Monthly Archives - October 2006

Shadows in Science and Art


Shadows are ubiquitous, but often go unnoticed. Shadows are important historically, for they provided early evidence that light travels in straight lines. Humans constantly, but unconsciously, use shadows to judge the shape of objects in their environment. Because shadows reveal much about an object’s extension in space, they are often used to heighten the illusion of depth in a painting.

Lets look at some exploratory activities using shadows that may be used to introduce geometrical optics and demonstrate applications of shadows in perception and the visual arts.

1. Simple Shadows

In a darkened room, use a point source of light to form the shadow of a small object, such as a small box or ball, on a screen. An LED flashlight with a single bulb or automobile tail light bulb serves as a good approximation to a point source. When a single point source is used to illuminate an object, two distinct regions should be observed. In one region, light from the source is completely blocked. This region is referred to as the umbra. Outside the umbra, light is not affected by the object.

When a second point source is introduced as shown in the figure below, you should observe two types of shadowing. Once again there is the umbra, a region on the screen that is in complete darkness. In the umbra, light from the two sources is blocked. Outside the umbra is the penumbra where light from one bulb reaches the screen but light from the other bulb does not.

Now replace the two point sources with what is referred to as an extended source. An extended source may be thought of as a very large number of point sources. A frosted light bulb and a fluorescent tube are examples of extended sources. Describe the shadows produced by an extended source.

To understand the shadows produced by an extended source, it may be useful to remember that each point on the surface of the bulb, acting as a point source, produces its own shadow. When all these point source shadows are superimposed, there will be total darkness (umbra) surrounded by a lighter region (penumbra) where only some of the individual shadows overlap.

During eclipses of Sun, the moon intervenes and casts a shadow on the earth. Observers in the umbra see a total eclipse, while observers in the penumbra see only a partial eclipse.

2001 Solar Eclipse Composite by Wendy Carlos, Williams College.

A Challenge for your Students:

The earth is approximately 93 million miles from the sun. At this great distance, can the sun be considered to be a point source of light? A simple experiment should provide an answer.

The next time you are out on a sunny day examine the shadow produced by a pole, a leaf, your hand, or virtually any other object. How will this observation help you answer the question?

2. Default Assumptions Regarding Shadows

Humans constantly, but unconsciously, use shadows to judge the shape and location of objects in their environment. In doing so, we all rely on the default assumption that sources of light are overhead. We live in a world where light almost always comes from above. Have you noticed how children never cease to be delighted by the effects produced by illuminating the face with a light from below? Why does this always bring chuckles? Humans are simply not used to seeing the shadows formed by a light source located beneath the face.

Sometimes this hard-wired assumption regarding light placement can lead to incorrect conclusions regarding the nature of an object. For example, in is this photograph we see large indentations among an array of rivets on the hull of a ship. This percept is based on the nature of the shadows and the assumption that the light source is overhead. When the photo is inverted, things change dramatically! Rivets become divots, and vice versa.

Image Right side up

Same image turned upside down

While students always enjoy this demonstration, some may ask “who cares.” You may wish to point out to them that astronauts landing on the moon care a great deal about the actual nature of the lunar surface.

In the figure below, we see a crater. However, when the photo is turned upside down (right), the shadows suggest otherwise. We now see a hill.

Crater Image

Crater Image Upside Down

In this photograph from “Walter Wick’s Optical Tricks,” we see a number of pieces of wood on a woodworker’s bench. The odd-shaped pieces of wood are illuminated from above as we can see from the shadows. When the photo is turned upside down, and the shadows shift, we see something entirely different! Do you see the deer surrounded by branches and leaves?

Deer demo of a page from Walter Wick’s Optical Tricks.

We no longer carry “Walter Wick’s Optical Tricks” book.

3.  Shadows in the Arts
Because shadows reveal much about an object’s extension in space, they are one of an artist’s most potent depth cues.  Notice how a circle becomes a sphere with the addition of shadow and shading. Where is the source of light in this drawing?


In this rather simple sketch of an elephant by Rembrandt, the sense of depth and solidity is due in large part to the adroit use of shadows.

Rembrandt van Rijn, An Elephant, black chalk and charcoal, around 1637

In Escher’s “Drawing Hands,” shadow and shading are used to create a sense of three-dimensionality. The hands seem to pop right off the piece of paper.

Escher, Maurits Cornelis: Drawing Hands 1948
In paintings such as “An Experiment on a Bird in the Air Pump” by Joseph Wright, the use of strong contrasts of light and dark may be used to discuss the nature and location of the light source as well as the inverse square law. The rather sharp shadows suggest a point source such as a candle. Notice too that even though the light source cannot be seen, its location can be inferred. And perhaps most importantly, the shadows establish the mood of the painting.

An Experiment on a Bird in an Air Pump by Joseph Wright of Derby, 1768
The scene in Edward Hopper’s “The Night Hawks” is totally devoid of harsh shadows. Why? When this work was created, fluorescent lights had become commonplace. The uniform lighting produced by a collection of extended sources does not produce sharp shadows. The result: a mood of detachment and loneliness.

Nighthawks (1942) by Edward Hopper.

Copyright NoticeThese images are of a drawing, painting, print, or other two-dimensional work of art, and the copyright for it is most likely owned by either the artist who produced the image, the person who commissioned the work, or the heirs thereof. It is believed that the use of low-resolution images of works of art; for critical commentary on, the work in question, the artistic genre or technique of the work of art, qualifies as fair use under United States copyright law.

4. Turning Things Inside Out with Shadows
A demonstration of the power of shadows that never ceases to amaze students involves reversed three-dimensional figures. By manipulating the light striking a concave object it is possible to make it appear convex.

To observe this reversal, cut an L-shaped piece of paper consisting of three segments about two inches square (see figure). Fold at the two lines joining the squares and join them with transparent tape to make half a cube.

With one eye closed, hold the concave corner at arm’s length and orientate it so that it appears to be convex. That is, at some orientation, the concave cube corner will appear to reverse itself! Amazing! Once you have achieved reversal of the corner, rotate it in your hand and notice that the cube appears to turn in the opposite direction.

An inexpensive plastic mask may be used to illustrate the same effect. With one eye closed, the concave side (backside) of the mask appears convex. Furthermore, the face seems to follow you as you move from side to side! Working in concert with the shadow cues is our expectation to see a convex face. We have rarely seen a convex face, so we tend to see what we believe.

Einstein Alive! You have to see it to believe it!

Shine a source of light at the back of this mask and look at the concave side. The mask appears to reverse, as if Einstein is looking at you! Move back and forth, and his face turns to follow you. Move up and down, and he nods his head.
See Einstein Alive

We just received these amazing photos that fit perfectly with our topic, so we thought we would share them with you. Click the link to see the whole series…

3D Mural Artwork by Eric Grohe

Sidewalk Artist Julian Beever amazing sidewalk art

Interesting Links: On colored shadows from the Exploratorium’s Online Science Snacks. Material/ A killer shadow illusion.


Atmospheric Optics: She comes in colors…

The sky offers a wide variety of stunning optical effects. A source of inspiration for poets and songwriters alike, these atmospheric phenomena include red sunsets, rainbows, mirages, halos, glories, and coronas. These effects are the result of the interaction of light from the sun or moon with the gases in the atmosphere, clouds, ice crystals, smoke, dust and other airborne particulates. Some of these phenomena can be seen almost every day; others occur less frequently. In this issue of CoolStuff we will examine examples of atmospheric optical phenomena and how they may be demonstrated in the classroom.

The sky is the daily bread of the eyes.
– Ralph Waldo Emerson

She comes in colors everywhere;
She combs her hair
She’s like a rainbow
Coming colors in the air
Oh, everywhere
She comes in colors…
She’s like a rainbow

– Mick Jagger / Keith Richards

A rainbow is a multicolored, circular band of light. The display of colors is due to refraction and internal reflection occurring in raindrops or other droplets of water.

Making Your Own Rainbow I: 
Direct a fine spray from a garden hose in a direction away from the sun. How far away do you estimate the rainbow to be? If you do this experiment with a group of people, does everyone see the same rainbow? Do you see your shadow? Where is it located in relation to the rainbow? If you want to explore further, stand on a ladder while producing your rainbow. Describe the rainbow you see now.
Making Your Own Rainbow II: 
In a darkened room, place a clear (the clearer, the better) plastic box approximately three-quarters full of water on the stage of an overhead projector. (Note: These boxes are the type often used to store shoes.) Cover or remove the projector’s top lens so that no light is projected into the room. Arrange the water-filled box so that students can see both of the rainbows formed (a rainbow is produced by each long side of the box.) Examine the array of colors produced by the water-filled plastic box. Are the rainbow colors in the same order as in a naturally-occurring rainbow?

Making Your Own Rainbow III: 
Shine light from the bright flashlight or a slide projector through a central hole in a piece of white cardboard. If a water-filled flask is illuminated with the light passing through the hole (see figure) a faint rainbow will appear on the cardboard. It has the shape of a closed circle and its angular distance is about 42 degrees, with red on the outside, as in a naturally occurring rainbow. You will need a completely dark room since the rainbow formed is quite faint.
Spectrum demonstration:
Discussions on rainbows and the optics of the sky always lead to the topic of the electromagnetic spectrum.

Spectrum Analysis Classroom Set

In Stock SKU: P2-9501

Another great classroom tool is the Giant Prism. Use it on your overhead projector to project a large class-size rainbow!

Giant Prism

In Stock SKU: 33-0230

Hiroto Ashikaga; Tottori Technical High School, Syozan 111, Tottori 689-1103 Japan

Making Your Own Rainbow IV: Tiny glass beads, such as those used by your local highway department to make highway signs and street markings highly reflective, may be used to produce rainbows like those seen in the center photo below. The beads, behaving like raindrops, work in concert to form a rainbow.

Most highway and public works departments will gladly give you a container of glass beads. Once you have obtained the beads, cover a piece of black foam core or poster board with a thin layer of spray glue. Now sprinkle the glass beads over the black surface until the surface is completely covered with beads. When a point source of light, such as a Maglite with reflector removed, is used to illuminate the beads, the beads will form a circular rainbow that seems to hover above the cardboard.

Concept: Blue light interacting with molecules in the atmosphere is absorbed and reradiated in all directions. Blue light is scattered much more efficiently than light with longer wavelengths, for example, red and green. As a result of scattering, the sky looks blue no matter where we look. By contrast, to an observer on the moon, the lunar sky appears black because there is no atmosphere to scatter light.

During sunrise and sunset, the distance that light travels from the Sun to an observer on Earth is at its greatest. This means that a large amount of blue light and some green light is scattered. Since white sunlight may be thought of as consisting primarily of blue, green and red light, the blue/green deficient light that we see coming directly from the sun appears red. 

Blue Sky/Sunset Simulation I: One of the most frequently asked questions is “why is the sky blue?” Using very simple equipment, you can demonstrate and explain the phenomenon to your students. Add a few drops of milk or a few grains of powdered milk to water in a beaker or fish tank and stir. The milk particles serve as scatterers just as air molecules do in the atmosphere. When light from a light bulb or slide projector passes through the liquid, scattered blue light may be seen throughout the container.

Shine light from a light bulb or slide projector through the liquid and observe the color of the transmitted light. With much of the blue light removed from the incident white light by scattering, only the orange-red portion of the spectrum remains. When viewed head on through the liquid, the transmitted light actually looks like a setting sun!

If you are using a slide projector and fish tank for the simulation, you may wish to carefully rotate the tank as it is illuminated. Allowing light to first pass through the narrow width, then through the length of the tank, allows students to observe how the color of the sun changes from a yellow-orange to an orange-red as it moves from its noon day position to the horizon.

Blue Sky/Sunset Simulation II: A second method of demonstrating why the sky is blue and the sunset red requires the use of two common chemical substances: dilute sulfuric acid (H2SO4) and sodium thiosulfate (Na2S2O3), hypo used in photography to fix developed films. (Caution: be careful when handling the acid.) First mix three teaspoons of thiosulfate with one liter of water. To this solution add ten to twelve drops of acid. After a few seconds, the solution will take on a bluish tint. With time the color will become more intense, then fainter. After a few minutes the liquid will turn white.

These changes are due to the scattering of white light from tiny grains of sulfur which gradually grow in size as the reaction progresses. Initially, the grains are very small and serve as scattering centers for short wavelengths of light, hence the blue color. Eventually the particles become so large that they scatter all wavelengths of visible light with equal intensity. This accounts for the final milky appearance of the liquid.

Note that a cardboard mask blocks the light not passing through the beaker.

Scattering from particles whose dimensions are much less than the wavelength of light is known as Rayleigh (pron. ray-lee) scattering. Rayleigh scattering is responsible for the blue appearance of the Earth’s sky. The non-preferential scattering by larger particles is known as Mie ( Scattering and is responsible to the white color of clouds.

A beautiful setting sun effect can be achieved by placing a beaker containing the H2SO4 – Na2S2O3 solution on the stage of an overhead projector (see image left). First mix three teaspoons of thiosulfate with one liter of water. To this solution add ten to twelve drops of acid. (Caution: be careful when handling the acid.)

A mirror is used to project the light passing through the beaker onto a screen. As the sulfur particles grow in size, the scattered blue light will become more intense while the light reaching the screen will change from white, to yellow, to orange and finally to a deep red.

The Color of Clouds

Concept: Clouds consist of water droplets and ice crystals that are significantly larger than the wavelengths of visible light. Unlike the smaller gas molecules that make up the Earth’s atmosphere, these larger particles scatter all colors more or less equally.

Looking at a cloud, an observer will, in most cases, receive all wavelengths of light and perceive it as white. However, a cloud’s actual appearance is governed by color of illuminating light, cloud thickness, shadowing by other clouds, age of the cloud, and the brightness of surrounding sky and clouds. Thicker clouds transmit little light and hence may appear darker. Larger droplets in older clouds scatter less and absorb more light than smaller drops and therefore appear darker.
The Whitest Cloud Around:
What we identify as white is simply the brightest gray in sight. A light gray cloud on a bright white background will look much darker than the same cloud on a dark or black background, in which case it might look white and bright. To demonstrate this, obtain a variety of paper samples, each of which appears to be white in isolation. Place them side by side, or cut them so that they can be nested on top of one another, for comparison. Usually only one will be perceived as white; the other samples will appear gray by comparison, as it is with clouds.
A halo is an optical phenomenon due to reflection and refraction of sunlight or moonlight in atmospheric hexagonal ice-crystals. Halos appear as bright rings around the sun or moon. Although they are more common in cold weather, halo-producing cirrus clouds can be present in warm weather. Colored halos are formed by refraction in the crystal; white halos are produced mainly by reflection. (see below left)
Free Download! Double-Slit Diffraction
With just a Laser Pointer and a Laser Printer each of your students can now generate their own double-slit patterns — and it’s FREE!  Click here
Produced by irregularly-sized droplets, these coronal fragments appear as wisps of iridescent pastel colors in clouds.

Cool Coronae:
To produce a corona, simply breathe on a cool piece of glass. More often than not, a corona will be seen by looking at a light source through the water droplets that condense on the glass. If you wear eyeglasses, simply exhale on one of the lenses. When you look at a light source through the lens you will see a corona whose colors change with time. Since the colors produced depend on droplet size, the colors change as the droplets get smaller and finally disappear.

You may not even have to breathe on glass to observe coronae. You may see them through a fogged windshield or on steamed up glass in the bathroom.

Iridescent Cloud in a Bottle: 
Iridescent coronae are often produced by the water droplets that make up thin clouds. So to produce coronae it would seem that all you need to do is make a cloud. Using a gallon jar, a rubber glove, some water and a match, you can do just that. First cover the bottom of the jar with a thin layer of water. Drop a lit match into the jar. Quickly place the fingers of the glove inside the jar and stretch the open end of the glove over the mouth of the jar. Put your fingers the glove and pull the glove outside the jar. Presto! You should see a wispy cloud inside the jar.

To observe a corona, shine light from a bright source such as a slide projector or flashlight through the jar. Initially smoke particles will scatter all wavelengths of light producing a white cloud. As the smoke disappears, leaving smaller droplets, pastel colors will be seen at certain viewing angles. You’ve just observed your first corona in a bottle!

The figure above shows a rare atmospheric optical phenomenon known as a circumhorizontal arc. Caused by the refraction of light through the ice crystals in cirrus clouds, it occurs only when the sun is high in the sky, at least 58° above the horizon.

Reminiscent of a rainbow, the circumhorizontal arc is produced only when the ice crystals making up cirrus clouds are shaped like thick plates. Furthermore, these plates must have their faces parallel to the ground. The chances of having all these conditions satisfied are low, hence the infrequent observation of this amazing optical phenomenon.

Other Cool Sky Stuff

In the photo shown here, the Aurora Australis is seen over the National Science Foundation’s Amundsen-Scott Pole Station.

Aurora Borealis

The Northern and Southern Lights, or more formally Aurora Borealis and Aurora Australis respectively, are produced when charged particles from the Sun pass through the Earth’s upper atmosphere. The high-speed particles energize gas molecules which in turn emit the ephemeral colored lights we associate with the Aurora.

This image is courtesy of UK photographer Rich Lacey. While spending time in Northern Canada Rich had to opportunity to capture the best Aurora photos we’ve seen. You can see more of his images and order prints for your class on his web site at

Light Pillars

Often seen in very cold weather, light pillars seem to be beaming up from terrestrial light sources such as street lamps. Many initially mistake light pillars to be searchlights. Light pillars result from the reflection of light from hexagonally-shaped, plate-like crystals. These crystals fall with their flat surfaces in a horizontal orientation. The flat surfaces serve as mirrors, reflecting the sun’s light downward.

A sun pillar is a vertical shaft of light extending upward or downward from the sun. Like light pillars, they are produced when sunlight reflects off the surfaces of plate-like ice crystals. Sun pillars are usually seen at sunrise or sunset when the sun is low on the horizon.

Interesting Links:

Northern Lights!

About Rainbows

Atmospheric Optics


Weather Optics