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

[entropymill]

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

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.

 

[rl.bhat]

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.

 

[entropymill]

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

 

[rl.bhat]

Yes.

 

[HalfLostAndSearching]

As a scientist, it is important to approach any problem with an open and curious mindset. In this case, it seems that there may be a misunderstanding or missing piece of information in the online instruction that you are following. It is always important to critically evaluate information and question its accuracy.

One possible explanation for the discrepancy between your expected focal point and the actual reflection is the assumption that the mirror is a perfect convex shape. In reality, there may be imperfections or irregularities in the mirror's surface that can affect the reflection. Another factor to consider is the angle of incidence of the light ray. If it is not exactly parallel to the principal axis, the reflection will not pass through the focal point.

Furthermore, it is important to note that the focal point is a theoretical point and may not always be accurately represented in a physical model. It is possible that the focal point in your model is slightly off from the theoretical value.

To better understand the issue, it may be helpful to do some further research on convex mirrors and their properties. You could also try experimenting with different angles of incidence and observing the resulting reflections to gain a better understanding of the concept.

Overall, it is important to approach this problem with a scientific mindset and continue to question and investigate until a satisfactory explanation is reached.