Spherical Reflections

• Utility or X-Acto knife
• Round holiday ornaments with mirror-reflective surfaces of any color, with hooks and collars removed (Note: use gloves when handling glass ornaments)
• Box with sides higher than the diameter of the ornaments
• Sheet of Styrofoam the size of the box or larger
• Black construction paper or flat black latex paint (oil-based paint is not recommended because it will dissolve the Styrofoam), enough to cover the bottom of the box

1. Cut the Styrofoam to fit the bottom of the box. 
2. Cover the Styrofoam with black construction paper cut to size or with the flat black paint.
3. Lay the holiday ornaments in the box in a single layer, packed as closely together as possible. Gently but firmly push the stem end of each ball into the Styrofoam so that it’s held securely in place. If you've lined the box with construction paper, push the stem end of each ball into the construction paper so that it makes a mark, then cut the paper at the marked points to make insertion into the foam easier. CAUTION: we recommend wearing gloves if you are handling glass ornaments and push gently or make cuts into the Styrofoam so the ornaments don't shatter.

Look at the mirrored ornaments from various angles. Notice that the image in each ball is a little different from that of neighboring ones. That’s because each mirror “sees” the world from a slightly different vantage point. Notice that if you point your finger at one sphere, the image of your finger in all the other mirrors will point at the chosen sphere.

Also notice that your image is very small in the mirrors and it appears quite far away.

Each round holiday ornament is a convex mirror—a mirror that curves out toward the source of light. Convex mirrors reflect images that are smaller than life size.

In the ray diagram shown below (click to enlarge), notice the reflection of two rays of light from a particular point at the tip of the pencil. Your eye and brain follow these reflected rays backward along a straight line to their apparent intersection behind the mirror. All other reflected rays from the point also seem to originate at this intersection. The reflected rays from all other points on the pencil also appear to intersect at specific points behind the mirror. All these intersection points put together create what’s called a virtual image.

Convex mirrors are often used as security mirrors in stores, since they reveal a broad field of view. Convex rearview car mirrors have a written warning cautioning that objects are actually closer than they appear. Your brain assumes that when a large object—a car, for instance—appears small in a mirror, then the object is far away. In a convex mirror, however, an image that appears quite small can actually be very close.

Where the ornaments come together, light can reflect from one ball to another many times. This results in images of images of images, each becoming smaller and smaller. Looking into the spaces between round holiday ornaments in an array is a good way to see a fractal pattern.