The iris is not placed where it can control what part of the image is visible. It simply acts as a gate, letting less or more light through as needed. Your brain also adjusts how sensitive your rod and cone cells are to light, so the scene might not look brighter or darker even though the amount of light coming in has changed.
When the iris is opened, each rod or cone cell is able to either take more light from the same spot (wherever the image is in focus), or from a larger area around the spot (out of focus). When the iris is closed, the rods and cells gather less light from a smaller area. This is the same reason why adjusting the aperture on a lens will not only change how much light is captured, but also the depth of field (the region where objects are in focus).
Although each individual cell can gather more light, it still reports only one brightness value (and also color if it is a cone). So all of the light that each cell receives is averaged out (especially where the image is out of focus).
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