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Compound lenses separated by a distance

  1. Feb 16, 2017 #1
    Capture.jpg


    Let ##s## be the object distance for the first lens #s'# the distance to the image for the first lens and ##s''## the final image distance:

    Using Gauss's lens equation ##\frac{1}{s}+\frac{1}{s'}=\frac{1}{f_1}## from this we get:
    $$s'=\frac{sf_1}{s-f_1} $$

    we can use the image from the first lens as the object for the second lens.

    $$\frac{-1}{s'-d}+\frac{1}{s''}=\frac{1}{f_2}$$
    Note - I feel my mistake is here, I think my algebra is correct after this.

    This gets us:
    $$\frac{1}{s''}=\frac{1}{f_2}+\frac{1}{s'-d}=\frac{s-f_1}{sf_1-sd+f_1d}+\frac{1}{f_2}$$

    The total focal length is given by:

    $$\frac{1}{f}=\frac{1}{s} +\frac{1}{s''}=\frac{1}{s}+\frac{1}{f_2}+\frac{s-f_1}{sf_1-sd+f_1d}$$

    Which doesn't get the desired result. The correct result is/should be:

    $$frac{1}{s}+\frac{1}{s'}=\frac{1}{f_1}+\frac{1}{f_2} + \frac{d}{f_1f_2}$$


    Thank you in advance
     
  2. jcsd
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