Throughout much of this book we will ignore the eyepieces altogether, as we will be frequently replacing them with cameras of various kinds. However, for normal non-photographic use, or when you have a trinocular microscope where the camera has its own separate tube, the eyepiece will be key to comfortable viewing.
For a monocular microscope, there aren't any controls on the eyepiece head other than perhaps a swivel so that two people can alternate viewing without moving their seats. The magnification of the eyepiece is generally fixed on professional microscopes (as opposed to zoom eyepieces often found on amateur or toy microscopes). To change the magnification, you change the eyepiece, swapping a 10x eyepiece for a 15x or a 20x.
A rule of thumb is to never magnify more than 1,000 times the numerical aperture of the objective lens. This is because more magnification than that does not increase the resolution of the image (no more details are seen), but simply makes little blurry things into big blurry things, and decreases the field of view in the process.
Binocular microscopes are more comfortable to use, and since both eyes are seeing the same image, there is better image fidelity. Your brain will merge both views, and you can see more detail.
Because each eye usually focuses at a different distance, even when vision is corrected by glasses or contact lenses, the eyepieces can be individually focused for each eye. On some microscopes, only one eyepiece is adjustable. In that case, focus the microscope using the non-adjustable eyepiece, and then adjust the other one until both eyes have a clear view.
Not everyone's eyes are the same distance apart. For this reason, the microscope has an inter-ocular adjustment, so the eyepieces can be moved farther apart or closer together. Some control this by sliding the eyepieces apart, and others rotate them apart.
The entire eyepiece head assembly can usually be rotated so that a second person can view the specimen without swapping chairs. This is done by loosening the head set screw. Loosening the screw even more allows the entire head to be removed, allowing a camera to be aimed down the tube.