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From: EinEchterHeiner on 4 May 2010 09:26
I want to find the function y=f(x) having a zero at +a and -a so that
the lens formed by f(x) and -f(x) in (-a,a) bundles all light coming
from the top into a single point P at [0,-t]. You are free to choose
t, but the refractive index n of the lens is given (eg for Glass it
would be around 1.5) and I guess that a is then determined by a and t.
Note that you cannot use a simple differential equation, because you
need the value of f(x) and f'(x) for two different values of x when
computing the path of a beam coming from the top.

This problem bothers me quite some years now, and i have no cue how to
solve it.
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