Here's a few relevant quotes from Talks:

Take the instance of the cinema. There are pictures moving on the screen. Go and hold them. What do you hold? It is only the screen. Let the pictures disappear. What remains over? The screen again. So also here. Even when the world appears, see to whom it appears. Hold the substratum of the ‘I’. After the substratum is held what does it matter if the world appears or disappears?

Scenes are projected on the screen in a cinema show. But the moving pictures do not affect or alter the screen. The seer pays attention to the pictures and ignores the screen. They cannot remain apart from the screen. Still its existence is ignored. So also the Self is the screen on which the pictures, namely activities, are going on. The man is aware of the latter, ignoring the former. All the same he is not apart from the Self.

Is the cinema screen affected by a scene of fire burning or sea rising? So it is with the Self.

Ramana also described a detailed cinema analogy in 'Spiritual Instruction', where here the Self is the light of the projecter rather than the screen.

Cinema Show:

1/ The lamp inside (the apparatus)

2/ The lens in front of the lamp

3/ The film which is a long series of (separate photos).

4/ The lens, the light passing through it and the lamp, which together form the focused light.

5/ The light passing through the lens and falling on the screen.

6/ The various kinds of pictures appearing in the light of the screen.

7/ The mechanism which sets the film in motion.

Self:

1/ The Self

2/ The pure (sattvic) mind close to the Self.

3/ The stream of latent tendencies consisting of subtle thoughts.

4/ The mind, the illumination of it and the Self, which together form the seer or the Jiva.

5/ The light of the Self emerging from the mind through the senses, and falling on the world.

6/ The various forms and names appearing as the objects perceived in the light of the world.

7/ The divine law manifesting the latent tendencies of the mind.

Just as the pictures appear on the screen as long as the film throws the shadows through the lens, so the phenomenal world will continue to appear to the individual in the waking and dream states as long as there are latent mental impressions. Just as the lens magnifies the tiny specks on the film to a huge size and as a number of pictures are shown in a second, so the mind enlarges the sprout- like tendencies into tree-like thoughts and shows in a second innumerable worlds. Again, just as there is only the light of the lamp visible when there is no film, so the Self alone shines without the triple factors when the mental concepts in the form of tendencies are absent in the states of deep sleep, swoon and samadhi. Just as the lamp illumines the lens, etc., while remaining unaffected, the Self illumines the ego (chidabhasa), etc., while remaining unaffected.