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In a typical concave mirror experiment, the “real” image can only be focused at a specific position, where the light rays meet. Yet, if I look at some stationary object behind me in a stationary concave mirror and move away from it, my eyes can always obtain an image of the object. How can that be possible?

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You do not need to stand at the theoretical distance where a real image is formed, because your eyes are an additional optical element focusing light on the retina. In the distance where a real image is formed, you wouldn't need the lens in your eyes at all, your retina would be enough to see a sharp image, because this is the distance where rays from the mirror overlap to form a sharp image. At all other distances the image isn't sharp, a canvas or your pure retina would receive a blurred image. So you need your eyes there to do the additional necessary focusing. The additional focusing power is different at any distance, but your eyes are very good in adapting (basically your lens is shaped by muscles resulting in a different focal length).

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