Why don't rough shiny surfaces don't make good mirrors?

Answer 1

The angle of reflection and coherence of the light coming off a surface relies on the surface being smooth to keep the reflected photons returning at very close to the same pattern as it hits the mirror. A rough surface reflects the photons at many different angles - there is some reflection but in general it is so degrade we can barely see a reflection. The law of law of reflection says that for smooth surfaces, the angle of reflection is the same as the angle of incidence. If the light hits at many different angles, the light returned comes at many different angles; not a good thing for perceiving a reflection.