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Reverse calculation of radius and principal planes of thick lens

  1. Dec 24, 2012 #1
    Dear All,

    I need you kind support in a problem, which I am unable to figure out. It is regarding thick lens.

    I am determining lens principal planes and radius using shaping factor and focal length. The forward problem I am using is,
    Focal length
    1/f = (n-1)*[1/r1 - 1/r2 +(n-1)*d/(n*r1*r2)]
    Shaping factor
    X = (r2 + r1)/(r2 - r1)
    Solving these two equations for r1 and r2, I get.
    1/r1 = (X+1)/ [f * (n-1)*(1+sqrt(1+(X^2-1)*d/(n*f)))]
    1/r2 = (X-1)/ [f * (n-1)*(1+sqrt(1+(X^2-1)*d/(n*f)))]

    These equations return complex number when (X^2-1)*d/(n*f) < -1. So I cannot use these equations for this domain and I have no idea how to determine radius and principal planes in such a case. Any body know a solution for this domain or more general equations?

    Thanks in anticipation for reading and support.
  2. jcsd
  3. Dec 25, 2012 #2
    Does these sources help ? :

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