Mirroring Spoons

We'll start off by understanding the scenario. Take a look at Figure 1. The picture shows two photos. In the left-side photo, the camera captures the reflection of the phone on a spoon facing up. In the right-side photo, the camera captures the reflection of the phone on a spoon facing down. On the phone is a post-it with an arrow. Notice in the first picture, when the spoon is face-up, the arrow is upside down. However, in the second picture with the spoon facing down, the arrow is right-side up. Our question today involves figuring out why this happens. The answer lies in the difference between concave and convex mirrors. When you look straight at a mirror it's simple to determine whether it is concave or convex. If the mirror "caves" out away from you, it is concave. This is seen when you hold a spoon with its face up, as shown on the left side of Figure 1. On the other hand, if the mirror is pushed in towards you, it is convex. This is seen when you hold a spoon with its face down, as shown on the right side of Figure 1. Light rays interact differently with convex mirrors as compared to concave mirrors.

We can predict what we see in certain situations by tracing the path that a light ray takes. Light rays will originate from the phone and go in all directions. These rays will bounce off the mirror (the spoon) and they will meet again at some spot. This spot is where we see the image. It's easiest to understand with an example. Take a look at Figure 2. Let's let the green rectangle be the phone. Light rays (blue) will come off the phone towards the mirror (red). These light rays (purple) will bounce off the mirror and they will meet at some point. This is the point where the mirror image (light green) will form. Take some time to look at Figure 2 and understand what's going on. You may have noticed that Figure 2 resembles the situation in which the spoon is facing up. This is because they are both concave mirrors, in which the mirror "caves" away from the object. The way the light rays bounce of the mirror in Figure 2 is special to concave mirrors. To put it as simple as possible, concave mirrors try to redirect light towards the perpendicular axis through it (red dotted line). Notice how the image is formed when the light is reflected off the concave mirror. The object (dark green) is above the perpendicular axis (red dotted line), but its image (light green) is below the axis. The object is flipped in the image. This is the case that resembles the upside-down arrow on the left side of Figure 1.

Convex mirrors reflect light in a different manner. When light rays bounce off a convex mirror, they tend to stray away from the perpendicular axis. Refer to Figure 3. Once more, light rays come off from the object to bounce off the mirror. However, reflected rays (purple) will actually never meet. This is because, on a convex mirror, they are pushed away from the perpendicular axis (red dotted line). However, if we draw lines (purple dotted lines) behind them, they will connect to create a virtual image. This is the image that we perceive when we look at the mirror. Notice that for this convex mirror, the image (light green) is on the same side of the perpendicular axis (red dotted line) as the object (dark green). This means that the object is right side up, as shown by the arrow on the right side of Figure 1. Lastly, notice how for both Figure 2 and Figure 3, the image (light green) is significantly smaller than the object (dark green). This is why the reflection of the phone and arrow in Figure 1 is smaller than its real-life size.