Parabola incoming ray not parallel to axis

[Drakkith]

I see where you're coming from here but a paraboloid shape will never allow you to be in that position. The sides are constantly diverging (just less and less). The shape that will let this happen is an Ellipsoid and rays will go through one focus - hit the walls and then arrive at the other focus (at the other end). But it is a closed shape and you can't send rays into it. I have never worked it out but I imaging that rays command through a window in the side may pass through both foci (severals times) before some of the energy emerges back out of the window.

It took me a few re-reads to understand this, but you're basically saying that a parabola has no "opposite parabola wall", right?

 

[jbriggs444]

Perhaps you could post this back of an envelope for me. The calculation would have to include the formal ellipse shape. I can't imagine a simple way through this.

The envelope is in tatters. Its supposed result is wrong. Thank you for revealing my mistake.

I had managed to convince myself that since an infinitesimally thin ray that passes through one focus of an ellipsoid will converge on a back and forth path running the long way through the ellipsoid (true) that any nearby and nearly parallel ray will have a path that similarly converges (plausible sounding) and that this means that a parallel ray will have a path that passes ever closer and closer to the foci as it converges to that center line path (provably false).

 

[sophiecentaur]

Drakkith: Both what you wrote initially and my thought processes are ancient history (to my aging brain at least) so I can't remember. (Sad old sod) My thought was, of course totally correct, incisive and brilliant haha.
That diagram on Post 30 says it all, really - except for the case of rays arriving very near the principle axis. These will reflect (only once) off the surface and will miss the wall of any finite sized parabola so they'll be lost out in another direction. I must say, I never considered this before and I am glad you guys pushed my mind in this direction; cheers.

jbriggs: My intuition told me it couldn't have been right - but you can't always trust intuition. I just remember that a ray through one focus will pass through the other one. So, up to a point, that will apply to an object or real image in the vicinity of one focus: it will appear at the other focus. I guess that's the theory behind the ' pink holographic pig' illusion.

I will have to reflect on this, some more.