Copied from Leupold's web site:
As the light rays traveling from the Leupold ScopeSmith Magnetic Boresighter (the Boresighter) to the objective lens of the scope are parallel to the bore of the firearm, the vertical or horizontal position of the Boresighter on the crown of a firearm barrel does not affect the scope settings necessary to get the first shot "on the paper" at a distance of 100 yards.
* Scope Alignment with the Bore of the Firearm
The purpose of any scope mount is to hold the scope used on the firearm in optically parallel alignment to the bore of that firearm. As there is always to be expected a certain amount of minor deviation from this parallel due to the configuration of receivers and other mechanical tolerances, scopes and some mounts are designed with adjustment mechanisms to correct this deviation.
There are also mounts, primarily intended for long range shooting, which are designed deliberately to bring the scope off parallel with the bore in order to allow the elevation adjustment dial of the scope to be set at a low extreme and thus allow for more elevation to be made available to compensate for large amounts of bullet drop at long distances. What must be remembered is that for getting "on the paper", the physical alignment of the scope main tube with the bore of the firearm is not as important as the optical alignment of the scope viewing direction with the bore of the firearm.
It is this optical alignment of the scope that is at the heart of the initial stages of sighting-in a scope and it is what the Boresighter does.
Once a shooter is "on the paper", the actual point of impact can be observed and minor adjustments can then be made to the direction of the scope's optical axis to hit the bull's eye.
* How the Boresighter Works in Conjunction with the Firearm
The Boresighter attaches to the crown of the muzzle of the firearm by means of a magnet. This magnet is designed to be perpendicular (at a 90º angle) to body of the Boresighter. It is assumed that the surface of the crown of the muzzle on the firearm is itself perpendicular to the bore of the firearm. It is important to be certain that the crown of the barrel is free of debris before attaching the Boresighter to it as such debris could alter the angle at which the Boresighter attaches to the crown.
Therefore, when the Boresighter is attached with the magnet to the crown of the firearm, the optical axis of the boresighter is assumed to be in parallel alignment with the bore of the firearm.
* How the Boresighter Works in Conjunction with the Scope
The target grid of the Boresighter is illuminated by ambient light from behind through a translucent white panel, thus presenting its image through the lens of the Boresighter to the objective lens of the scope being sighted.
The Boresighter's lens is permanently focused to make the target grid seem to be positioned a great distance away from the scope, just like a target on the range.
* How the Scope Works in Conjunction with the Boresighter
Because the Boresighter body is positioned so close to the objective lens of the scope and since the optical system of the scope is designed to clearly view objects at great distances rather than a few feet away, the target grid of the Boresighter is seen through the scope as the primary image in the field of view, with the edges of the Boresighter indistinct and disappearing into the background image.
When the scope's objective lens receives the image of the target grid from the Boresighter, it processes the light rays that contain the image through its internal optical system, finally concentrating it on the plane of the reticle and projecting the resulting combined image of reticle and target grid through its ocular lens to the eye of the person sighting the scope.
* The Key Concept: Parallel Light Rays
It is an optical property of riflescopes that all light rays entering the objective lens of the scope that are parallel to one another will be focused by the scope in the same place within the scope, regardless of where they strike the face of the scope's objective lens.
It is this fact that allows the Boresighter to be placed (so long as it remains in an upright, or 12 o'clock position), in various vertical and horizontal locations on the muzzle of the firearm (that is, at various points on the x,y axis) without any reduction of its effectiveness.
The image of the target grid from the Boresighter is presented to the objective lens of the scope by light rays that all travel parallel to the direction of the bore of the firearm. Thus, the location of the image of the boresighter scale seen in the scope is independent of the location of the Boresighter on the muzzle and is in the same direction the bore is actually pointing.
* Why the Target Grid Seems to Move During Scope Adjustment
It has been established that so long as the rays of light carrying the image of the target grid enter the objective lens of the scope parallel to the bore of the rifle, the target grid image will appear in the same place in space, relative to any distant objects in the field of view, regardless of the physical position of the Boresighter on the muzzle. Yet when the windage and elevation adjustment dials of the scope are turned, the image of the target grid appears to move in relation to the reticle.
This is due to the fact that these adjustment dials move the optical axis of the scope relative to its mechanical axis by making very small tilts of the internal erector system.
The reticle is fixed relative to the mechanical axis of the scope, but the direction of the optical axis (the center of the field of view) is not.
So by moving the windage and elevation adjustments, the image of the target grid (the bore direction) can be moved and made coïncident with the center of the reticle.
* A Note Advising Against Using the Boresighter with Non-magnified Reflex (Red Dot) Sights
Due to the fact that non-magnified reflex sights (such as the LG-1 and LG-35) do not offer magnification of the target to the shooter, the use of the Boresighter with these products is not recommended. It would simply be too difficult to use as the image of the target grid presented to the shooter would be too small to be of any benefit.