Learn Spanish (Latin America): Capaz que necesito dilatar tu pupila.

While capaz does mean "capable," the phrase capaz que is a very common colloquial expression in Latin America meaning "maybe," "might," or "it's possible that." In this sentence, it works just like a lo mejor or tal vez.

Since capaz que expresses possibility ("I might need"), why is necesito in the indicative mood rather than the subjunctive?

While phrases expressing doubt like es posible que or puede que usually force you to use the subjunctive, capaz que is an exception in everyday speech. Just like a lo mejor, it is frequently followed by the indicative mood. You could use the subjunctive (capaz que necesite), but the indicative (necesito) is extremely common and perfectly natural here.

Why does the speaker use the possessive tu pupila instead of the definite article la pupila for a body part?

You probably learned that Spanish usually uses the definite article for body parts (e.g., me duele la cabeza). However, when someone else (like a doctor) is performing a direct action on your body, and they aren't using an indirect object pronoun (like te) to show who is affected, they will often use the possessive adjective (tu) to make it completely clear whose body part they are examining.

Does only mean "to dilate" in a medical or physical sense?