Touch the Spring

• Wood to build a support stand for the mirror and a small box for the lightbulb
• Black paint
• Two light sockets, only one with an electrical cord and plug
• One 3 × 5 index card (closest metric equivalent is A1)
• A concave mirror with a 16-inch (40-centimeter) diameter (you can also use the bottom mirror from a commercially made Mirage Maker or Mind Boggling Optic Mirage or the smaller, less-expensive 3-D Mirascope—all available from scientific supply houses and various vendors online)
• A lightbulb, 40 to 75 watts (if you are using the toy-sized 3-D Mira­scope, be sure to use a flashlight bulb instead of a full-sized bulb)

1. Make a small wooden box with one open side as shown in the diagram below (click to enlarge). 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 lightbulb.
   
2. Paint all surfaces of the box black.
3. Mount the socket that has no electrical cord or plug so that it is centered on top of the box.
4. 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 diagram above.
5. Build the mirror support as shown in the drawing, and place the mirror in it. (Be careful! These mirrors are easily scratched.)

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.

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 (click to enlarge diagram below).

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.

Although we use a lightbulb here, you can also make a real image of an object that is not illuminated. (In the original Exploratorium exhibit, we used a spring as the object—hence the name of this Snack.)

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.