How do mirrors reflect light? 

When you say mirror, let's assume we're talking about a silver metal coating, and this is also why other metals are shiny. All atoms have electrons, and these electrons can interact with light. In the case of metals, these electrons are only loosely attached to the metal atoms, so they can move around (which is related to the fact that metals conduct electricity). When light hits the metal, the electrons interact with the light and cause it to reflect. Specifically, light with a given frequency causes the electrons to rattle with that same frequency. In the case of visible and infrared light, which are low frequency, the electrons can match the speed and reflect the light. However, in the case of UV light, the frequency is too high, and the electrons can't rattle fast enough to match the frequency of the light. For this reason, metals are actually transparent to UV radiation!!! So, if you were underneath a piece of metal, it could be totally dark (because no visible light gets through) but still get sun-burnt! Neat!