reaction of the eye to tubercular antigens.
\[ \boxed{\text{Phlyctenular conjunctivitis}} \]