parabolic magnification...

[GAHD]

See attached diagram.

The goal is to enlarge an emitted image to appear to be 100X it's actual size, and to make it appear to be at a distance from the user. The optics cannot exceed 3mm in thickness and the mitted image must have a clear path to the first reflection point(perfect normal to sizing chamber entrance point)
The emitter is a 1mm x 1 mm suface.The glass can be any refractive index from 1.5-1.9 .

What parabolas for the 2 mirrors would acheive
this goal? How does the math behind it work?
*not shown* The 'z' axis would have to be expanded by a combination of initail spreading through reflection and then straightening of the image through refraction at the upper entrance point of the sizing chamber('z' axis is not in agreemnent with the norm).
I'm very interested in learning the way parabolic mirrors work mathematically. How would I define the curve of the optics in question were I to order them ground?


Just to make shure I've been using the right math;
The Law of Refraction: n1 sin(theta1) = n2 sin(theta2)
n = index of refraction Determins how the light refracts initially in the unseen Z axis warping, and a small degree of infuence on incoming light.

Spherical mirror: 1/o + 1/i = 2/r o = distance of object form mirror i = distance if image from mirror r = radius of curvature of mirror could a parabolic formula replace radious for purposes of calculations?
Triangle calculations, for manual plotting of refraction points.
tan(theta)=y/x sin(theta)=y/R cos(theta)=x/R sinA/a=sinB/b=sinC/c c^2=a^2 + b^2 -2ab cos(theta)