I'm not an expert in lens design. I need to build a lens having fixed the focal point $f$, the lens diameter $D$, the maximum thickness $d$, the refractive index $n$ and the half-angle $\theta$ entering on the lens and the angle that I want at the exiting from the lens. With these, I want to find the radius of curvature $R_1,R_2$.
In some books of optics that I used in my course of physic and I found the Lensmaker equation (because I cannot use the thin lens approximation).
$\frac{1}{f} = (n-1)\left [ \frac{1}{R_1} - \frac{1}{R_2} + \frac{(n-1)d}{nR_1R_2} \right ]$
This equation don't allow me to play with the lens diameter, so looking around I found the relation between this and the numerical aperture NA
from Fresnell equation but I'm not sure how can help me.
$n_1\sin\theta_{in} = n_2\sin\theta_{out}$
$NA = n\sin\theta = n\sin\left [ \arctan \left ( \frac{D}{2f} \right ) \right ]$
Can you help me figuring out these radius knowing all the previous variables and how take into account the whole lens diameter?
This is my geometry. The focal point is known since I have a diverging source and I want to have a planar wavefront after my lens.