Do mirrors reflect ultraviolet and infrared light too?

There are different types of mirrors. Your bathroom mirror is probably aluminum covered by glass. Aluminum has good reflectivity fairly deep into the infrared part of spectrum. It is reflective but increasingly lossy at UV wavelengths. read more

These can reflect UV and IR light if they are designed to do so. Off-the-shelf options are available roughly between 300-2000 nm, but custom coatings can extend this range. read more

However, if the aluminum is on the Back Side of a piece of glass, the glass will absorb most of the UV light and therefore, No, a back-face mirror will not reflect much of the UV light. Unless the glass is special glass that has a a high transmissivity for UV. read more

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. read more