Step 1: Understand the two effects.
Mydriasis means widening of the pupil. Cycloplegia means paralysis of the ciliary muscle, which stops the eye from focusing near objects. Some drugs cause both, and some cause only one.
Step 2: Group the drugs by their action.
Atropine, homatropine, and tropicamide are all antimuscarinic drugs. They block the parasympathetic supply to the eye, which relaxes the sphincter pupillae (causing mydriasis) and also relaxes the ciliary muscle (causing cycloplegia). So all three give both effects together.
Step 3: Look at phenylephrine separately.
Phenylephrine is a direct acting sympathomimetic drug. It works on alpha-1 receptors in the dilator pupillae muscle and contracts it, which widens the pupil. It does not act on the ciliary muscle at all, so it does not affect accommodation or near focus.
Step 4: Apply this to the question.
The question wants a drug that dilates the pupil for a fundus exam but leaves accommodation intact, since the patient is a young adult who may still need to focus normally soon after the exam. Phenylephrine fits this need exactly, and its action also wears off faster than the antimuscarinics.
Step 5: Rule out the other options.
Atropine ointment has the longest duration, sometimes days, and gives strong cycloplegia, so it is not suited here. Homatropine and tropicamide are shorter acting antimuscarinics but still cause cycloplegia along with mydriasis, so they do not meet the mydriasis only requirement.
Final Answer:
Phenylephrine gives pure mydriasis without cycloplegia.
\[ \boxed{\text{Phenylephrine}} \]