A microscope’s resolution is its ability to form separate images of lines or dots. It’s defined in terms of the actual distance between details on the object. The wave nature of light puts a practical and theoretical limit on the resolution of a white-light microscope at about half a wavelength of visible light, about 250 nanometers or a quarter-micron. This also limits the highest useful magnifications to the range of 1000x-2000x.
Resolution depends solely on the objective lens, as the eyepiece just magnifies light from the objective. In addition to its optical quality, the width of the cone of light captured by the objective determines its resolution. This is governed by its design and whether or not oil is used between the specimen and objective lens. Both a wide-angle design and oil immersion capability will increase the resolving power of the objective lens. In any case, it cannot exceed the limit described above for the visible spectrum.
To calculate an image scale, you need to use the apparent field of view of the microscope objective in degrees. SInce that figure is usually not available, image scale can be approximately calculated as follows: the size of the field of view in a typical optical microscope (in millimeters) is about 200 divided by the magnification. As an example, a 400x power microscope magnification gives a field of view of 0.5mm. Multiply by 1000 to get the field of view in microns. For this example it is 500 microns. However, digital microscopes often use narrower field of view objectives, often yielding only a third as much field of view as the same magnification with a traditional optical microscope.
The image scale in microns per pixel is the field of view divided by the camera resolution. Take the field of view as the long dimension of the view. For a 2MP resolution 1600x1200 imaging device-camera and the field of view of the above example, the numbers work out to be 500/1600 or 0.3 microns per pixel.