Well, only if the LED were positioned at the focal point of the curve. Look at how integrating spheres work. They donāt focus the light back to the LED. They are spherical, yet they scatter the light evenly in every direction. The position of the light source influences where the curve will focus the light back to.
If the led is not at the focus point the light will scatter, thats why reflectors are parabolic, all light is reflected at a known angle, light from the source must be reflected at different angles at different places of the reflector so they all come out the front at the same required angle.
Put a led pointing in at the focal point of a parabolic dish with edges at 45 degreeās and all of the light emitted will be focused by the reflector 
Cheers David
Reflectors in flashlights are getting hit with light from behind. Or, you could say, from the back edge of the parabola. The light is travelling in a specific way and the parabola forms it a specific way in order to focus a beam outward. Here, weāre talking about a light source pointing toward the front of the curve, not from the back. That makes things a bit different. If you think about a perfect sphere, and a point source at the center, all the light is focused back to center, as you said before. If you move the point source, the light will still be focused but not to the same place or at the same angle. That is because the angle that the light hits the curve is no longer perpendicular or 90 degrees to the surface of the curve.
I just did a quick online search and found this webpage. The āLesson Threeā talks about concave mirrors and how light reflection works with them. I was unable to find specific mention of a distinction between parabolic vs spherical surfaces. But, the way the text was worded suggests that they are assuming a spherical mirror shape.
Edit: Ah, here we go, another website says this:
So, you are perfectly correct, except that under certain circumstances, I am also correct.
Sorry for the thread hi-jack Fmc, it finishes here
nuff said
Cheers David
A google search for parabolic reflectors, turns up some stuff in the 12" diameter range and less than $50.
I know it's not AU links, but I would think there's stuff like this over there too. Maybe not.
Hell, it's almost cheaper if I buy one and send it to you. What a difference in price!
Good thing you did post this link. Otherwise, FmC might not know that the satellite dish is a no-go for this project, because it is off-axis.
I wonder if you could shape a parabolic mold negative(think beehive shape) then use it to cast a Fiberglas and epoxy reflector. Do your best Richard Dreyfus imitation. Whom knows? You might even be able to pick it up. Kind of like the way integrating spheres are done but in a parabola.
Hollyā¦
Canāt wait to see all the progress and final product!
Hereās a parabolic mirror on ebay that is in bidding. As of 1:00 PM EST, it has one bid and is at $9USD. Listing says it will ship to Australia. Has free shipping.
Edit: It is 40.5cm size.
68 cm focal length. At that distance you would need an intermediate lens to get the light onto the surface.
Thanks for the discussion, guys.
Believe me, I spent a lot of time searching on-line for something suitable, with a reasonable price.
I'm choking on forking out for four XHP's, never mind ~$150 for a reflector...
I have some "97%" reflective flexible adhesive mirror squares in the mail, so I'm really just looking for a suitable shape to coat with them, although a 'ready to go' reflector would be nice.
Explain to me why I can't use the satellite dish if it's tilted on an angle, or if the emitters are off-center?
:beer:
I assume you have seen
It's ideal, apart from;
"Asking 325
Shipping 18
U.S. Only"
:)
You can, however the focal length is a bit long.
Cheers David
Thanks David, got it :)
The search continues...
For the recordā¦ I absolutely love that statement. 
Pure brilliance! I want to use that as my sign off line. 
Go for it! 
I guess I was too dumb to know how brilliant I was being. 
This seems to be the best option I can find in a pre-made solution. Almost perfect size for the body I have, good focal length, only costs half the earth... I know I can get it in a couple of days, being local to me. Not sure what impact the small hole in the center would have, but I could patch that with some reflective material.
Of course, the other solution is to make something.... after a bit more searching, I came across this site, which made understanding the parabola easier for me.
I'm also planning to make a few cardboard parabola cut-outs that I can take to the dollar-store, in the hope that they may have a dish/bowl that just happens to have a parabolic contour.
That Edmund Optics mirror looks so perfect! Have fun trying to find/make something. Hope it goes well for you. Iām looking forward to seeing your finished product!
That 40.5cm mirror I linked earlier is still at one bid $9USD and has 14 hours left to go. It will probably end up well below the $62 price of that Edmund Optics mirror. If nobody else bids on it, somebodyās gonna get it for $9USD. It can ship to Australia, and shipping is free.