Mirror play
Toddlers and babies often like to look at themselves in a mirror. Babies look in the mirror to see the other baby. At about two-years-old, toddlers realise that it is a reflection of themselves in the mirror.
Toddlers can sometimes be upset when a parent has their hair cut or wears glasses, because they are not sure if you are still the same person. By experimenting with a hat and a mirror, they can see that even when they look different, it's still them.
Your child might enjoy looking into other mirrored reflective objects such as spoons, foil, metallic dishes and plates, and puddles.