Consider n convex (or concave) thin lenses with a focal length fn( > 0 or < 0 ), placed at positions zn. An object of size L0 is located at position Z0=negative infinity. We want to derive the position Z1 of the image, and the magnification M as a function of all given parameters. All values of positions are algebraic, i.e. can be either > 0 or < 0. 

(a) For n=2, choose 5 distinct combinations of lens types / values positions. Find Z1, M, and draw what the ray tracing optics look like. 

(b) For n=3, choose 7 distinct combinations of lens types / values positions. Find Z1,M, and draw what the ray tracing optics look like.