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I know that the sign of the effective focal lenght (f) of a lense will determine if a that lense is divergent(f<0) or convergent(f>0), but with a system made of a combination of thick lenses and thin lenses, that no longer holds true, so how do i know if the system is divergent or convergent? I have heard that it has to do with the principal planes,but i was not able to understand why or how.

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This method does not use the concept of principal planes, but can be used as a way to find if the system behaves as convergent or divergent

You may try making an image of an object kept at infinity, by the combination.

  • If the image formed is real, and the image is formed in from of the last - the combination acts as convergent.

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  • If the image formed is virtual, and behind the last lens - the combination is divergent.

enter image description here

This method might be calculation wise a bit long, but it'll work.

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