Image construction with concave and convex mirrors

[eneacasucci]

image construction with concave and convex mirrors

I don't know exactly how to explain it but what I have noticed is that when I use the rules for image construction with concave and convex lenses the image is wrong if I don't use the extension of the ray to the tangent to the mirror (purple line).

If I stop the ray at the mirror the rays do not all converge at one point. Does this mean that I actually have to construct the image by making the rays go beyond the mirror?
The correct construction is the green one but I thought that the rays stop at the mirror (like the red construction), but this way the result does not come.

I have applied the rules in both cases:
a) The rays passing through C are not deflected.
b) Rays passing through F are reflected parallel to the optical axis.
c) Rays parallel to the optical axis are reflected in the focus F.

 

[Ibix]

Your stated rules are the rules for the paraxial approximation, where all angles are small and all optical components are approximately thin flat surfaces.

The image you've drawn, however, clearly doesn't fit that approximation. For such a strongly curved surface you'd need to do proper ray tracing - draw the normal where each ray strikes the surface and apply equality of angles of incidence and reflection. The resulting rays will still not all go through the same point, which is the origin of the phenomenon called spherical aberration.

 

[eneacasucci]

Thank you, i Think it is clearer now. I couldn't find on books proper information about those geometrical constructions.
So it should be something like this

 

[Ibix]

Looks right, yes. Obviously the normals all point at $C$.