Study Guide for the Reflections Event Thursday, January 23, 2014
This study guide provides material to assist coaches in teaching concepts of light, color and optics to 4th- and 5th-graders. Some background material on atomic properties of matter is also included, but kids will not be responsible for understanding it. This study guide draws heavily from Paul G. Hewitt’s Conceptual Physics, an excellent introduction to many physical concepts. What is light? Light consists of electromagnetic waves. Electricity can be static, like what holds a balloon to the wall or makes your hair stand on end. Magnetism can also be static like a refrigerator magnet. But when electricity and magnetism change or move together, they make waves -‐ electromagnetic waves. Shake the end of a stick back and forth in still water, and you will produce waves on the water surface. Shake an electrically charged rod back and forth in empty space, and you will produce electromagnetic waves. Waves can be described in terms of their wavelength, frequency, and energy. The source of all waves-‐ water, sound, and light waves-‐ is something that is vibrating. The frequency of the vibrating source is the same as the frequency of the resulting wave. How quickly something vibrates is its frequency (the number of vibrations per second). When something vibrates more frequently we say it has a high frequency. A lower frequency means fewer vibrations per second. Wavelength is the distance from wave crest to wave crest (think of the distance between successive water wave peaks). Something that vibrates more frequently (with higher frequency) typically has greater energy. Wavelength, frequency, and energy are all related to each other. Shorter wavelengths result from a source that is vibrating more frequently (higher frequency), with greater energy. Longer wavelengths result from a source that is vibrating less frequently (lower frequency) with lower energy. The wavelengths of the light we can see range from 400 to 700 nanometers (or billionths of a meter). The frequency is the number of waves that pass a point in space during any time interval, usually one second. We measure it in units of vibrations (waves) per second, or Hertz. The frequency of visible light determines its color, and ranges from about 430 trillion hertz, seen as red, to about 750 trillion hertz, seen as violet. Electromagnetic waves in this frequency range activate the “electrical antennae” in the retina of the eye.
The Electromagnetic Spectrum In a vacuum (a space devoid of matter) all electromagnetic waves move at the same speed (“c” for constant speed). The waves differ from one another in their frequency. The classification of EM waves according to their frequency (wavelength and energy) is the EM spectrum. Electromagnetic waves are everywhere. Our universe is a dense sea of radiation.
Transparent Materials Just as a sound wave can force objects into vibration, a light wave can force electrons of materials into vibration. Materials such as glass and water allow light to pass through in straight lines-‐ these materials are transparent to light. Atomic Model (background information) To understand how light gets through a transparent material we must first be able to imagine what an atom looks like. For this, a useful model to describe an atom is a solar system model of the atom. An atom is made up of a dense nucleus and orbiting electrons, much like our solar system has planets orbiting the sun. Now visualize the electrons in an atom to be connected by springs to the atomic nucleus. When light shines on them, they vibrate. Materials that are springy (elastic) respond more to vibrations at some frequencies than others. (Everything has a natural frequency at which it tends to vibrate. Using another sound analogy, just as bells ring at particular frequencies, with high or low pitch, and tuning forks vibrate at a given frequency, so do electrons have natural frequencies that depend on how strongly they are attached to their atoms or molecules.)
Electrons in glass have a natural frequency in the ultraviolet range. When UV light shines on glass, resonance occurs and vibrations build (like pushing someone on a swing and having your pushes match the natural back and forth of the swing causing it to go higher and higher). Resonating atoms in glass can hold onto the energy of UV light for quite a long time. During this time the atom vibrates and collides with neighboring atoms and gives up its energy as heat. Thus, glass is NOT transparent to UV light; the energy of the UV light is not re-‐emitted. At lower frequencies, like visible light, electrons in glass vibrate just a little so they hold onto the energy for less time, with fewer chances for collisions with neighboring atoms and molecules, and less energy transformed to heat. The energy of the vibrating electrons is re-‐emitted as visible light.
Clear glass is transparent to all frequencies of visible light. The frequency of the re-‐emitted light that is passed, in a chain of absorptions and re-‐emissions, from molecule to molecule through the glass, is the same as the frequency of light that shined on it. The principal difference is a slight time delay between absorption (“gulp”) and re-‐emission (“burp”). This time delay results in a lower average speed of light through a transparent material. In a vacuum, light travels at 300,000 kilometers per second (186,000 miles per second); this is a constant, “c”. Although light travels extremely fast, its speed is still finite, and in vacuum that speed is independent of frequency, wavelength, and energy. For example, it takes sunlight about eight minutes to travel from the Sun to the Earth. Light travels a bit slower than this in the atmosphere (but it is still usually rounded to “c”). In water it travels 75% of c (.75 x c); in glass approximately 67% of c; and in diamond 41% of c. Infrared waves, with frequencies lower than visible light, vibrate not just the tiny springy electrons, but entire molecules of the glass. This vibration increases the internal energy and temperature of the glass-‐ which is why IR waves are often called heat waves. Glass is transparent to visible light, but not to ultraviolet and most infrared light. Opaque Materials Opaque materials absorb light without re-emission. The vibrations caused by light turn into random kinetic energy (energy of motion)-‐ internal energy-‐ and they become slightly warmer. The Earth’s atmosphere is transparent to visible light and some IR , but, fortunately, it is quite opaque to high frequency UV waves. Small amounts of UV getting through can cause sunburns. Color Perception (background) Strictly speaking, the colors of objects are not in the substances of the objects, or even in the light they emit or reflect. Color is in the eye of the beholder. Color vision is possible because of the cones in the retina of the eye. The retina is the back part of the eye that has cells that respond to light. Cones resonate to the incoming light like little antennae. The color we see depends on the frequency of light we see. Different frequencies are seen as different colors, from low-‐frequency red light to high-‐ frequency violet light, with an infinite number of hues in between. We group them into seven colors – red, orange, yellow, green, blue, indigo, and violet. Together these colors appear white.
Selective Reflection Most objects reflect light, rather than emit light, and they reflect only some of the light that shines on them. This reflected portion of the light gives the objects their color. Colors of things depend on the colors of light that illuminate them. A red apple reflects red light. If sunlight is passed through a prism to separate the colors (frequencies), the apple will appear brown or black in all parts except when it is illuminated by the red part of the rainbow. This shows that the red apple has the ability to reflect red light, but not other kinds of light. (Green leaves reflect green and absorb, to varying degrees, other light. Some of the energy of the absorbed light is used to drive the chemical reactions involved in photosynthesis.) Atomic View (background): Atoms and molecules have their own natural frequencies. Electrons of one type of atom (those in the skin of the apple) can be set into vibration at frequencies that are different from the frequencies of other atoms (those in the leaves). At the resonant frequencies (where the electrons natural vibrations are magnified), light is absorbed. At frequencies above and below the resonant frequency, light is re-‐emitted. Reflected light travels back into the medium from which it came. A white sheet of paper reflects all visible frequencies and will appear the same color as the light that shines on it. A black piece of paper absorbs all frequencies, and reflects none. (It absorbs the light because the frequency of vibration of the light waves matches the natural frequency of vibration of the atoms in the object, so the electrons get really “bouncy”. As a result, atoms collide with one another and the object gets warmer.) Black objects get warmer when light shines on them. The reflected colors of most objects are not pure single frequency colors, but a spread of frequencies. Color Depends on the Light Source Objects can only reflect frequencies present in the illuminating light source. Candle light does not have much blue in it; it is yellowish. Incandescent light bulbs give light that is richer in the lower frequencies, enhancing the reds. Fluorescent lights give more of the high frequencies, so blues are enhanced under them. It is sometimes difficult to tell the true color of objects. Colors appear different in sunlight from when illuminated by various lamps.
Mixing Colored Light When sunlight is passed through a prism, or a glass of water to land on a wall, the resulting rainbow colored spectrum demonstrates that white light from the sun contains all the visible frequencies. Solar frequencies are most intense in the yellow-‐green part of the spectrum and our eyes have evolved to have maximum sensitivity in this range. (We see a yellow-‐green fire engine better than a red one.) The perception of white light also results from the combination of only red, green and blue light because we have cones in our eyes that are sensitive to the low (red), middle (green) and high (blue) frequency range of the visible spectrum. If we project these three colors, independently, on a screen, overlapping each other, the colors add to produce white. When beams of light reflect off a white screen, the light is seen as an additive mixture because the beams are added together before we see them. By adding red, green, and blue, in various amounts, we can produce any color in the spectrum. Red, Green, and Blue are called additive primary colors Red + Green + Blue = White A television creates various colors by mixing together bright red, green and blue light in different proportions. This is also how computer monitors (RGB monitors) generate colors. Cyan (turquoise), magenta (light purple), and yellow are the complementary colors of red, green, and blue.
Try this: Using the color paddles in your kit, experiment to determine what combination of primary colors gives each of the complementary colors. Directions: Hold a red color paddle in front of one flashlight, and a green color paddle in front of another flashlight (or rubber band 1-‐2 sheets of red cellophane over one flashlight, and green cellophane over another flashlight). Go into a darkened room, turn the flashlights on and shine them against a white wall so that the beams overlap. Record below the color combinations you discover: Red + Green = _________ Red + Blue = ___________ Green + Blue = _____________ Key: R + G = Yellow R + B = Magenta G + B = Cyan Complementary colors are any two colors that can be added together to produce white. Red + Cyan = White Green + Magenta = White Blue + Yellow = White Now, since R + G + B = White, can you see why red and cyan are complementary colors? Answer: Red + Cyan = R + (G + B) = White Mixing Colored Pigments Mixing colored paints (inks, dyes, crayons) is an entirely different process from mixing colored lights. When colored lights are mixed, we are adding frequencies of light (colors). When paints are mixed, we are subtracting frequencies. Another way to make colors is to subtract (absorb) some of the frequencies of light, and thereby remove them from the white light combination. The absorbed colors are the ones you don't see -‐-‐ you see only the colors that come bouncing back to your eye. This is known as subtractive color, and it's what happens with paints and dyes. The paint or dye molecules absorb specific frequencies and bounce back, or reflect, other frequencies to your eye. The reflected frequency (or frequencies) are what you see as the color of the object. Recall the example of the red apple and the green leaves. The green leaves contain a pigment called chlorophyll, which absorbs the blue and red colors of the spectrum and reflects the green.
Atomic View (background): You can explain absorption in terms of atomic structure. When the frequency of the incoming light wave is at or near the natural vibration frequency of the electrons in the material, the electrons resonate and hold onto the energy longer. As a result, the amplitude of the electron oscillations increases and atoms collide, giving up this energy as heat. Let’s consider color in terms of the three primary colors red, green and blue. Red pigment absorbs green and blue light and allows red to get through. This is selective transmission.
Think about it: What light would be reflected by a mixture of red and green pigments? Recall that when red and green colored lights are added, the complementary color yellow is seen. Do you think that red and green paints would mix to form yellow paint? (Certainly not!) Now, based on the model of selective transmission (subtractive color), seen above, determine what light would be reflected by a mixture of red and green paints. Try it: Using your primary color paddles, overlap the red and green paddles so that one flashlight (that is set to deliver diffuse light, rather than a sharp concentrated beam) shines through both paddles onto a white wall about 3 ft. away. What light comes through? Answer: None-‐ the mixture absorbs all the white light (RGB). The red pigment absorbs the green and blue frequencies of white light and the green pigment absorbs the red (and blue) frequencies of white light.
Ink or paint colors can appear quite different if the light shining on them is itself colored. For example, red paint under blue light may appear black because the red paint subtracts the blue light, leaving no light at all! Try it! The mixture of absorbing pigments results in a subtraction of colors; the observer sees the light left over after absorption takes place. Students may want to experiment with other color combinations. It is good scientific practice to first predict what will happen, then test your hypothesis. What light would be reflected from a mixture of cyan and yellow pigments? Answer: Green is reflected (red and blue are absorbed) What light would be reflected from a mixture of magenta and yellow pigments? Answer: Red is reflected (green and blue are absorbed) What light would be reflected from a mixture of cyan and magenta? Answer: Blue is reflected (red and green are absorbed) Magenta, yellow and cyan are the subtractive primary colors. In painting and printing, the primaries are often said to be red, yellow and blue. More precisely, they are magenta, yellow and cyan. They can be combined to produce any color in the spectrum in painting or printing.
Summary of color addition and subtraction The basic rules of color addition and color subtraction can be deduced from the figure below and demonstrated with color paddles and flashlights.
Additive Primary Colors We see that the sum of blue and red is magenta; the sum of green and blue is cyan; and the sum of red and green is yellow. We say that magenta is opposite green; cyan is opposite red; and yellow is opposite blue. A color plus its opposite appear white. Again, any two colors that add together to produce white are complementary colors. Subtractive Primary Colors When white light passes through overlapping sheets of the subtractive colors, all frequencies are absorbed (subtracted) and we have black. Where only yellow and magenta overlap, all frequencies are subtracted but red; where cyan and magenta overlap, all frequencies are subtracted but blue; where yellow and cyan overlap, all frequencies are subtracted but green.
Reflection from Mirrors Most things do not emit their own light; they are visible because they re-‐emit most of the light reaching their surface from a source – the sun or a lamp, or the illuminated sky. Light that shines on a surface is usually re-‐emitted at the same frequency or absorbed and turned into heat. When re-‐emitted light is returned to the medium from which it came, it is reflected. Atomic View (Background): Recall that light interacts with atoms as sound interacts with tuning forks. When light strikes a surface the electrons of the atoms and molecules behave like optical tuning forks-‐ they are set into vibration. These vibrating electrons send out electromagnetic (light) waves. Let’s look at the case where the reflection is from a very smooth surface like a mirror. Imagining light as a ray makes it easy to describe reflection, refraction, (and scattering). In reflection, a light ray strikes a smooth surface, such as a mirror, and bounces off in one directon. A reflected ray always comes off the surface of a material at an angle equal to the angle at which the incoming ray hit the surface. This is the law of reflection. We say "the angle of incidence equals the angle of reflection."
Of course, we live in an imperfect world and not all surfaces are smooth. When light strikes a rough surface (like an apple, leaf, paper, or painting), incoming light rays reflect at all sorts of angles because the surface is uneven. This scattering occurs in many of the objects we encounter every day. The surface of paper is a good example. You can see just how rough it is if you peer at it under a microscope. When light hits paper, the waves are reflected in all directions. This is what makes paper so incredibly useful -‐-‐ you can read the words on a printed page regardless of the angle at which your eyes view the surface. In contrast, when light rays hit a smooth surface (such as a mirror) the rays all reflect off the surface at the same angle; light is not scattered.
For example, when practicing for the reflection competition using the mirrors to direct a flashlight beam from mirror to mirror (and to the target), you may find it challenging, sometimes, to be sure that your beam is hitting the next mirror. This is because the light reflects off the mirror at a very specific angle: the angle of reflection. Curved Mirrors
A convex or diverging mirror, which bulge outward, reflects at a wider angle near its edges than at its center, creating a slightly distorted image that's smaller than actual size.
Concave or converging mirrors curve inward like a spoon (the side that holds soup). This gives these mirrors the ability to create an image when their curvature bounces light to a specific area in front of them.
Refraction Refraction occurs when a ray of light passes from one transparent medium (air, let's say) to a second transparent medium (water). When this happens, light changes speed and the light ray bends, either toward or away from what we call the normal line, an imaginary straight line that runs at a right angle (perpendicular) to the surface of the object. The amount of bending, or angle of refraction, of the light wave depends on how much the material slows down the light.
The cause of refraction is the changing of the average speed of the light going from one transparent medium to another. Consider pulling a wagon along a smooth sidewalk onto a grass lawn or edge of sandy soil. If the wheels meet the grass lawn at an angle (that is, if one wheel hits the soft surface before the other) they will be deflected from their straight-‐line course. The wheel that hit the soft surface will slow down causing the faster moving wheel to pivot about the slower wheel. (It travels farther in the same time the other wheel travels a lesser distance.) This bends the direction of the rolling wheels toward the “normal.”
The Principle of Least Time Light (rays) travel in straight lines and take the path that requires the least time. Light bends and takes a longer path when it encounters a transparent medium (like water or glass), at an angle. The longer path is still the path that requires the least time. It is like the path taken by a lifeguard to rescue a struggling swimmer in the diagram below. The lifeguard can run faster on hard sand than he/she can move through the water swimming. Taking a straight-‐line path to the swimmer takes more time than running a longer path on sand so that the path to swim is made shorter. This is the path that takes the least time. For light, the angle of incidence is larger than the angle of refraction by an amount that depends on the relative speeds of light in air and water.
Illusions The refraction of light is responsible for many illusions.
Bend a pencil using light
You Will Need: Water, a pencil, and a clear water glass
What to Do:
1. Fill the glass with water so it is about 2/3 full.
2. Hold the pencil straight up and down in the glass so that it is touching the bottom.
3. Take a look from the side. How does it look? (It probably still looks straight.)
4. Now let the pencil lean to the side of the cup. You don't need to hold it anymore. The top part of the pencil should still be sticking out of the water.
5. How does it look from the side this time? (It's bent?! Whoa... how did that happen?)
When light enters the water, it can't move as fast and it has to slow down slightly. It's kind of like how if you are walking, you can walk at a normal speed but if you walk in water, you can't walk quite as fast.
If light from the image enters the water straight, then the image looks normal -‐ which was what you originally did when the pencil was straight up and down. If the light enters the water at an angle, then the change in speed between the open air and water causes the light beam to bend away from its original path. When the pencil was at an angle, the image was at a bigger angle in the water than in the air and made the pencil look like it was bent.
For a pencil partly immersed in water, the submerged part seems closer to the surface than it really is.
A fish appears nearer to the surface and closer than it really is
Because of refraction, submerged objects appear to be magnified. The apparent position is closer and thus gives the illusion of being bigger.
Prisms The natural, or resonant, frequency of most transparent material is in the UV range so the electrons in the atoms and molecules of transparent materials absorb UV light. The high frequencies of visible light (violet, blue, green) have a lower average speed through transparent material than the lower frequencies (yellow, orange, red). This is because light frequencies near the natural frequencies of the atoms and molecules of the transparent material interact more often in the absorption/re-‐emission sequence and, therefore, have a lower average speed. Think about it: When walking across a crowded room, if there are a lot of people who are “on your wavelength,” you make several momentary stops to greet people along the way. Your average speed across the room is less because of the time delays of your stops. Similarly, the speed of light is less because of the time delays of interactions with atoms along its path. Different frequencies of light travel have different speeds through transparent materials. Because they travel at different speeds they refract differently and bend by different amounts. The lower the average speed through the transparent material, the more the light is refracted (bent). In a prism, light is bent twice making the separation of colors more noticeable.
The colors of rainbows are spread (dispersed) from the sunlight by thousands of tiny water drops that act like prisms.
Lenses A lens is a curved, transparent material (usually of glass) that refracts (bends) light rays. Various types of lenses have different functions. The lens of an eye or camera focuses light rays. In telescopes, microscopes, and magnifying glasses, lenses enlarge the apparent size of objects. A lens in a reducing glass reduces apparent size. In a motion-‐picture or slide projector, lenses project images so that they will appear on a screen. Some lenses are used to bend light rays in such a way as to correct distortions. The lenses used in eyeglasses correct a person's vision or enhance it by making distant objects appear closer or small objects appear bigger. Lenses serve to refract light at each surface. As a ray of light enters the transparent material, it is refracted. As the same ray exits, it's refracted again. The overall effect of the refraction at these two boundaries is that the light ray has changed directions. Think of a lens as a set of several matched prisms of glass arranged as so
The prisms refract incoming parallel light rays so they converge to (or diverge from) a point. In both cases, the greatest deflection of rays occurs at the outermost prisms (because they have the greatest angle between the two refracting surfaces.)
Review Questions Light Does visible light make up a relatively large part or a relatively small part of the electromagnetic spectrum? Electromagnetic Spectrum What is the principal difference between radio waves and visible light? What color do the lowest visible frequencies appear? How does the wavelength of light relate to its frequency? Transparent Materials What happens to the energy in ultraviolet light when it shines into glass? What happens to the energy in visible light when it shines into glass? Why are the answers for the above two questions different? How does the average speed of light in glass compare to its speed in a vacuum? Opaque Materials Why do opaque materials become warmer when light shines on them? Light and Color What is the relationship between the frequency of light and its color? Selective Reflection What happens to white light that shines on white paper and what happens to white light that shines on black ink? Does the color of an object appear different when lit by candle light compared to the light from a fluorescent lamp? Why? Selective Transmission What is a pigment?
What color light is transmitted through a piece of red glass? Which will warm quicker in sunlight, a clear or a colored piece of glass? Why? Mixing Colored Light How can you demonstrate that white light is a combination of all the colors of the spectrum? What frequency ranges of the visible light spectrum do red, green, and blue light occupy? Why are red, green, and blue called the additive primary colors? Mixing Colored Pigments Why does a mixture of red and green pigments appear blackish? Why does a mixture of cyan and yellow pigments appear green? Why are magenta, yellow, and cyan called the subtractive primary colors? If you look with a magnifying glass at the pictures printed in full color in magazines, you’ll notice three colors of ink plus black. What are these colors? Rules for Color Mixing What color do you see when equal intensities of red, blue, and green light are combined? What color do you see when equal intensities of blue light and green light are combined? What color do you see when equal intensities of red light and cyan light are combined? Why are red and cyan called complementary colors? Reflection and Refraction Distinguish between reflection and refraction. Law of Reflection What is the law of reflection?
Mirrors Is the law of reflection the same for flat mirrors and curved mirrors? Which side of a spoon has the shape of a concave mirror? A convex mirror? If you look taller and thinner in a funhouse mirror, does that mirror have a convex or concave surface? If you look shorter and wider in a funhouse mirror, does that mirror have a convex or concave surface? Refraction If you look at a drinking straw that is leaning in a glass of water, will the submerged part of the straw appear closer or farther from the surface? If you were to try to spear a fish that is several feet in front of you, would you aim your spear above, or below, or directly at the fish you see to make a direct hit? Challenge! If you instead used light from a flashlight as your “spear,” would you aim above, below, or directly at the fish you see? Does refraction make the bottom of a swimming pool look deeper or shallower? Which travels faster through glass, red light or blue light? Which is refracted more? Lenses Is a converging lens thicker at its center or at its edges? Is a diverging lens thicker at its center or at its edges? Which type of lens can be used to bring sunlight together at a point to start a fire? Other Resources: The Ann Arbor Hands-‐On Museum has Light and Optics exhibits-‐ including color, mirrors, lenses, optical illusions, just to name a few. Bill Nye the Science Guy Youth DVD’s: Light optics, Light and Color; Magic School Bus Makes a Rainbow: a Book about Color both available at the Ann Arbor District Library Do an internet search using combinations of keywords: Light and Color for Kids Much of the material and some figures in this study guide are drawn from Paul G. Hewitt’s Conceptual Physics.