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It's slightly more complicated. A shiny polished mirror bounce the 'light' back at a angle whereas a white cloth will not. Instead those angles becomes all messed up due to the lights ability to penetrate further inside the cloth before reflected and so getting diffused in all kind of directions., It also has to do with the material used, a mirror is normally coated with a thin metal layer. That layer when 'hit' by electromagnetic rays (sunlight) reacts by creating a opposing 'field' of EM that stops the sunlight from penetrating. A white cloth creates no such field and so the light can lose itself inside it.