Convex mirror reflection

1. The problem statement, all variables and given/known data

For self study, I’ve been trying to understand my convex mirror.
Some online instruction I’ve been following states that if an incidence ray parallel to the principal axis (red line in my model) hits a convex mirror (full curvature outlined in black, centre C), the reflected vector (purple) runs through the focal point (F).

2. Relevant equations
In my graphed model below, the points & vectors are
centre of curvature, C is at origin
focal point, F = (25,0)
normal to incident, N = (0.91128…,-0.41178…)
incident, I = (-1,0)
reflected, R = (0.66087…,-0.75049…)

3. The attempt at a solution

Attachment 67188

I graphed my model (above) but the reflected vector does not run exactly through my focal point as expected. I’ve checked this is not simply a rounding error (or any other obvious mistakes). There are also other problems when I plot more incident vectors emanating from the same point (not shown): the reflected vectors do not converge on a virtual image point as expected. Something crucial is missing from my understanding of this problem.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Attached Images
File Type: png wtf.png (8.9 KB)

http://ift.tt/NL3rIO

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