Why doesn't my convex mirror reflection match the expected focal point?

AI Thread Summary
The discussion revolves around the behavior of light rays in convex mirrors, specifically addressing why reflected rays do not converge at the expected focal point. The user graphed a model of a convex mirror and found that the reflected rays do not pass through the focal point as anticipated, despite verifying their calculations. It was clarified that the principle of rays passing through the focal point applies primarily to paraxial rays, which are close to the principal axis. For other incident rays, the reflection may approach the focal point but will not converge exactly there. The conversation highlights the nuances of ray behavior in convex mirrors, emphasizing the approximation involved in using the focal point concept.
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Homework Statement



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 (red line in my model, below) parallel to the principal axis (black line) hits a convex mirror (full curvature outlined in black, centre C), the reflected ray (purple) extended back passes through the focal point (F).

Homework 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...)

The Attempt at a Solution



wtf.png


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.
 
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In the concave mirror, the reflected ray will pass through F if the ray is parallel to the principle and close to the principle axis. Such rays are called par axial rays.
 
Are you just saying the principle is an approximation. I.e. in fact it never passes exactly through F at all (except of course when the incident ray is along the principal axis), but the reflected ray gets very close to F when the incident is close to the principal axis
 
Yes.
 
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