What x20 x40 x100 magnification means? I want to buy a biologic microscope for fiber analysis, thus I need to see details of a fiber of around 20μm. 
Could you please explain what "x20" magnification means? I understand that it will not convert 1mm to 20mm at a picture... 
Thanks!  
 A: A lens with a given magnification $m$ makes the rays emanating from the object under observation reach our eyes in such a way that our eyes perceive it to be $m$ times the size of an object at the same distance i.e., a sphere of $1\ cm$ diameter appears to be a sphere of $m \ cm$ diameter at the same the same distance as original. 

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A: The magnification on a microscope is similar to the magnification of lenses. A $\times20$ magnification WILL make the image height $20$ times the height of the object. Hence $1$mm will appear to be $20$mm under the microscope.
Important Note: To obtain magnification of microscope, you have to multiply objective magnification with eyepiece magnification.
A: As the others have already answered your question, I don't try to answer it again. However, from my perspective you are asking the wrong question. A microscope is not fully described by its magnification. Therefore, this is not the only quantity which you should consider. Especially in your case, it seams as if you are most interested in the spacial resolution of the microscope.  In particular, you like to resolve (transversal) structures which are smaller than 20um. Therefore, you should ask for the transversal resolution of the microscope and the field of view. 
One more thing: Don't aim for the smallest transversal resolution, because this also effects the longitudinal resolution if the microscope. if your longitudinal resolution becomes small, only a small part of the field of view will be in the focus. Thus, the image becomes blurred. 
