Recently I was studying about optical instruments and in my book I came across a point which stated that
When non axial parallel rays are incident on an ideal spherical mirror at a small angle or a parabolic mirror, the rays meet at a point on the focal plane rather than the focus point.
Also in the section about refracting telescopes, diagrams drawn show that the non axial parallel rays meet at a point on the focal plane.
Please note that I'm talking about concave mirrors and convex lenses and aberration and other non idealities are ignored.
I mean, can we show that non axial parallel rays will always converge at a point on the focal plane?
I tried to proceed by attempting to find the equation for the focal plane but I don't think that will work at all.
Could anybody please tell me a way to do this?
How do we guarantee that a group of parallel (non axial) rays incident on a spherical mirror or a lens will always converge at the focal plane (assuming ideality)?
I also saw this SE post and tried to follow the "Physics Teacher" link mentioned in comments but couldn't reach it.
Any kind of approach, either geometric or mathematical will help. Thanks for any suggestions.