Effective Focal Length of Multiple Lenses

  1. In my Optics book (Hecht, 4th edition) the author discusses how, when dealing with a multiple lens system (say, with n many lenses), one can think of the system as a single lens system, with an effective focal length given by:

    1/f(effective) = 1/f1 + 1/f2 + ... + 1/fn

    My question is this: Where is the resulting "effective" lens located, with respect to the original source (or with respect to the original lenses)? I am dealing with a simple two lens system, and I've tried placing the lens at the midpoint between the original two, and at the location of lens 1, but neither gives the correct answer.
  2. jcsd
  3. Nevermind. I just answered my own question; I read what I wanted to see, not what was actually there. The formula I quoted applies only to thin lenses which are in contact with each-other, in which case the position of said "effective" lens is already well-defined.
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