C5 - This is a carry over from another one of your threads, I thought that I'd try to answer it on the other thread but thought better of it.
scattergunner - If you've followed this thread over from the other thread, nice try but you missed the mark.
Daa pretty much hit the technical side of things. I'd like to make it simple.
An Adjustable Objective (AO) in the long run has nothing to do with the relative power or power setting of a given scope. You can find this feature on several tactical scopes that range in powers as low as 6x but in general you will not find AO on most scopes until the high end power reaches about 12x. Most lower powered scopes will not have an AO adjustment.
So what is AO. Have you ever looked into a scope and noticed that the cross hairs will jump around when you move your head around slightly on the stock while looking in your scope? If you have this is called parallax, the cross hairs are not opticly on the same plain as your target. Difficult concept I know, the same concept works for a survey instrument. Bacicly inaccuracies occure due to improper parallax adjustment. Properly adjusted cross hairs will not move on your target while moving your head slightly on the stock if parallax is adjusted properly.
Now for some of what DAA spoke about. Various scope manufacturers in non-AO scopes adjust to a parallax free conditions at certain distances, most center fire rifle scopes are set at 100 yards or a little more but never more than 200 yards (rim fire scopes are around 50 yards). This is the distance where most of us shoot. With very little variation this setting works very well especially if you have really good consistent mounting technique. The big bennifit in this type of scope is simplicity, you simply can't have youe scope set wrong.
Well then why a parallax adjustment?
It can be assumed that the higher powered scopes will be used at extended range where accuracy is much more important. In this case a parallax adjustment is important. Lots and lots of people think that a AO adjustment is there for to focus the scope and indeed you will find that focus is part of the equation, but the most important part of the equation is adjusting parallax out of your scope. As a matter of face your scope may not be at its sharpest image adjustment when the parallax is properly adjusted. Parallax is important for pin point accurate long range shooting. Now remove the bench from the equation and back track a little, off the bench and in the field it is the focusing factor that will get you in trouble most of the time with an AO scope.
How?
You are at the bench, the scope poweer is set at 14x, you are focused (and parallax free) on that 300 yard target and things are going better than expected so you jump up and run out to the field for a little calling. You sit down and absolutely fool a coyote almost into your lap, a 20 yard dead coyote so you draw down on the coyote to shoot but instead of the coyote you see nothing but hair, lots and lots of very very fuzzy hair, you have absolutely no idea if you are looking at your coyote or a dead tree. Then comes in the "Fiddle Factor" that we've all talked about. You've got to fiddle with your scope, not only turn the power down to a reasonable level but to adjust the focus (AO) ring so you have a clue as to what your looking at. Too much fiddling around and the coyote wanders off laughing at you. For the vast majority of shooting situations out to ~250 yards parallax adjustment is unecessary therefore the AO feature on most coyote hunting scopes are unnecessary.