Remember that bullets fly in an arc as they move from the muzzle to target, which means that at a given distance, your bullet will impact at a different point than your point of aim. The bullet will pass the point of aim at 2 points, once as it passes the sight line heading up (your initial zero crossing), and then again as the bullet drops after apogee (your zero sighting distance). This can be seen in the following chart.
Consider an AR-15 with iron sights and a carry handle mounted scope. The iron sight sits 2.65 inches above the center of the bore, and the scope sits 3.65 inches above the center of the bore. The point of impact using a 55grain bullet, zeroed at 225 yards for both scope and iron sight, compared to the point of aim is given on this chart: You will notice that when using the scope, the bullet 'starts' at -3.65 inches below the sight line. This is an inch lower than the sight line used with the iron sights. When you zero both sights at the same distance, what you have in effect done is set your rifle to fire at a slightly higher angle for the scope (when mounted higher than the iron sights). The bullet still hits at the same point at 225 yards, but will take a slightly different path to get there.
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