Microscope resolution depends on the wavelength of light (λ) and the numerical aperture of the objective lens (NA). Use 550 nm for white light.
Lateral resolution = 0.61 λ / NA Objective
or if you include the condenser: Lateral resolution = 1.22 λ / (NA Objective + NA Condenser)
Depth (Z) resolution = 2 λ / NA squared
NA (numerical aperture) is a measure of the ability of the lens to gather light from a wide solid angle.
NA = n. Sin(α)
n = refractive index of immersion medium (air = 1, oil = 1.5, glycerine = 1.5, water = 1.3)
α = half the solid angle of light gathered by the lens (max 90 deg)
Cameras and Pixels
Image pixel size depends on the camera, C mount and objective lens:
Image pixel size = CPS / (Mag * CM)
Camera field of view = (CPS * NPix) / (Mag * CM)
CPS = camera pixel size (typically 2 μm – 7 μm)
NPix = camera number of pixels in X and Y dimensions
Mag = objective lens magnification
CM = C mount magnification (typically 0.4x – 1x)
Field of view = Eyepiece Field Number (mm) / Objective Magnification
This graph shows you if the camera is over sampling or under sampling the microscope image. For example, if you are using an objective with a NA of 0.8 then the pixel size must be 0.2 microns or smaller. This can typically be achieved for a 20x objective with a 1.4 MPixel camera, i.e. it is surprising how few camera pixels are required to correctly sample the microscope image.