Why do two beams of light pass through one another without interacting?

Why is it that if I have two torches, each shining rays in perpendicular directions at perpendicular screens, such that the beams cross, then the images on the respective screens are independent of whether the alternate torch is switched on? In other words, why does light seem to pass through itself without interacting?

Apologies if this question is basic, and apologies if there is a similar question somewhere on the site but I haven't managed to find an answer.

Thanks, A.