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"Depth of an image" as you call it, is usually referred to as "depth of field". This is purely a function of the physical aperture size used at the moment the picture is taken at a given distance, and is not limited to digital cameras. However, if your question is more about the spatial relationships between objects in the scene, this is called "perspective" and is controlled by the distance from the object to the observer. Contrary to what some people believe, focal length does not control or distort perspective (although short focal lengths can introduce linear distortion).

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Q: How does the lens on a digital camera change the apparent depth of an image?
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