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Suppose there's an object located at some position $x_O$, which emits light in the direction of sensor screen located at $x_S$, and the screen has some lens nearby at $x_L$, which partially focuses the image at the screen.

I need to magnify the image on the screen and focus it better. I guess both of actions would require placing some lens at $x\in(x_O,x_L)$. But:

  1. What should be different in case of magnification from the case of focusing?
  2. How can these actions be combined?
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In essence you are describing making a microscope: in the simplest case that is a two-lens system, where the magnification comes about from having a lens near the object (the objective lens) close to the focal distance of that lens, and a second lens (the ocular) collecting that light and focusing it for you (onto your eye, or onto a screen / sensor etc).

The basic equation for a microscope can be found at http://www.schoolphysics.co.uk/age16-19/Optics/Optical%20instruments/text/Microscope_/index.html

In your case, you need to move the ocular lens so that you get a real image instead of a virtual image - in other words, you have to put the objective lens closer to the object than its focal length.

What I just described essentially amount to "taking a photograph of the object with a magnifying glass in front of it", with the added proviso that you can "focus" the image in the camera by playing around with the distance from the magnifying glass to the object. It's much easier to to this by just playing around with the lens rather than computing it - because the actual distance from a lens (especially a compound lens) to a screen / sensor can be quite hard to determine from physical measurements of the lens, but is easy to derive from the optical performance.

Do you know how to take it from there, or do you need more help with the equations?

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  • $\begingroup$ What makes one lens an objective lens and another ocular lens? Just their positions with respect to object and another lens? Or maybe there should be some special relations between focal lengths or whatever so that we could definitely say like "lens A is an objective and lens B is an ocular, but not vice-versa", even if we rotate the microscope upside down? $\endgroup$ – Ruslan Sep 15 '14 at 13:03
  • $\begingroup$ The one closest to the object is the objective lens, the one close to the eye ("oculus") is the ocular lens. $\endgroup$ – Floris Sep 15 '14 at 13:48
  • $\begingroup$ Hmm... which one is then mostly for magnification, and which for focus? Does this for some reason depend on their position with respect to object and observer? $\endgroup$ – Ruslan Sep 15 '14 at 14:19
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    $\begingroup$ The objective provides much of the magnification although in a microscope you will find both objective and ocular have a designation like "40x" or "10x" - you then get the total magnification by multiplying. Typically the objective has the greater number. $\endgroup$ – Floris Sep 15 '14 at 15:04

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