(1 hour or less)
Make a small wooden box with one open side as shown in the drawing. The height of the box should be slightly less than half the height of the mirror, and it should be wide enough and deep enough to hold the light bulb. Paint all surfaces of the box black.
Mount the socket that has no electrical cord or plug so that it is centered on top of the box. Mount the other socket (the one with the cord and plug) upside-down inside the box, directly beneath the empty socket, as shown in the drawing.
Build the mirror support as shown in the drawing, and place the mirror in it.
(30 minutes or more)
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) - 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 a 3 x 5 inch (8 x 13 cm) 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 focal point.
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 that 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.
In the Exploratorium exhibit, 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.
The image you see is formed by the concave spherical mirror. Light rays spreading out from one point on the lightbulb are reflected by the concave mirror so that they come back together at a point in space - creating a real image of that point.
The rays continue on through this convergence point and strike your eye. The lens of your eye brings the rays together once again to create an image on your retina. Your eye and brain can't tell the difference between a retinal image of the reflected bulb and a retinal image of the actual bulb.
In some respects, however, the reflected image of the lightbulb differs from the actual bulb. Placing an object behind the reflected image will obscure the lightbulb. Many people feel queasy when they see this seemingly unnatural occurrence.
Though we use a lightbulb here, you can also make a real image of a nonglowing object. A small plastic animal, like a toy cow or pig, can be fun to use. You can add an additional flourish by shining a flashlight onto the image of the toy animal. A spot of light will appear on the image! The mirror collects the light from the flashlight and then images it onto the real toy animal.
A closely related Exploratorium exhibit that you can create with the same concave mirror is called Shake Hands with Yourself. In this exhibit, your hand is placed two focal lengths from a concave mirror, resulting in a real, inverted image the same size as your hand. This image is also located two focal lengths from the mirror. Thus, your actual hand can touch the image of your hand, and you can "shake hands with yourself."
In 1990 Nakamura began selling a small plastic parabolic mirror with which to make miniature versions of the Touch the Spring exhibit. Related Snack: Parabolas.