Trying to get a wide throw to light up the whole dome from a standard projector is rather difficult. You just can't get the projector far enough away from the dome surface to make the projection big enough to cover a decent sized area. And since people are supposed to stand inside the dome to see the demo, it isn't really possible to use a lot of mirrors to increase the focal distance. So custom lensing is really the only way to make it work.

But where to get custom lenses? And how to know what to need?

Well, I figured that a standard rear projection TV would probably have the proper lenses to get a wide throw, since their tubes are a lot closer to the screen. Fortunately, people regularly abandon these by the side of the road, and a few minutes looking like a crazy man with a screwdriver can net these fine items for one's own use!

The type of projection TV with tubes in it still has some troubles to iron out, tho. It turns out that the area between the tube and the lenses is filled with oil, and that oil seems to be a part of the lensing system, and it doesn't really work without it!
Having let the magic oil out of two of the three lenses, I managed to save only one tube and lens assembly with oil intact.
The next problem is to break away enough of the tube to project on the inside surface without breaking or removing or even loosening the tube from the rest of the lens assembly.

I approached our kind friend V, a talented glassworker who attends the 23b Shop Hackerspace, and he agreed to grind out the back of the tube with his special glass grinding wheel. Here is the result!

Now I have a much larger area to project onto, and the oil/lens is still intact!

He even cleaned up the edges so that they weren't so sharp!

Now, the next thing is to determine how to lens the output of the projector so that it can place an image in focus on the inside area of this assembly. Currently, I can't get any of them to focus that closely.
One thing that *IS* now possible is to write things on transparency that can be placed on the surface of the lens and project them on things using a bright, bright light!

The dome experiment continues!