The formula to find the best microscope objective and eyepiece combination is to take the numerical aperture (NA) and multiply it by 500 to determine the low end magnification and NA x 1000 for the high end magnification. Once you determine the range, then take the objective magnification x eyepiece magnification and if it results in a magnification outside your optical magnification it would be best to use a different eyepiece / objective combination.
The chart below lists common NA values for objectives in the left column. The boxes with the "x" are optimal magnification combinations. For a calculation example let's look at the 40x objective with 20x eyepieces. The 40x NA is 0.65. If we multiply 0.65 x 1000 = 650x. The actual magnification of this combination is 20 (eyepiece) x 40 (objective) = 800x. Since this magnification is outside the optimal magnification of 650x, this is not a good combination for optimal magnification and will result in empty magnification.
Empty magnification is the result of an objective + eyepiece combination that falls outside the realm of optical magnification (see the blue boxes in the chart above). Once magnification rises above the optical magnification there is a bit of added magnification, but the image resolution deteriorates and may almost appear to be out of focus. This is "empty magnification" and will not allow you to view fine details in your specimens.For more information on microscope resolution click here.
