(Note: light scattering is actually a quite complex idea and there are various types of scattering that occur based on several factors like the relative size of the light wavelength and the size of the particles. These issues are well beyond the scope of this text.)
Remember that light travels in waves.
We see this in a movie theater when you look up and can see the movie going to the screen.
In order to see the movie on the screen, the projector shines light at the screen. The light bounces off of the screen and goes into your eye.
In order for you to see the "beam" of light traveling TO the screen, the light would have to change direction on the way.
Since we know that light travels in straight lines, the only way that this is possible, is if the light was re-directed by particles in the air. In a theater, those particles are generally dust.
This same effect is related to why the sky is blue.
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