I made a Wolcott camera a few years ago. There are only a few in the world, even though they are pretty simple. It is essentially a dark, wooden box with a large concave mirror inside at one end. In the middle you have your film standing upright, directly in the path of light. You have a large hole in the other end of the box. There is no lens, only the mirror, which acts as a lens. Light comes through the large opening, goes "around" the film (sheet of film has opaque backing on it), bounces off the concave mirror and is focused back onto the film surface.

Here I am simply aiming my camera into the camera, looking past the back of the film, into the mirror, and onto the face of the film (in this case, replaced by a piece of card). Light travels in a straight line, so you can get some weirdness in the dead center of a picture, however if the subject is farther away, the concavity of the lens picks up most information accurately and focuses with decent results.

This camera was the very first photography related item ever given a US patent. Patent No. 1,582, May 8, 1840