Plug in the lightbulb and place the box with its open side facing the mirror. To find the focal length of the mirror, place the mirror far from the lightbulb—at least 20 feet (6 m) away—so that its concave (hollow) side is facing the lightbulb. The mirror will then make a real image of the lightbulb close to the focal point of the mirror. Find the distance from the center of the mirror to the image of the lightbulb, and you will find the focal length of the mirror.
To find the location of the image, take the file card and hold it near the center of—and touching—the surface of the mirror. Move the card slowly away from the mirror. When the image of the bulb is in sharp focus, the card is near the mirror’s focal point. The distance from the focal point to the mirror is the focal length.
Place the mirror two focal lengths from the lightbulb. The concave mirror will reflect an image of the glowing bulb. This image will appear in space in front of the mirror. By carefully adjusting the vertical and horizontal position of the box, you can position the image so that it appears to be in the empty socket on top of the box. (You may have to place magazines or books under the box to adjust its height.)
The illusion works best in a darkened room. Have people stand back about 15 feet (5 m) so they see a bulb in the upper socket. Then have them move slowly toward the bulb. They may have to bend or straighten slightly or move right or left slightly to maintain an undistorted image. When they are about 6 feet (2 m) from the image of the bulb, pass your hand through it. The illusion of your hand passing right through a lightbulb is impressive, even when everything is out in the open.
The Exploratorium has an exhibit that showcases this illusion. Everything is inside a large cabinet. To touch the image, you must reach through a small opening. The cabinet hides all the clues and enhances the illusion but is a more elaborate construction project with associated storage problems.