You cannot 'watch' a photograph, since it is not in motion. You could 'scrutinize' a photograph if you were a photography contest judge or a detective. And they both do that 'with much interest', which is far too formal a phrase to use to your sister.
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Mister MicawberIt is sometimes difficult to know when a non-native speaker is joking. 'Scrutinize' remains the wrong word choice here.But "examine" is not quite as odd.