When shooting pictures at very short distances, exposure

Chapter 6, Problem 68GP

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Problem 68GP

When shooting pictures at very short distances, exposure times must be increased because of the increased distance of the lens from the film for a focused image. (a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, ∞), given the same illumination and f-stop. (b) Show that if do is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.