Increasing microscope magnification can be a delicate balance between an increase in magnification and a loss in resolution. Before we discuss increased magnification, it is good to make sure it is understood where total magnification comes from. Microscope magnification is a combination of the eyepiece magnification and the objective lens magnification.
stereo microscope image above you can see the eyepieces (which are changeable) and the objective lens (which is built into the microscope and therefore not changeable). On a standard stereo microscope (not a common main objective stereo microscope) the objective lens is built into the microscope and the only way to change this magnification is by adding an auxiliary lens to the existing objective lens. These are typically available in increments of 0.5x, 0.75x and 1.5x magnification. The most common way to increase magnification on a stereo microscope is by adding one of these auxiliary lenses. Keep in mind however, that with added magnification comes decreased field of view. Another common problem that accompanies increased magnification on a stereo microscope is the increase need for brighter illumination. Typically anything above 80x magnification on a stereo microscope requires the minimum of a 150w halogen fiber optic ring light or fiber optic pipe illuminator.
biological microscope image above note the eyepieces and the objective lenses. These provide total magnification for the microscope. Both can be changed. However, many times the microscope user thinks the easiest way to increase magnification is by simply increasing the magnification of the eyepieces. To maintain useful magnification with satisfactory clarity and resolution, it is important to avoid empty magnification or making the specimen appear bigger but not clearer. In general, total magnification should not exceed 750x-1000x the N.A. of the objective. For example, with a 40x, N.A. 0.65 objective, the total magnification should be between 480x and 650x. Using this example, if you were to try to use 20x eyepieces with this 40x objective lens, you would end up with 800x magnification - a number that is outside this range. Pairing these higher magnification eyepieces with the 40x objective would result in an image that is in fact magnified, but does not have clear and crisp resolution.