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Optical microscopes are quoted as having a maximum magnification of 1500x to 2000x - what is this calculated from?

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If you stick 200x lens and 20x eyepiece - you theoretically can have 4000x magnification, but you would not be able to see more details compared to 100x lens and 20x eyepiece, because resolving the smallest visible details is limited to Rayleigh criterion (i.e. limited to diffraction).

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Where λ is wavelength in nm, and NA is numerical aperture of the lens. So for violet light λ=405nm, and good lens with oil immersion (NA=1.25), you can have resolution 197nm.

So, in conclusion, optical microscopes are limited to ~x1500 because going any further does not resolve smaller details.

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Thanks for your answer. Please could you clarify, how does 197nm relate to 1500x? –  Rupert Maximum Sep 24 '12 at 5:31
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No direct relation. What I say is that you can make microscope with 10'000x magnification, but you won't see more details. So, typically at 1500x magnification human eye can comfortably see 197nm details and higher magnification is not required nor helpful. –  BarsMonster Sep 24 '12 at 11:16
    
To put some numbers in, 1500x magnification makes 197nm features look like they're about a third of a millimeter. You can zoom in on the image but it will get really grainy after that. –  Emilio Pisanty Sep 24 '12 at 14:25
    
Thank you. How does this relate to digital image capture - presumably the magnification has to take into account the pixel size of the detector? So you might need a higher magnification to get the same resolution as an eye? –  Rupert Maximum Sep 24 '12 at 16:22
    
With digital cameras usually noone talks about "magnification". Usually what is important is how many microns/nanometers is in each pixel. For example, on my microscope and my 5mp camera, on 10x lens 1 pixel=408nm. And this information is usually more important than magnification. –  BarsMonster Sep 24 '12 at 19:57

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