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
アオハライド » Volume 12 » Page 42
からかい上手の(元)高木さん » Volume 1 » Page 113
Supplemental examples
俺物語!! » Volume 3 » Page 170