The mirror becomes fogged up due to a process called condensation which occurs when a vapor (gaseous form) to the liquid form without passing through the solid form. As you take the shower, many water vapors are formed that rise up. The mirror’s temperature is quite low; equivalent to vapor’s dew point temperature. This means that whenever vapor comes into contact with the mirror, they are directly converted into dew or liquid form and hence the mirror gets fogged up.
