Benham's Disk - A rotating black-and-white disk produces the illusion of color!

   

Benham's Disk

A rotating black-and-white disk produces the illusion of color.

When you rotate this black-and-white pattern at the right speed, the pattern appears to contain colored rings. You see color because the different color receptors in your eyes respond at different rates.

• Posterboard or cardboard
• Glue stick or other suitable adhesive
• Pattern disk (provided here)
• Access to a copy machine
• A black marking pen
• A rotator You can use a turntable, variable speed electric drill, hand drill, portable electric mixer, or electric screw driver. Attach the disk with adhesive Velcro™, or if a drill with a chuck is used, a bolt can be used as a shaft, with two nuts to hold the disk. You can also reduce the size of the disk on a copy machine, then mount it on the flat upper surface of a suitable toy top, or you can devise your own spinner for the disk. Try spinning the mounted disk on a pencil point, or on a pushpin stuck into a pencil eraser.
• Adult help

 

(15 minutes or less)

Copy the pattern disk in the drawing provided as a separate page, here and mount it on a cardboard backing with the adhesive. If your copier does not make good solid blacks, fill in the black areas with a black marking pen. You can reduce or enlarge the pattern disk if you like.

Attach the mounted disk to a rotator. 
 

(15 minutes or more)
Spin the disk under bright incandescent light or sunlight. (Fluorescent light will work, but there is a strobing effect that gives the disk a pulsating appearance and makes it harder to look at.)

Notice the colored bands that appear on the disk. Look at the order the colors are in. What color do you see at the center? What about the next few bands?

Reverse the direction of rotation and compare the order of colors again, from the center of the disk to the rim.

Try varying the speed of rotation and the size of the pattern, and compare the results with your initial observations. 
 

Different people see different intensities of colors on this spinning disk. Just why people see color here is not fully understood, but the illusion involves color vision cells in your eyes called cones.

There are three types of cones. One is most sensitive to red light, one to green light, and one to blue light. Each type of cone has a different latency time, the time it takes to respond to a color, and a different persistence of response time, the time it keeps responding after the stimulus has been removed. Blue cones, for example, are the slowest to respond (have the longest latency time), and keep responding the longest (have the longest persistence time).

When you gaze at one place on the spinning disk, you are looking at alternating flashes of black and white. When a white flash goes by, all three types of cones respond. But your eyes and brain see the color white only when all three types of cones are responding equally. The fact that some types of cones respond more quickly than others -- and that some types of cones keep responding longer than others -- leads to an imbalance that partly explains why you see colors.

The colors vary across the disk because at different radial positions on the disk the black arcs have different lengths, so that the flashing rate they produce on the retina is also different.

The explanation of the colors produced by Benham's disk is more complicated than the simple explanation outlined above. For example, the short black arcs that are on all Benham's disks must also be thin, or no colors will appear. 
 

Benham's disk was invented by a nineteenth-century toymaker who noticed colors in a black-and-white pattern he had mounted on a top. Toy spinning tops with Benham's disks are still available in the Exploratorium Store and in toy stores.

The three different color sensors in a color television camera also have different latency and persistence times. When a color television camera sweeps across a bright white light in its field of view, it often produces a colored streak across the television screen.

When your eye scans a black-and-white pattern containing fine detail, you will sometimes see subtle colors. For more information, see the book Seeing the Light, by David Falk, Dieter Brill, and David Stork (Harper & Row, 1986).

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Balancing Stick - Does it matter which end is up?

Balancing Stick

 

Does it matter which end is up?

The distribution of the mass of an object determines the position of its center of gravity, its angular momentum, and your ability to balance it! 

 

• One 1/2 inch (1.25 cm) wooden dowel, approximately 3 feet (90 cm) long.
• A lump of clay. (such as electrical tape). 

 

(5 minutes or less)
Place a lump of clay about the size of your fist 8 inches (20 cm) from the end of the dowel.

(5 minutes or more)
Balance the stick on the tip of your finger, putting your finger under the end that's near the clay. Now turn the stick over and balance it with the clay on the top. Notice that the stick is easier to balance when the clay is near the top.

The dowel rotates more slowly when the mass is at the top, allowing you more time to adjust and maintain balance. When the mass is at the bottom, the stick has less rotational inertia and tips more quickly. The farther away the mass is located from the axis of rotation (such as in your hand), the greater the rotational inertia and the slower the stick turns. An object with a large mass is said to have a great deal of inertia. Just as it is hard to change the motion of an object that has a large inertia, it is hard to change the rotational motion of an object with a large rotational inertia.

You can feel the change in inertia when you do the following experiment. Grab the end of the dowel that's near the clay. Hold the dowel vertically, and rapidly move the dowel back and forth with the same motion you would use to cast a fishing line. Next, turn the dowel upside down, and hold it at the end that is farthest from the clay. Repeat the casting motion. Notice that it is much harder to move the dowel rapidly when the clay is near the top. The mass of the stick has not changed, but the distribution of the mass of the stick with respect to your hand has changed. The rotational inertia depends on the distribution of the mass of the stick.

As an alternative, do not demonstrate the Snack in advance. Instead, give a group of people the clay and dowel separately, and challenge them to see who can balance the dowel the longest. Let them discover the role of the clay.

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Balancing Ball - Suspend a ball in a stream of air!

Balancing Ball

 

Suspend a ball in a stream of air

A ball stably levitated on an invisible stream of air is a dramatic sight. When you try to pull the ball out of the airstream, you can feel a force pulling it back in. You can alsofeel that the airstream is being deflected by the ball. This Snack shows one of the forces that give airplanes lift. 
 

Small Snack

• A hair dryer (blower)
• A spherical balloon or table tennis ball
• Tissue paper
• Optional: a stand for the blower

Large Snack

• A vacuum cleaner
  It should come with a reversible hose, like a Shop Vac has, so it can be used as blower.
• A light-weight vinyl beach ball
• Tissue paper
• Optional: A stand for the hose

 

None required. Note, though, that you can make a large or a small Snack (see "Materials"). Depending on the blower you choose, some experimentation may be necessary to find a satisfactory ball. You might want a partner to help you, or you can devise some sort of stand for the blower. That way, your hands will be free to experiment with the ball in the airstream.

(5 minutes or more)
Blow a stream of air straight up. Carefully balance the ball above the airstream. Pull it slowly out of the flow. Notice that when only half the ball is out of the airstream, you can feel it being sucked back in. Let go of the ball and notice that it oscillates back and forth and then settles down near the center of the airstream.

With one hand, pull the ball partially out of the airstream. With the other hand, dangle a piece of tissue paper and search for the airstream above the ball. Notice that the ball deflects the airstream outward. On the large version of this Snack, you can actually feel the deflected airstream hit your hand.
Tilt the airstream to one side and notice that the ball can still be suspended.

Balance the ball in the airstream and then move the blower and the ball toward a wall (try the corner of a room). Notice the great increase in height of the suspended ball. 
 

When the ball is suspended in the airstream, the air flowing upward hits the bottom of the ball and slows down, generating a region of higher pressure. The high-pressure region of air under the ball holds the ball up against the pull of gravity.

When you pull the ball partially out of the airstream, the air flows around the curve of the ball that is nearest the center of the airstream. Air rushes in an arc around the top of the ball and then continues outward above the ball.

This outward-flowing air exerts an inward force on the ball, just like the downward flow of air beneath a helicopter exerts an upward force on the blades of the helicopter. This explanation is based on Newton's law of action and reaction.
Another way of looking at this is that as the air arcs around the ball, the air pressure on the ball decreases, allowing the normal atmospheric pressure of the calm air on the other side of the ball to push the ball back into the airstream.

People immediately raise several questions when they hear the second explanation:

Why does air flowing over a surface in an arc exert less pressure on that surface? To answer this question, consider a rider in a roller coaster going over the top of a hill at high speed. The force that the rider exerts on the seat decreases as the rider goes over the top of the hill. In the same way, the air that arcs around the side of the ball exerts less force on the ball.

Why does air follow the surface of the sphere? Consider what would happen if the air did not curve around the ball. An "air shadow" would be formed above the ball. This air shadow would be a region of low pressure. The air would then flow into the low-pressure air shadow. So the air flows around the ball.

An alternative explanation is provided by the Bernoulli principle. If you pull the ball far enough out of the airstream, then the air flows over only one side of the ball. In fact, the airstream speeds up as it flows around the ball. This is because the middle of the ball sticks farther into the airstream than the top or bottom. Since the same amount of air must flow past all parts of the ball each second, it must flow faster where it is pinched together at the middle. The Bernoulli principle states that where air speeds up, its pressure drops. The difference in pressure between the still air and the moving air pushes the ball back into the center of the airstream.

When you approach a wall with the balanced ball, the highpressure region under the ball becomes a region of even higher pressure. The air that hits the bottom of the ball can no longer expand outward in the direction of the wall. The higher pressure drives the ball to a greater height.

This exhibit illustrates one of the reasons that airplanes fly. A flat wing will fly if it is tipped into the wind, so that it forces air downward. Newton's third law tells us that for every action there must be an equal and opposite reaction: The reaction to the downward force of the wing on the air is the upward force of the air on the wing. You can feel this lifting force if you hold your hand out the window of a moving car and tip your hand so that it forces the air downward.

A wing that is curved on top will deflect air downward and produce lift even if it isn't tipped. The explanation for this is essentially the same as the one given in this Snack. The wing collides with air, creating a region of high pressure in front of the wing. This high pressure produces drag, which is always associated with lift. The high-pressure air in front of the wing accelerates air over the curved surface of the wing. This air then flows downward behind the wing. Airplanes fly because their wings throw air downward.

It is sometimes said that air must flow faster over the curved top surface of a wing than over the flat bottom. This is said to happen because the air has to meet up again at the far end of the wing, and since the air traveling over the curved path must travel farther, it must travel faster. This is not true. Two parcels of air that start together, then split to flow over different sides of a wing, do not, as a rule, rejoin at the far end of the wing.

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Anti-Gravity Mirror - It's all done with mirrors!

Anti-Gravity Mirror

 

It's all done with mirrors.

A reflection of your right side can appear to be your left side. With this Snack, you can appear to perform many gravity-defying stunts. 

 

• A large, flat, plastic mirror, 2 x 3 feet (60 x 90 cm) or larger
  It is important to get a good, flat mirror, since distortions will ruin the effect. Plastic mirrors are expensive, but glass mirrors can be dangerous. Look in your local yellow pages for a nearby plastics store.
• A length of 2 x 4 inch wood and a router tool, or ring stands and clamps,
  This makes a stand to hold the mirror upright.
• Optional: A sturdy table on which you can stand.
• A partner. Adult help.

 

(with stand:15 minutes or less: without: 5 minutes or less)
You can make a stand for the mirror from a length of 2 x 4 inch wood. Use a router to cut a groove that is just wide enough to slip the mirror into. To help stabilize the mirror, you can nail some scrap wood to the ends of the board. You can also hold the mirror in a vertical position using ring stands and clamps, or just with your hands. An assistant might be of help here.

(15 minutes or more)
Stand the mirror on the floor or on a sturdy table. Put one leg on each side of the mirror. Shift your weight to the foot behind the mirror. Lift your other leg and move it repeatedly toward and away from the mirror. To an observer, you'll appear to be flying. If you use this Snack as a demonstration, you can make the effect more dramatic by covering the mirror with a cloth, climbing onto the table, straddling the mirror, and then dropping the cloth as you "take off."

A person standing with the edge of a large mirror bisecting his or her body will appear whole to a person who's watching. To the observer, the mirror image of the left half of a person looks exactly like the real right half. Or if the person is standing on the opposite end of the mirror, the right half looks like the real left half. The person looks whole because the human body is symmetrical. The observer's brain is tricked into believing that an image of your right side is really your left side. So just straddle the mirror, raise one leg, and you'll fly!

Try this out in department stores that have full-length mirrors available. If your school has a dance room with a mirrored wall and a doorway cut into it, you may be able to use it. With these full mirrors, stand at the edge of the doorway so that just half of your body is being reflected. This will be an even more convincing flight.

The cars that floated across the desert in the movie Star Wars each had a full-length mirror attached along their lower edge, hiding the wheels. A camera pointed at a car saw a view of reflected sand and shadow in the mirror. That is how the cars appeared to float above the sand.

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A flash of light prints a lingering image in your eye.

 

Afterimage

A flash of light prints a lingering image in your eye.

After looking at something bright--such as a lamp or a camera's flash--you may continue to see an image of that object when you look away. This lingering visual impression is called an afterimage. 

• A flashlight
• White paper
• Opaque black tape (such as electrical tape).

(15 minutes or less)
Tape a piece of white paper over a flashlight lens. Cover most of this paper with strips of opaque tape. In the center of the lens, leave an area uncovered, so that the light can shine through the paper. This area should be a square, a triangle, or some other simple, recognizable shape.

(15 minutes or more)
In a darkened room, turn on the flashlight, hold it at arm's length, and shine it into your eyes. Stare at one point of the brightly lit shape for about 30 seconds. Then stare at a blank wall and blink a few times. Notice the shape and color of the image you see. Try again--first focusing on the palm of your hand, and then focusing on a wall some distance from you. Compare the size of the image you see in your hand to the image you see on the wall. Close your left eye and stare at the bright image with your right eye. Then close your right eye and look at the white wall with your left eye. You will not see an afterimage.

You see because light enters your eyes and produces chemical changes in the retina, the light-sensitive lining at the back of your eyes. Prolonged stimulation by a bright image (here, the light source) desensitizes part of the retina. When you look at the white wall, light reflecting from the wall shines onto your retina. The area of the retina that was desensitized by the bright image does not respond as well to this new light input as the rest of the retina. This area appears as a negative afterimage, a dark area that matches the original shape. The afterimage may remain for 30 seconds or longer.

The apparent size of the afterimage depends not only on the size of the image on your retina, but also on how far away you perceive the image to be. When you look at your hand, you see the negative afterimage on your hand. Because your hand is near you, you see the image as relatively small--no bigger than your hand. When you look at a distant wall, you see the negative afterimage on the wall. But it is not the same size as the afterimage you saw on your hand. You see the afterimage on the wall as much bigger--large enough to cover a considerable area of the wall. The afterimage is not actually on either surface, but on your retina. The actual afterimage does not change size; only your interpretation of its size changes.

This helps explain a common illusion that you may have noticed. The full moon often appears larger when it is on the horizon than when it is overhead. The disk of the moon is the exact same size in both cases, and its image on your retina is also the same size. So why does the moon look bigger in one position than in the other? One explanation suggests that you perceive the horizon as farther away than the sky overhead. This perception might lead you to see the moon as a large disk when it is near the horizon (just as you saw the afterimage as larger when you thought it was on the distant wall), and as a smaller disk when it is overhead (just like the smaller afterimage in the palm of your hand).

Negative afterimages do not transfer from one eye to the other. This indicates that they are produced on the retina, and not in the visual cortex of the brain where the signals would have been fused together.

For up to 30 minutes after you walk into a dark room, your eyes are adapting. At the end of this time, your eyes may be up to 10,000 times more sensitive to light than they were when you entered the room. We call this improved ability to see night vision. It is caused by the chemical rhodopsin, in the rods of your retina. Rhodopsin, popularly called visual purple, is a lightsensitive chemical composed of vitamin A and the protein opsin.

You can use the increased presence of rhodopsin to take "afterimage photographs" of the world. Here's how:

Cover your eyes to allow them to adapt to the dark Be careful that you do not press on your eyeballs. It will take at least 10 minutes to store up enough visual purple to take a "snapshot." When enough time has elapsed, uncover your eyes. Open your eyes and look at a well-lit scene for half a second (just long enough to focus on the scene), then close and cover your eyes again. You should see a detailed picture of the scene in purple and black. After a while, the image will reverse to black and purple. You may take several "snapshots" after each 10-minute adaptation period.

For a more complete desciption of this experiment, see Paul Hewitt's Conceptual Physics Lab Manual (HarperCollins College Publishers, New York, 1993).

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