Great optical 'illusion'

Pretty useless but somewhat cool. What would make someone want to project the outside upsidedown on their wall?
True, but can you do it twice to 'correct' the image? Not sure if you can retain the image quality when doing that of course.

Then again the whole opaque part means you need to 'kill a window to make a virtual one'.
I did this when I lived at the beach, fifteen years ago. I covered the one bedroom window with black black paper and sealed it with black camera tape. I cut a hole, the size of a pencil eraser, in the paper, and the outdoors was then spread out across the room. I had it up for two years.

You don't need a lens, if the hole is small. But the image will be dim and fuzzy. The smaller the hole, the sharper and dimmer the image.

If you use a lens, the focal length of the lens should be equal to the distance from the lens to the wall in order to focus on infinity. You may want to focus somewhere closer, which would need a shorter focal length.

If anyone wants to try with a lens, the formula is:
1/f = 1/p + 1/q
f is the focal length of the lens
p is the object distance (from lens to outdoor object to focus on the wall)
q is the image distance (from lens to the wall)

The larger the lens diameter, the brighter the image, but the shallower the depth of focus will be.

Mike, you could use two lenses and get an upright image by refocusing an 'aerial' image, but you will loose most of your light.
It's called a "camera obscura" - Latin for "dark room." I believe that's where we get the word camera from (it means room).