Breakdown of Мы засмотрелись на обоих актёров.
мы
we
на
on, at / by (transport) / to (a place) / to (in answer to)
актёр
actor
оба
both (m/n)
Questions & Answers about Мы засмотрелись на обоих актёров.
How do the за- prefix and -ся postfix change the meaning of смотреть in this sentence?
This specific combination of prefix and postfix (за-...-ся) is used to show that the subject got completely absorbed, distracted, or carried away by an action. Here, the base verb смотреть (to look or watch) becomes засмотреться (to get lost in watching, to stare transfixed).
Why do we use the preposition на here instead of another construction?
Even with the added prefix and postfix, засмотреться keeps the same grammatical requirements as its root verb, смотреть. Just as you say смотреть на + accusative (to look at something), you use the exact same на + accusative structure for getting carried away looking at something.
Why is the word for "both" spelled обоих here instead of оба?
оба is the nominative form for masculine or mixed-gender pairs. Because it follows the preposition на (which requires the accusative case here), and it modifies living people, the accusative form must match the genitive form. The genitive/animate accusative of оба is обоих.
Wait, if обоих актёров has genitive endings, is it actually in the genitive case?
No, it is technically in the accusative case. Because актёры (actors) are living beings, this triggers the Russian animacy rule. For plural animate nouns and their modifiers, the accusative case endings perfectly mirror the genitive case endings.