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Is it possible to measure the zoom in an android phone?
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I'm not sure precisely what you consider "zoom". Some android phones have some hardware that allows the change in the "focal length" of the optics similar to a zoom lens on an interchangable lens cameras (optical zoom). Some digital cameras also have "digital zoom" where they crop out the pixels in the middle and thow away the pixels around the edge. Back before digital cameras, photographers called this enlarging and cropping and was done in the darkroom when printing negatives onto paper.
There are various android operating system functions that can be used to determine what the properties of the camera are in an android phone and there are functions that control the various settings of the camera hardware that application software can make use of. If you aren't developing your own camera application for your phone, then whether this information is available through the camera application in use is determined by the software application you bought and are using.
If you want to determine what the combined effective focal length is, you can take a picture of a known sized object at a known distance and then measure the size of the object in the printed image. The reproduction ratio original size:reproduced size is the combination of the focal length of the camera lens and the equivalent focal length of the enlarger/printing process. Without knowing what the physical dimensions of the digital sensor in the phone are, the focal length of the camera lens can't be reverse engineered from these measurements.
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