The formula for focal length of a mirror is
FL = R/2. The R is the point at which any light going to a spherical mirror (from it's ROC) returns right back to the ROC (all points on a spherical surface have as thier perpindicular the ROC point to surface line) and as you remove the source, the point at which the light focuses gets closer to the mirror. At some point the light gets infinitely far away and thus the light coming in is parallel. This means that the angle of reflection is such that at that point, the light focuses to a point which is essentially 1/2 of the distance it did when the light was at the ROC. Please note that the discussion has delt with paraxial (near the center) rays which are, like the calculus idea for measuring areas and volumes, an infinitely small distance away from the center of the axis. The difference between the parabola and the sphere is insignificant at those distances. At larger distances (for a 10" F4 scope for example) the difference between the parabola and the sphere does make a difference as to where the edge rays hit the center of the axis vs. the ones nearer the center.
The proper way to do the ROC test is to have the light shine through the paper (or other more opaque material) and then get the focus of the hole on the paper near the hole.