Observing with 観る
観る means to look at something intentionally, to focus one’s attention on something.
In comparison, 見る is more passive and unconcious (such as casually watching television) whereas 観る is more active and aware, observing (such as carefully watching television).
Examples
Shall we go see a movie with 観る

After talking with her boyfriend in the hall, Futaba returns to her classroom and walks over to her friends.
- 双葉:
- 「この映画一緒に観に行かない?」
- “How about going to see this movie?”
- 悠里:
- 「え どの映画?」
- “Oh, which movie?”
See Also
Watching the news with 観る
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As Nishikata watches the news, his daughter sits down to watch.
- 西片:
- 「ちーはニュースも観るのかー。」
- “You watch the news too, huh, Chi?”
- ちー:
- 「テレビすきー。」
- “I like television.”