I've been wondering for quite some time how double-parabolic mirrors (such as the ones for sale here and here[yes, same product, different pages]) work. Specifically, I'd like to know the issues behind image coherency and the focal points of the mirrors.

 

Thanks in advance.

The diagram at <http://www.optigone.com/m2000.htm> shows a ray diagram for how a real image of an object placed at the bottom appears just above the top hole.

That only tells you the focal point of one of the parabolas, I believe - unless we are assuming that they are both identical.

 

More importantly, that still doesn't tell me how it works. I guess a more appropriate question would be, why is the virtual image produced?

Sorry, I meant a virtual image.

That ray diagram is not only for a focal point.

Its shows how the image of the object is produced.

Yeah, I see that, but it's not what I mean. I'm trying to explain it to a friend, and he doesn't think that the virtual image would be produced (I know it is, I've seen these things in action)... Can you explain to me how, exactly, the image is produced and why the image is actually there?