Objectives are too sensitive to be manhandled by the novice, their mounts however… -K
Modern stands, particularly those intended for student use, at first seem to lack provision for adjusting the objective to improve alignment or centering. This is not any great failure, quality manufacturers produce stands that are near enough to alignment as designed that they might suffer a large amount of mishandling. If one is using a new stand, adjustment will likely be unnecessary. If one has a used stand, one should first check their alignment before making any adjustment. Luckily, identifying misaligned objectives is a simple matter.
All but the oldest and most basic stands will have a simple provision for rapidly changing objectives, a rotating nose-piece is most common. Such a nose-piece provides a rapid method of identifying if alignment is acceptable or not. To make the determination one need only place a prepared slide (a stained blood smear is well suited to the task as one may position an easily recognizable white blood cell in the center, a stage micrometer or other calibration slide would also be highly precise) on the stage and bring it to sharp focus with a particular objective. One will then take care in positioning just in the center of the field of view some conspicuous portion of the specimen. Upon switching to the next objective in the changer the conspicuous portion of the specimen would ideally be still in the center of the field of view, it is never likely to be so.
Perfection of positioning from objective to objective would only be possible should each individual optical component (every lens from light to eye) be precisely centered. Considering the number of individual lenses in each objective, one must accept that if the conspicuous portion is still in the central area of the field of view, the objective is centered. In figure one below, where circle A represents the field of view, one might be satisfied if the conspicuous object remains within the area of circle D from objective to objective.
There are rotating nose-pieces where each objective mount is fully individually center-able, but they are few and far between; look instead to see if some less exact provision for adjustment is provided. On the Bausch & Lomb nose-piece seen below are small adjustable plaques that serve as positioning apparatus unique to each objective. Moving the position of the plaque moves the location at which the objective stops along arc B-C as depicted in figure one. Although it will not truly center the objective it can be used to position the circle D for each objective along arc B-C.
On many other rotating nose-pieces, plaques of the above sort are lacking. However, they operate on the same principle and the arm may be adjusted to achieve the same effect.
A final word of caution, one should focus on achieving the most perfect alignment with the most powerful objective one intends to use. By virtue of having the smallest field of view the most powerful objective will be the one most sensitive to adjustment.