These ornaments are available in the months preceeding Christmas from Michael's Craft Stores.
Using a band saw cut the top off one half of the ornament creating a circular hole that is about 3.5 cm in diameter. You will be trimming only 0.5 cm off the top. Then trim a slice 1.8 cm off the bottom of the same half. Remove the little bits of plastic carefully with a soft cloth. Place the trimmed half inside the unaltered half.
Place an object, such as a pushpin, inside the sphere. View the image at an angle nearly horizontal to your eye. Locate the image of the object that has the same orientation as the object. Touch the image with a finger.
You are seeing an image formed by two concave mirrors facing one another. The object is placed at the center of the bottom mirror. The curvature of the mirrors is such that the object is at the focal point of the top mirror.
When light from a point on the object hits the top mirror, it reflects in parallel rays. These parallel rays hit the bottom mirror and reflect so that they reassemble to form a point located at one focal length from the bottom mirror. The mirrors are placed so that the focal point of the bottom mirror is located at the hole in the top of the device. The end result is that light from every point on the object is assembled into an image in the hole.
The ray diagram may help explain this effect.
Heidi Strahm Black