How does the distance from a flashlight to a screen affect the size of the illuminated area?

The bigger the distance between the lit torch and the screen, the bigger the illumination area.

Explanation:

Part of the reason is that with increasing distance the light, beam interacts with air molecules that disperse it. The more the air molecules (and note that these air molecules have kinetic energy) it interacts with, the higher the dispersion. It is also important to note that light waves have duality. They also behave like a wave. As a wave disperses from a single point (the torch), it propagates outwards in all direction. The area covered, therefore, increases with distance. Its intensity will also decrease with distance.