## Reverse calculation of radius and principal planes of thick lens

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.

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 Quote by taimoortalpur 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.
Does these sources help ? :

http://hyperphysics.phy-astr.gsu.edu...t/priplan.html
http://www.math.ubc.ca/~cass/courses/m309-04a/sol4.pdf

 Tags geometric optics, optics, optics lens, thick lens