When looking directly into a film projector lens, the viewer sees an inverted image because the film is loaded upside down, and the eye's optics further invert the image. However, when projecting onto a screen or paper, the image appears right-side up due to the lens inverting the already inverted film image. The discussion highlights the difference between viewing through the lens as a magnifying glass versus projecting onto a surface, where the light rays behave differently. The eye's position relative to the lens affects the image's focus and orientation. Overall, the inversion of the image is a result of both the film's orientation and the optical properties of the lens and the eye.