Look at the back of a spoon and your reflection appears right side up. Look into a spoon's bowl, and your reflection's upside down. How come?
To answer this, imagine a giant spoon bowl, five feet tall, and a bucketful of extra-bouncy superballs. Don't worry, we'll get back to the real spoon, but this is a good place to start. Light bounces off mirrors much like superballs bouncing off hard surfaces. Let's walk around to the back of the giant spoon and start throwing!
When you bounce a ball off the top of the outward curving surface, it bounces up and away, eventually hitting the ceiling. Throw one at the bottom and it bounces down toward the floor. These bouncing balls show you the path light would take when it reflects off the back of a real spoon (although light bounces into your eye, not out of it). As these bouncing superballs show, the spoon's top reflects the ceiling, and the bottom reflects the floor. In other words, the reflection is right side up.
Now let's walk around to the concave inner surface of our giant spoon. When you throw a ball at the top now, that downward curving angle pushes the ball down, toward the floor. When you throw one at the bottom of the curved surface, that upward sloping angle will make the ball bounce up toward the ceiling. Just like before, these bouncing balls show you the path reflecting light would take off a real spoon. In this case, the top reflects the floor, and the bottom reflects the ceiling. What does that mean? It means your reflection appears upside down!