For monochrome applications the pixel size is multiplied by factor 1.41 (=square root of two). The result is the diagonal of the pixel.

For color applications you can generally use factor 2.

Now you can calculate how many of these details fit on 1 millimenter = 1000um

The result is 1000 / ( pixel size * factor) for the value “lines per millimeter”.

That’s half as many “line pairs”, so we divide 1000 by two and get
line_pairs_per_mm = 500 / (pixel size in um * factor)

Example: 5.5um pixel monochrome corresponds to 500/(5.5*1.4) = 500 / 7.7 = 65 lp/mm
Example: 2.2um pixel color corresponds to 500/(2.2*2) = 500 / 4.4 = 114 lp/mm