In the figure below, the 3D segment AB is projected by a standard perspective camera to the image
segment ab. The point C on AB bisects AB in a ratio of t:(1‐t), and its projection c bisects ab in a ratio
of s:(1‐s). Denote by ZA,ZB,ZC the depths of A,B and C.
A. Express t as a function of s,ZA,ZB (in particular show it is independent of the focal length).
B. Express ZC as a function of s,ZA,ZB (simplify the result).