At least one eye is required for shooting.
The ability to aim and judge when the rifle is pointed in the right direction is the first step in shooting. You could shoot a ten upside-down from a trapeze if your aim was on.
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This is how images are actually 'seen' by the eye. Light is refracted through the lens and projected on to the retina. The muscles in the eye can adjust the curvature of the lens to focus an image.
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The fovia at the very back of the eye is where you will see the clearest picture.
Your eye can only see the image really clearly for a few seconds before it needs relief, so time is of the essence.
Consistency is key in shooting! While relying heavily on muscles for a few shots is alright, after 4 hours of shooting your muscles get tired and do not work as consistently. This includes the many muscles in your eye. The object of tinkering with the sighting system is to reduce the strain on your eye so it can accurately judge good shots for longer.