The minimum height of a wall mirror in which you can view your entire body is half

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The minimum height of a wall mirror in which you can view your entire body is half your height, with the distance from the floor to the bottom of the mirror equal to half the distance between your eyes and feet. This relationship between mirror height/position and object height does not hold for objects that are far behind you, however. How large (height, width, or both) a reflecting surface is needed in order for you to see the entire image of a large distant object-a tree, say? (What quantity is different when you view your own image as opposed to when you view the image of a distant object?)

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