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bouquet

Nineteenth-century books of science recreations often included the “phantom bouquet” (Figure A), which produced an upright real image of a bouquet of flowers hidden in a box below. The flowers had to be upside down because the concave mirror inverts the image.

You can duplicate this pretty effect with the concave side of a large shaving or cosmetic mirror, as shown in the old engraving in Figure A.

A somewhat more stable version uses a wooden box or stand enclosing the bouquet on all sides except the one facing the mirror. Paint the inside of the box matte black, or, better yet, line it with black plush or velvet cloth. Illuminate the bouquet, perhaps with a small desk lamp. The bouquet, and its image, will both be a distance R from the mirror, where R is the mirror’s radius of curvature.

A nice variation is the “phantom light bulb.” A light socket is fastened to the top of the box, and a second one is fastened upside down inside the box below it. Only the latter is powered. When the lower bulb is lit, its image appears in the socket above, if everything has been well aligned. If you use a clear bulb, get two of them. Put one bulb in each socket. Turn on the power, and the bulb above seems to be glowing. You can then unscrew the bulb and remove it, yet its phantom remains.

If you use a small-diameter mirror, the object should be relatively small. Use an old Christmas lamp and socket, or a decorative candelabra lamp. Frosted bulbs work best. Electrical and electronics supply stores have sockets that can be mounted on a flat surface.

One problem remains. You need a large concave mirror for the most effective presentation, and shaving or cosmetic mirrors are a bit small. Larger mirrors can be purchased at scientific supply houses, but are a bit pricey.

An Educational Toy and A Work of Art

For less than $50 you can buy such mirrors, packaged as a device that produces another neat version of this illusion. The Mirage is made by Opti-Gone (optigone.com) in two versions: with 9″ or 22″ mirror diameter.

Assembled, it looks something like the conventional flying saucer, complete with a hole in the top from which you’d expect tiny aliens to emerge (Figure B). It’s sold by science stores, museum shops, and science-supply sources.

Most people put this device on a table and display the illusion as a work of art (Figure C). But I’m sure MAKE readers will want to take it apart and see what else can be done with its parts.

The Mirage consists of two parabolic mirrors, the upper one having a large hole in its center. The mirrors fit together in a clamshell arrangement, separated exactly two focal lengths apart. When light from a distant object falls on a spherical mirror, the rays converge to a point called the focal point that is about R/2 from the mirror, where again R is the mirror’s radius of curvature. The convergence isn’t perfect, and it’s much better when the mirrors are parabolic. For mirrors this size, you don’t notice the slight difference between spherical and parabolic.

The mirrors of the Mirage can be used separately. In a darkened room, let the light from an open window fall onto one mirror. An image of the window will appear near the mirror’s focal point. You can only see it if the reflected rays from the mirror surface enter your eyes, so you have to look back toward the mirror surface. This is a bit tricky because your head gets in the way of some of the incoming light. Or, you can place a small sheet of paper at the image location, and see a reduced-size image of the window projected onto the paper.

You can also demonstrate the convergence of distant light to a focal point by using the sun as a distant source. A small tissue of paper placed at the focal point can be easily ignited.

CAUTION: Don’t let reflected sunlight fall into your eyes. Never look directly at the sun using any optical instrument, such as binoculars or a mirror. Children should always be supervised when doing experiments with bright light.

Physicists call these images real images because convergent light really passes through them, and then diverges just as scattered light would diverge from a real object. Real images are distinguished from virtual images, such as those from a flat or convex mirror, where the light rays don’t actually pass through the space where the image appears to be located.

Touching the Real Image

Using only one mirror, place your finger at a distance of about R from the mirror’s center. You should see a real image of your finger. With a little manipulation of its position you can create the illusion of your real finger just touching the real image of your finger

(Figure D). Since you have two eyes, you see this illusion in three dimensions and can confirm the location and orientation of the real image in space. Note that the image is reversed in all ways: up/down, right/left, and top/bottom.

The Phantom Reflects

Carefully place a small object at the very bottom of the lower mirror. Now assemble the clamshell with the upper mirror in place. Floating just above the hole in the upper mirror, you’ll see a real image of the object inside (Figure E). Note that the image is rotated 180° about a vertical axis, with respect to the object, but the image is still right side up.

One illuminating demonstration isn’t mentioned in the user’s manual. Place the mirrors in the standard arrangement, with a small object inside. Its image appears just above the hole. Now shine a flashlight onto the image, but aimed so that the light actually passes down into the hole of the upper mirror. The image will display shadowing just as if it were a solid object being illuminated by the flashlight. This can be startling if done in a darkened room with the flashlight as the only source of light.

Aim a laser pointer beam at the image (again, at an angle such that the beam really passes through the mirror hole), and a small spot on the image will be illuminated by the laser beam (Figure F). You can even use a small, flat mirror as an object, then get a reflected image from the image of the mirror!

The ray diagram (Figure G) for this device reveals the reason. Room light falling from many directions through the hole illuminates the object lying on the bottom mirror. It scatters onto the top mirror, then reflects to the bottom mirror and back up through the hole. All rays from a particular point on the object finally converge to a particular point on the image, just above the hole, and then diverge just as scattered light would diverge from a solid object.

But what about the laser beam? Here an important principle of optics comes into play. The path of light through optical systems is reversible. Light from an object point may take a complicated path to reach the image point. But light from that image point can be directed back to reach the object point. When you send a laser beam through a point on the image, it reaches a point on the object, then scatters, and goes back through the optical system to the image point again, and proceeds as if it originated there.

Other Demonstrations

» The Mirage comes with a small, pink plastic pig. Lay it on its side, and its image will appear to have accidentally fallen over. Now watch people, seeing this for the first time, reach for the pig to set it upright, and find nothing there.

» Place a coin in the center of the lower mirror. Put a sheet of flat glass over the upper hole. The coin image seems to be resting on the glass. Place a real coin on the glass, aligned perfectly. Tell your victim how real the image looks, then reach down and pick it up, leaving the real image there.

» A single Mirage mirror can be used in the vertical position to re-create the classic phantom bouquet and phantom light bulb illusions.

» Sound reflects in the same manner as light, so a mirror can be used to make a parabolic microphone. Put a microphone at its focal point. One mirror can be used as a sound transmitter and the other as a receiver, separated by large distances (Figure H).

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