The Electromagnetic Classroom Activities Spectrum

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TheElectromagneticSpectrumThe light that we see with our eyes – visiblelight – represents only a small portion of theelectromagnetic spectrum. Developing the technology to detect and use other portions of theelectromagnetic spectrum – the “invisible” lightthat our eyes cannot see – has had a tremendousimpact on our daily lives. When you listen to aradio, heat your food in a microwave oven, use aremote control, or have an X-ray taken, you areusing “invisible” light.Classroom ActivitiesOverviewIn astronomy, scientists use the propertiesof light to learn about celestial objects thatare too far away to visit. Each portion of theelectromagnetic spectrum provides uniqueclues about the nature of our universe. Themissions and research programs in NASA’sAstronomical Search for Origins programuse innovative technologies to observe theuniverse at a variety of wavelengths (ultraviolet, visible, and infrared) in search of theanswers to two enduring human questions:Where did we come from?Are we alone?VocabularyElectromagnetic energy: A form of energy that travels through space as vibrations of electric andmagnetic fields; also called radiation or light.Frequency: Describes the number of wave crests passing by a fixed point in a given time period(usually one second). Frequency is measured in hertz (Hz).Spiral galaxy: A large pinwheel-shaped system of stars, dust, and gas clouds.Wave: A vibration in a medium or in space that transfers energy from one place to another. Soundwaves are vibrations of air. Light waves are vibrations of electric and magnetic fields.Wavelength: The distance between two wave crests, which is the same as the distance betweentwo troughs.This poster contains three classroom activitiesdesigned to introduce middle and high schoolstudents (grades 6–12) to different portions of theelectromagnetic spectrum, including those usedby Origins missions. Suggested science standards,vocabulary, and science background information areprovided to facilitate lesson planning. The activitiescan be done separately or together.The Visible Spectrum provides instructionsfor creating a visible spectrum with an overheadprojector. Introduce the electromagnetic spectrumby showing students that white light is composedof a rainbow of colors. Students can draw thevisible spectrum and explore how common objects“filter” light. Use these activities to engage students’interest in electromagnetic energy.The Herschel Infrared Experimenthelps students to expand their knowledge of theelectromagnetic spectrum. Students will discoverthe “invisible” light that lies just beyond the redend of the visible spectrum – infrared light. Usethis as an outdoor class laboratory activity, a studentlearning station, a demonstration, or aspart of a science fair project.Invisible Light Sources and Detectorsgives students direct experience with radio, infrared,visible, and ultraviolet waves. Students will identifysources of visible and “invisible” forms of light inour everyday lives, and identify ways to detect andto block these types of light. Teachers can use theseconcepts to discuss how we protect ourselves fromharmful forms of light.Visit the NASA Space Science Education ResourceDirectory (http://teachspacescience.org) or theOrigins Education Forum website (http://origins.stsci.edu) to find additional education resourcesdeveloped by NASA’s Origins missions andprograms.

Background Information1. What is the electromagnetic spectrum?The electromagnetic spectrum consists of all thedifferent wavelengths of electromagnetic energy,including radio waves, microwaves, infrared light, visiblelight, ultraviolet light, X-rays, and gamma rays. Theonly region in the entire electromagnetic spectrum thatour eyes can detect is the visible region. Although thewavelength ranges for forms of light other than visibleare not precisely defined, typical wavelength ranges areas follows: gamma rays, less than 0.001 nanometers;X-rays, 0.001 to 10 nanometers; ultraviolet light, 10 to400 nanometers; visible light, 400 to 700 nanometers;infrared light, 700 nanometers to 1 millimeter; andradio waves, longer than 1 millimeter. The shortestradio waves (wavelengths between 1 millimeter andabout 30 centimeters) are also referred to as microwaves.(One nanometer equals one-billionth of a meter.)2. What is the relationship betweenwavelength, frequency, and energy?The speed of light equals the frequency times thewavelength. This means that the frequency is equal tothe speed of light divided by the wavelength. Becauseall electromagnetic waves travel at the same speed(300,000,000 meters per second) in the vacuum ofempty space, the shorter the wavelength is, the higherthe frequency. The energy of a wave is directly proportional to its frequency, but inversely proportional toits wavelength. In other words, the greater the energy,the larger the frequency and the shorter (smaller) thewavelength. Short wavelengths are more energetic thanlong wavelengths.3. Do all types of electromagnetic energyreach the Earth’s surface?Our atmosphere blocks out harmful energy like X-rays,gamma rays and most ultraviolet rays. It also blocks outmost infrared energy, as well as very low energy radiowaves. Visible light, most radio waves, some ultravioletrays, small wavelength ranges of infrared light, andsome microwaves pass through the atmosphere.4. Why do we put telescopes in space?Astronomers put telescopes in space to studyelectromagnetic energy that does not reach theEarth’s surface. Each type of electromagnetic energyprovides important clues about the properties ofcelestial objects. We also put telescopes in space tostudy visible light, even though visible light passesthrough the Earth’s atmosphere. Turbulence in ouratmosphere blurs the images that scientists obtainwith telescopes on the ground. By placing telescopesin space, above the Earth’s atmosphere, scientists canobtain a much sharper view of the universe.5. How do we detect “invisible” formsof light?Scientists build electronic devices that are sensitiveto the light our eyes cannot see. Then, so that wecan visualize these regions of the electromagneticspectrum, computer image-processing techniquestranslate the “invisible” light into pictures that wecan see.6. What are the different images of theWhirlpool Galaxy on the front of theposter?The upper image, which was obtained by theHubble Space Telescope, is a visible-light image ofthe Whirlpool Galaxy. This detailed image helpsastronomers to study the structure and star-formingprocesses of this spiral galaxy.The visible-light image in the lower portion ofthe poster shows a wider view of the same HubbleSpace Telescope image, revealing a smaller, nearbycompanion galaxy. Four additional images, obtainedwith various space-based and ground-basedtelescopes, measure the “invisible” light emitted bythe two galaxies. To visualize the “invisible” light,scientists have used computer image-processingtechniques to translate the various electromagneticenergies into pictures we can see.Each image provides important clues about theproperties of this system. The visible-light imageshows sweeping spiral arms, clusters of youngstars, and clouds of molecular gas and dust. Youngstars dominate the appearance of the ultravioletimage, which provides a unique view of the spiralstructure. The X-ray image shows clouds of multimillion-degree gas and point-like objects associatedwith black holes and neutron stars. Longer infraredwavelengths track warm dust heated by recent starformation. The radio image maps the locationsof star-forming regions and supernova remnantsproduced by the deaths of massive stars.7. How do scientists use theelectromagnetic spectrum tolearn about the universe?The images of the Whirlpool Galaxy on the frontof the poster show how combining informationfrom each region of the electromagnetic spectrumleads to a more complete understanding of acelestial object. In addition to taking imagesof celestial objects, scientists also use devicescalled spectrographs to disperse, or separate, thelight from celestial objects into its componentwavelengths. Features in the resulting spectrumhelp astronomers to measure an object’s properties,such as its temperature, composition, density, andmotion.Scientists in NASA’s Astronomical Search forOrigins program will image stars and galaxiesat ultraviolet, visible, and infrared wavelengths.We will also look for characteristic patterns oflight, or spectral “fingerprints,” emitted by atomsand molecules to measure elements in the earlyuniverse and to search for signatures of life.Combining the light from multiple telescopeswill allow us to achieve the capabilities neededto identify and study terrestrial planets orbitingnearby stars.

The VisibleSpectrumTarget Grade Levels: 6–12PurposeTo introduce the electromagnetic spectrum.Understanding electromagnetic energy often beginswith studying the visible spectrum. Visible lightis accessible and emphasized in most textbooks.Students bring personal observations of thespectrum from the natural world: rainbows; prisms;diffraction grating glasses; and other commercialitems decorated with refractive materials (pencils,signs, etc.). Begin with these observations to engagestudents' curiosity about light and, more broadly,electromagnetic energy.MaterialsOverhead projector; diffraction grating*;and two pieces of 8" X 10" dark paper.ORSlide projector; diffraction grating*; one 35-millimeter slide mount; and unexposed film or blackelectrical tape.Color pencils or crayons; common transparentobjects like sunglasses; colored report covers; andplastic wrappers.Projecting the VisibleSpectrumThe visible spectrum can be boldly projected witha diffraction grating or, less optimally, a prism* usingan overhead projector or a slide projector as a lightsource. Both projectors produce a full spectrum ofwhite light. (Note: video projectors do not produce afull spectrum.)To use an overhead projector, place two pieces of 8-inchby 10-inch dark paper on the projector to create a “slit”about 2.5 centimeters (1 inch) wide on the base plateof the projector. Turn on the projector lamp and focusthe “slit” on a white wall or screen. Place the diffractiongrating (about 4 or 5 inches square) in front of the upperlens (head) of the overhead, and rotate the grating untilthe spectrum appears on either side of the projected sliton the wall or screen.spectrum appears to have boundaries. Asking ifthere is anything beyond the red and violet ends ofthe spectrum introduces the notion of “non-visible”electromagnetic energy. Human skin is sensitiveto the ultraviolet energy beyond the violet light;it sunburns. And, skin senses the infrared energybeyond the red light as heat.To use a slide projector, create a 35-millimeter slide thathas a clear “slit” about 0.5 centimeters (1/4 inch) wide byusing unexposed film, or black electrical tape in a slidemount. Turn on the projector and focus the “slit” on thewall or screen. The diffraction grating is placed in frontof the lens. Again, rotate to produce the spectrum onthe wall.Transparent, colored objects transmit only aportion of the visible spectrum. Place commontransparent objects like sunglasses, colored reportcovers and plastic wrappers on the “slit” of theoverhead projector (or into the beam from the slideprojector) to discover how they “filter” light. Thefilters used for theatrical lighting are designed toselectively transmit color, and offer a more dramaticdemonstration of how light is filtered. Viewingobjects in different regions of the electromagneticspectrum through the use of filters and differentkinds of telescopes gives astronomers more information about the universe.With either type of projector, the spectrum will appear onboth sides of the “slit” You can move the projector to placethe spectrum at the best place for students to observe.Note that this works best in a darkened room.Activities1. The Colors of the Visible SpectrumStudents use color pencils or crayons to draw and labelthe spectrum. They may record more or fewer colorsthan the classic “ROY G BIV” (red, orange, yellow,green blue, indigo, violet) scheme. (Many people do notdistinguish dark blue [indigo] from violet.) The visible2. How Do Color Filters Work?*Note on Diffraction Gratings and Prisms:Diffraction gratings produce a bright, broad visiblespectrum that students find easier to observe.Holographic gratings perform best. A prism placedin a light beam of a slide projector will also producea visible spectrum, but it will likely be fainter, withthe colors dispersed in a narrow band.Going FurtherThese activities were adapted from Active Astronomy: Classroom Activities for Learning About InfraredAstronomy. Active Astronomy offers hands-on activities and demonstrations that focus on sensinginfrared energy as a way of exploring “invisible” light.Download Active Astronomy on the Web at: http://www.sofia.usra.edu/Edu/materials/edu materials.html.The Visible Spectrum — page 1 of 1

Herschel InfraredExperimentTarget Grade Levels: 6–12PurposeTo perform a version of the experiment of 1800,in which a form of electromagnetic energy otherthan visible light was discovered by the famousastronomer Sir Frederick William Herschel.BackgroundHerschel discovered the existence of infrared lightby passing sunlight through a glass prism. Hisexperiment is similar to the one described here. Assunlight passed through the prism, it wasdispersed into a rainbow of colors called aspectrum. A spectrum contains all of the visiblecolors that make up sunlight.Herschel was interested in measuring the amountof heat in each color and used thermometers withblackened bulbs to measure the various color temperatures. He noticed that the temperature increasedfrom the blue to the red part of the visible spectrum.Herschel then placed a thermometer just beyond thered part of the spectrum in a region where there wasno visible light. He found that the temperature waseven higher!Thermometersplaced in spectrumPrismBlueJustbeyondYellow redHerschel realized that there must be another type of lightbeyond the red, which we cannot see. This type of lightbecame known as infrared. Infra is derived from the Latinword for “below.” Although the procedure for this activityis slightly different than Herschel's original experiment,you should obtain similar results.MaterialsOne glass prism (plastic prisms do not work well for thisexperiment); three alcohol thermometers; black paintor a permanent black marker; scissors or a prism stand;a cardboard box (a photocopier paper box works fine);and one blank sheet of white paper.PreparationYou will need to blacken the thermometer bulbs to makethe experiment work effectively. One way to do this is topaint the bulbs with black paint, covering each bulb withabout the same amount of paint. Alternatively, you canalso blacken the bulbs using a permanent black marker.(Note: the painted bulbs tend to produce better results.)The bulbs of the thermometers are blackened in order toabsorb heat better. After the paint or marker ink has dried,tape the thermometers together so that they line upas in Figure 1.ProcedureThe experiment should be conducted outdoors on a sunnyday. Variable cloud conditions such as patchy cumulusclouds or heavy haze will diminish your results. Thesetup for the experiment is depicted in Figure 2. Beginby placing the white sheet of paper flat in the bottom ofthe cardboard box. The next step requires you to carefullyattach the glass prism near the top (Sun-facing) edge ofthe box.If you do not have a prism stand (available from sciencesupply stores), the easiest way to mount the prism is tocut out a notch from the top edge of the box. The cutoutnotch should hold the prism snugly, while also permittingSpectrumBoxSheet ofpaperPrismFigure 2its rotation about the prism's long axis (as shown inFigure 3). The length of the notch should be slightlyshorter than the length of the prism. The notchshould be slightly deeper than the prism’s width.Next, slide the prism into the notch cut from thebox and rotate the prism until the widest possiblespectrum appears on a shaded portion of thewhite sheet of paper at the bottom of the box. TheSun-facing side of the box may have to be elevated(tilted up) to produce a sufficiently wide spectrum.After the prism is secured in the notch, place thethermometers in the shade and record the ambientair temperature. Then place the thermometers inthe spectrum so that one of the bulbs is in the blueregion, another is in the yellow region, and the thirdis just beyond the (visible) red region(as in Figure 1).PrismDetailBoxFigure 3Figure 1Herschel Infrared Experiment — page 1 of 2

It will take about five minutes for the temperaturesto reach their final values. Record the thermometertemperatures in each of the three regions of thespectrum: blue, yellow, and “just beyond” thered. Do not remove the thermometers from thespectrum or block the spectrum while reading turein the shadeTemperaturein the spectrumWhat did you notice about your temperaturereadings? Did you see any trends? Where was thehighest temperature? What do you think exists justbeyond the red part of the spectrum? Discuss anyother observations or problems.After 2 minutesRemarks to the teacherAfter 3 minutesAsk students to answer the above questions. Thetemperatures of the colors should increase fromthe blue to the red part of the spectrum. The highesttemperature should be just beyond the red portion ofthe visible light spectrum. This is the infrared regionof the 3(just beyond reAfter 1 minuteAfter 4 minutesAfter 5 minutesHerschel's experiment was important not onlybecause it led to the discovery of infrared light, butalso because it was the first time someone showedthat there were forms of light that we cannot seewith our eyes. As we now know, there are manyother types of electromagnetic energy (“light”)that the human eye cannot see (including X-rays,ultraviolet rays and radio waves).You can also ask the students to measure thetemperature of other areas of the spectrum, includingthe area just beyond the visible blue. Also, trythe experiment during different times of the day.The temperature differences between the colorsmay change, but the relative comparisons will remainvalid.Going FurtherFor more activities and further information on the Herschel infrared experiment, see:http://coolcosmos.ipac.caltech.edu/cosmic classroom/classroom activities/herschel experiment.html.Herschel Infrared Experiment — page 2 of 2

Invisible LightSources andDetectorsTarget Grade Levels: 6–12PurposeAt classroom stations, students gain direct experience with different sources of electromagnetic energy— most of which is not visible to the human eye.Each station will have a source of electromagneticenergy, possible “detectors,” and sheets of materialto test as potential “transmitters” or “shields” forthe electromagnetic energy. Detecting and blocking(“shielding”) various forms of electromagnetic energyhelps students realize there are forms of electromagnetic energy that we cannot see.Note: X-rays and gamma rays are not included aspart of this classroom activity for several reasons,most importantly because they are harmful if notused properly.MaterialsFor the class:Activity worksheets for each student3-6 station number signs3-6 sets of shields/transmitters in a manila folder orenvelope, one for each station, plus one additionalset for the demonstration station. Each set has thefollowing materials:blank overhead transparencyaluminum foil, 12" X 12"plain white paper, 8 1/2" X 11"cloth, 12" X 12"black plastic, 12" x 12", 2-4 mil thickclear plastic baggie, 1 gallon sizewax paper, 12" X 12"For the stations:Demonstration StationVisible LightSOURCE: flashlight (with batteries)DETECTOR: plain white paper 8 1/2" X 11"Radio (FM)SOURCE: radio stationDETECTOR: small battery-operated FM radio.Aluminum foil (enough to completely coverthe radio, its antenna, and any headphones).[For large classes, set up two of each of the numberedstations.]Station 1Infrared LightSOURCE: infrared light (heat lamp)DETECTOR: student’s handStation 2Infrared LightSOURCE: VCR/TV remote controlDETECTOR: TV monitor or other device triggeredby remoteStation 3Ultraviolet LightSOURCE: black light — fluorescentDETECTORS: sheet of “bright” paper; styrofoampeanuts; detergent; tonic water containing quinine;glow-in-the-dark stars; ultraviolet beads.**Note: Black light sources are often found in partyshops or entertainment/theater catalogs. Ultravioletbeads are available from many science educationsuppliers. The white beads that turn red in ultravioletlight are preferred.Safety IssuesWe advise against incandescent black light bulbs.If that type of bulb is the only one available, beaware that they can become very hot, so cautionstudents not to touch the bulb. And althoughnormal fluorescent black lights are consideredcompletely safe, please advise students not tostare directly into the fluorescent bulbs forextended periods or from close range. Shorterwavelength black lights used in mineral exploration or to sterilize surfaces should NOT be used.They can be dangerous to eyes and skin and canburn them much like a severe sunburn.ProcedureDemonstration – Defining Sources,Detectors, Transmitters, and Shields1. Sources. Shine the flashlight from the demon-stration station at students. Say, “This flashlight is asource of light.” Ask, “What are some other sourcesof light energy that we can see?” Explain that whilemost objects reflect light, they are not considered tobe the source of that light. Sources of light generateand emit the light themselves.2. Detectors. Ask, “Can you tell me where thereare light detectors in the room?” [The students’eyes!—If necessary give them the hint that somelight detectors are a couple of centimeters below theireyebrows!] Then ask, “Are there other light detectorsthat you know of?” [Cameras, camcorders.] Explainthat the white paper at the demonstration stationreflects visible light so that our eyes can detect it.We can call the white paper a “detector,” but oureyes are the real detectors.Invisible Light Sources and Detectors — page 1 of 3

3. Transmitters and Shields. Explain that somematerials let light through and are called transmittersof light. Other materials do not let light through;they block the light, and can be called shields. Usethe test shields at the demonstration station to showhow different objects/materials can either transmit,partially transmit, or block visible light. For each testshield listed in the Visible Light worksheet, ask theclass to predict whether the material will transmit/partially transmit (T) visible light or block/shield(S) visible light, and to record their predictions onthe worksheet. Insert each material in the flashlightbeam and have students record the observed results.Completing the Visible Light worksheet in thisfashion will prepare students for the experimentswith invisible light.?SourceDetectorTest Shield4. Exploring Invisible Light. Tell the class that,in addition to the visible light energy they cansee in the room, there is a lot of invisible energytoo. For example, the radio at the demonstrationstation detects radio waves from a radio station.[With radios, it is easy for confusion to arise aboutthe energy source. In addition to the radio wavesemitted by the radio station, the radio is powered bya battery, and there is also sound energy. Emphasizethat it is the radio waves we are concerned withhere.] Tune a small battery-operated radio to an FMmusic or news station.To show how invisible energy can be blocked, completely wrap the radio and its antenna in aluminumfoil or place it in a box completely lined withaluminum foil (including the lid). [Headphones andheadphone cords, if present, also should be wrapped infoil since headphone cords often contain an antenna.]The radio waves from the radio station should now beshielded (blocked), and static will be heard. The staticindicates that the radio is still working, and reinforcesthe fact that the signal — the radio energy — hasbeen blocked. Tell the class that the other materialsat the demonstration station will not block the radiowaves.Student Experiment and Discussion5. Explain that the stations set up around the roomeach have a source of energy, a detector of that energy,and a set of materials (test shields) to see whichmaterials transmit or block the invisible energy.a. Have students identify the Source and Detectorat each station (as listed in the “Stations” section ofthe Materials list above).b. Divide the class into groups. Tell students theywill have about 7–10 minutes per station. Explainthat students will use the procedure demonstratedwith visible light to determine which materialstransmit/partially transmit or shield (block)invisible light. Ask students to record their predictions and results on the Invisible Light worksheet.When a given time period is up, have students goto the station with the next highest number, unlessthey are already on the highest number, in whichcase they should go to Station 1.6. Discussion of results. Ask questions about eachstation, such as the ones below. Each group will reporttheir results to the class. Encourage other groups toask questions of the reporting group, and be sure toask students in the reporting group for any questionsthey still have. What did you find out? What was the source? What was the detector? What blocked the source? What let the invisible light through? Did anything surprise you?7. Summarize the class experiences on a largepaper or the overhead so students can view the conclusions and unresolved questions. Help familiarizethem with the names for each type of invisible lightand the electromagnetic spectrum by looking at thefront of the poster.8. Consider other invisible sources.a. “What kind of invisible energy do we use tocook with?” [microwaves and infrared] Explainthat water is especially good at absorbing microwaves, so any food containing water (most food)will be efficiently heated in a microwave oven.b. X-rays. If possible, show the class an X-rayimage, and ask, “Where did the rays come from?”[an X-ray machine] “When you get a dentalX-ray, they put a lead shield on you. Why?” [toprotect you from any dangerous effects associated with the X-rays] “Why don’t they use analuminum foil shield?” [Aluminum foil will notblock X-rays.] “They had you bite on something.What was it?” [It holds the film (which detectsthe X-rays).] “What was between the X-ray sourceand the film?” [teeth]c. Let students know that even though peoplecan’t see invisible waves, some animals can. Wecan’t see infrared rays, but snakes can. We can’tsee ultraviolet waves, but bees and some otherinsects can. Can we see radio waves? [No]Invisible Light Sources and Detectors — page 2 of 3

Code: T TransmitterLight Sources, Detectors, and Shields WorksheetS ShieldTest ShieldVisibleLightFlashlight(Visible earplasticPredictionLight tionResultTest ShieldBlack light(Ultraviolet)Heat esultPredictionResultPredictionResult 2002 by The Regents of the University of California-LHS GEMS: Invisible Universe MAY BE DUPLICATED FOR CLASSROOM OR WORKSHOP USE.About the ActivityThis activity is adapted from The Invisible Universe, a teacher’s guide in the Great Explorationsin Math and Science (GEMS) series, available from Lawrence Hall of Science, (510) 642-7771.E-mail: gems@berkeley.edu. On the Web: http://www.lhsgems.org.The Invisible Universe was created with support from NASA’s Swift Gamma-ray Burst mission.For more information, see http://swift.sonoma.edu.Invisible Light Sources and Detectors — page 3 of 3

What is the Astronomical Search for Origins?Recent discoveries have given us a vastly expanded sense ofthe universe and our place in it. We have measured the glowof the “Big Bang” – the cosmic event that gave birth to theuniverse – and observed distant galaxies. We have capturedsnapshots of newborn stars and discovered planets aroundother stars. We now know that liquid water once flowed onthe surface of Mars and may still exist below the icy crust ofJupiter’s moon Europa. Life on Earth has been traced backnearly 4 billion years and found thriving in extreme environments, from Antarctic rocks to boiling hot springs. We appearto be on the brink of answering some fundamental questions:Where do we come from? Are we alone? The missions andresearch programs comprising NASA’s Astronomical Searchfor Origins program seek to answer these questions.National StandardsEach activity can be used to support the following National Science Education Standards(National Academy Press, 1996):Grades 5–8: Physical Science: Content Standard B: Transfer of Energy: “The sun is a majorsource of energy for changes on the earth's surface. The sun loses energy by emitting light. Atiny fraction of that light reaches the earth, transferring energy from the sun to the earth. Thesun's energy arrives as light with a range of wavelengths, consisting of visible light, infrared,and ultraviolet radiation.”Grades 9–12: Physical Science: Content Standard B: Interactions of Energy and Matter:“Electromagnetic waves result when a charged object is accelerated or decelerated.Electromagnetic

The Visible Spectrum provides instructions for creating a visible spectrum with an overhead projector. Introduce the electromagnetic spectrum by showing students that white light is composed of a rainbow of colors. Students can draw the visible spectrum and explore how common objects “filter” light. Use these activities to engage students’File Size: 243KBPage Count: 9

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