Conceptual question regarding resolving power of optical instruments

  1. I've been wrestling with this problem for a while, and I really cannot understand it.

    As I understand it, the limit of the resolving power of the eye is related to diffraction: when Rayleigh's criterion is just satisfied, then two objects which are close together can just be resolved, i.e. we can tell that they are two separate objects. Taking the example of optical microscopes, the larger aperture of the microscope means that diffraction occurs to a lesser extent when light passes through the microscope slit, hence the resolving power of the microscope is greater than that of the eye.

    However, I cannot follow why the resolving power of the microscope should enable us to resolve objects which are closer together than the actual resolving power of the eye. I understand that diffraction occurs to a lesser extent when light passes through the microscope aperture, but at the end of the day, in order for an image to be formed on our retina, the image must still pass through our eye slits, and will still experience diffraction then. In this case shouldn't the resolving power still be limited by that of the eye?

    The only explanation I can think of is that the optical instrument magnifies the image, which increases the angular separation of the two images and thus allows our eyes to resolve the two objects separately. Is this true or am I missing some key concept here?
     
  2. jcsd
  3. Redbelly98

    Redbelly98 12,020
    Staff Emeritus
    Science Advisor
    Homework Helper

    Wow, this is a good question.

    Without working through any of the math or drawing an actual ray diagram, I think that is 100% right on the money.
     
  4. I've been looking in many texts and none of them address my question directly. Can anyone point me to a site which answers this question specifically? I've been trying to draw ray diagrams on my own but I'm not very sure how to show the light waves after they've passed through the optical microscope aperture but before they've entered our eyes.
     
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