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How can I calculate the distance to an object of known size in a photo using scale (I do not have any camera lens info, and will likely need to perform this calculation several times on different objects in different photos)

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If you don't know the lens info, you can't tell. In the small angle approximation, an object at 4 km in a 400mm lens looks the same as the same object at 8 km in an 800 mm lens. The angular size is just $\frac {\text{size}}{\text{focal length}}$ in radians. If the angle isn't small, there are corrections, but you still can't tell the distance without some other information.

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