Why is a camera lens usually kept fully open while a photographer is viewing and focusing?

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A camera lens is kept fully open while viewing and focusing to provide the brightest possible image on the viewing screen, which makes it easier for the photographer to assess sharpness and compose the shot.1

Because the depth of field—the range of distance within which objects appear acceptably sharp—increases as the lens aperture is stopped down (using higher f-numbers), using a smaller aperture during the focusing process would make the image on the screen significantly darker and harder to evaluate. Consequently, cameras with viewing screens, such as single-lens reflex models, utilize automatic-diaphragm systems that keep the lens wide open for viewing and focusing, only stopping it down to the chosen working aperture at the moment of exposure.21