The equivalent expression in many languages employs a preposition translated as “on” in most other contexts (e.g. “sur” in French). In English, however, the correct preposition is “in”:
The boy in the photo looks sad.
The boy on the photo looks sad.
The pattern is the same no matter what word we use for the visual media (e.g. image, photo, picture, drawing):
There are no trees in the picture.
There are no trees on the picture.
We only use “on” when we mean that something is on top of a physical object; for example “there's a cup on a photo” means that the cup lies on a photo. However, “on” can also be used when one thing is part of the top layer of another thing. This can be a little confusing for words like “postcard”. You would say:
There's a house on the postcard.
There’s a house in the postcard.
The reason is that a postcard is the piece of paper itself, not what's printed on it (unlike the word “picture”, which refers to the actual visual content). What you mean is in fact: “There's a house (in the picture that is) on the postcard.”
Similarly, if you saw a picture of a man drawn on an envelope, you wouldn't say that there's a man in an envelope, would you? The (picture of the) man is on the envelope.
A few more examples of correct usage:
The cat in the drawing is very realistic.
The cat on the drawing is very realistic.
She found a mistake in the image.
She found a mistake on the image.
The details in the painting are exquisite.
The details on the painting are exquisite
And a few examples of the words where the preposition “on” is appropriate:
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Jakub Marian