If I connect a video camera to a screen, so that whatever is seen by my camera appears on the screen, what do I see when I point it towards the screen itself? Is it, in terms of optics, this configuration the same as having two mirrors facing each other (or photographing the image in a mirror)?
It’s not the same as having two mirrors, the camera-screen setup doesn’t involve the same physics.
In the camera-screen setup, the only optical phenomena taking place is the absorption of photons by the camera’s sensor. Once the image is formed in the camera, all other effects are electronic, digital or electromagnetic in nature. The representation of the image in the screen doesn’t involve any reflection, and after a frame is presented, those photons would reach the sensor and absorption occurs again. There is no paradox here because all the energy that the sensor absorbs has been previously generated by an electronic process in the screen that consumes a certain amount of energy. As for the first frame, if the camera-screen system is in a black box with no other sources of energy, the camera wouldn’t see a thing and nothing would show up in the screen.
It is quite similar - but there is a delay. The camera "sees" a frame, then processes it, and displays it. It is like the dual mirrors, but while the dual mirror setup "instantaneously" shows an infinite array of mirrors-in-mirrors, there is a delay (typically 1/30 of a second) for the camera from frame to frame, so the frame-in-frame happens more slowly.
The other difference is intensity. If the camera is calibrated "perfectly", then the intensity it sees of one frame is accurately represented in the frame-in-frame. If the gain is off even slightly, the inner frames will either end up brighter, or darker, than the outer frames. By contrast, ordinary mirrors only ever absorb light, so that the inner frames will look darker than the outer frames.
Finally - if the camera is focused on the screen, all the "images" will be equally in focus. If you try to observe the mirror-in-mirror images, they are all at a different distance and would require a different focus.
This was commonly used by students to make artsy videos to music that were played on U.S. PBS TV stations.
If the camera and the screen are not perfectly aligned, each frame in the regression is rotated relative to the previous frame. This gives a spiral effect and simply twisting the camera to the rhythm of the music caused the spiral rate to change. Turning in various ways gives the dual mirror effect of a curving tunnel. The tunnel shifts about and twists, etc.
Unlike two mirrors, with the camera you can have the rotation, magnification, or most often used, reduction so that the images get smaller quicker.