English teacher here. Articles in English can be really confusing but essentially we use the definite article in this situation because:
- Uniqueness: In most situations, there's only one mirror in a room or a home that's readily available for someone to look into.
- Generality: Similar to "going to the bathroom," "look in the mirror" refers to the general act of using a mirror to see oneself, not interacting with any specific mirror.
Now there's an idea.