Let us back up a bit and more fully define parallax as it applies to telescopic sights. The following is,as best as I remember) from a Wikipedia article:
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'Parallax problems result from the image from the objective not being coincident with the reticle. If the image is not coplanar with the reticle,that is the image of the objective is either in front of or behind the reticle), then putting your eye at different points behind the ocular causes the reticle crosshairs to appear to be at different points on the target. This optical effect causes parallax induced aiming errors that can make a telescopic sight user miss a small target at a distance for which the telescopic sight was not parallax adjusted.
To eliminate parallax induced aiming errors, telescopic sights can be equipped with a parallax compensation mechanism which basically consists of a movable optical element that enables the optical system to project the picture of objects at varying distances and the reticle crosshairs pictures together in exactly the same optical plane. There are two main methods to achieve this.
• By making the objective lens of the telescopic sight adjustable so the telescopic sight can compensate parallax errors. These models are often called AO or A/O models, for adjustable objective.
• By making an internal lens in the internal optical groups mounted somewhere in front of the reticle plane adjustable so the telescopic sight can compensate parallax errors. This method is technically more complicated to build, but generally more liked by parallax adjustable telescopic sight users—unlike AO models, which are read from the top, the sidewheel's setting can be read with minimal movement of the head. These models are often called side focus or sidewheel models.
Most telescopic sights lack parallax compensation because they can perform very acceptably without this refinement. Telescopic sights manufacturers adjust these scopes at a distance that best suits their intended usage. Typical standard factory parallax adjustment distances for hunting telescopic sights are 100 yd/m to make them suited for hunting shots that rarely exceed 300 yd/m. Some target and military style telescopic sights without parallax compensation may be adjusted to be parallax free at ranges up to 300 yd/m to make them better suited for aiming at longer ranges. Scopes for rimfires, shotguns, and muzzleloaders will have shorter parallax settings, commonly 50 yd/m for rimfire scopes and 100 yd/m for shotguns and muzzleloaders. Scopes for airguns are very often found with adjustable parallax, usually in the form of an adjustable objective, or AO. These may adjust down as far as 3 yards,2.74 m).
The reason why scopes intended for short range use are often equipped with parallax compensation is that at short range,and at high magnification) parallax errors become more noticeable. A typical scope objective has a focal length of 100 mm. An optical ideal 10x scope in this example has been perfectly parallax corrected at 1000 m and functions flawlessly at that distance. If the same scope is used at 100 m the target-picture would be projected,1000 m / 100 m) / 100 mm = 0.1 mm behind the reticle plain. At 10x magnification the error would be 10 * 0.1 mm = 1 mm at the ocular. If the same scope was used at 10 m the target-picture would be,1000 m / 10 m) / 100 mm = 1 mm projected behind the reticle plain. When 10x magnified the error would be 10 mm at the ocular.'
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The one thing that is hard to quantify is the potential aiming error due to parallax error. The magnitude of the angular error in the scope is primarily due to the axial difference between the image plane and the plane of the reticle. However the apparent error or change in POI relative to POA is due to the alignment of the shooters eye with the optical axis of the objective image and reticle center. For example, I have a scope with AO that I've tested, with the objective set for infinity the maximum parallax aiming error at 100 yards is a 2 MOA circle about the target POA,the locus/path of the cross hair center) as the eye is moved around.
There is a popular assumption that if the eye is perfectly centered on the exit pupil image there will not be a 'parallax' error. This is not correct. If the parallax is set for the wrong range, the parallax error still exists in the scope. The potential for an aiming error is still dependent on the eye position. The aiming error will be zero only if the eye position used to zero the scope is the same as that used for each shot on the target.
If you have a fixed power scope with either AO or side parallax adjusters, readjust for zero parallax,not for target focus) at each change of range. If you have a variable power scope with the zoom cell between the objective and the reticle,typical with '2nd focal plane' reticle variables in US) you should also readjust for zero parallax with changes in power.