The maximum useful magnification of a compound light microscope is approximately 1,000 times the numerical aperture (NA) of the objective lens. The numerical aperture is a measure of the light-gathering ability of the objective and is determined by the refractive index of the medium between the objective and the specimen, as well as the angle of the cone of light that can be focused on the specimen.

In practice, however, the maximum useful magnification is often limited by factors such as the quality of the optics, the amount of background illumination, and the observer's eyesight. As magnification increases, the image may become dimmer and less detailed due to diffraction of light and other optical aberrations. Additionally, the depth of field, which is the range of distances that appear sharp in focus, decreases as magnification increases.

Therefore, while a compound light microscope can theoretically achieve a magnification of 1,000 times the NA, the actual useful magnification may be lower depending on the specific microscope and the conditions under which it is used.