advanced physics course chapter 12: light waves · advanced physics course chapter 12: light waves...

A D V A N C E D P H Y S I C S C O U R S E

C H A P T E R 1 2 :

L I G H T W A V E S

FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS

This is a complete video-based high school physics course that includes videos, labs, and hands-on learning.

You can use it as your core high school physics curriculum, or as a college-level test prep course. Either way,

you’ll find that this course will not only guide you through every step preparing for college and advanced

placement exams in the field of physics, but also give you in hands-on lab practice so you have a full and

complete education in physics. Includes text reading, exercises, lab worksheets, homework and answer keys.

BY AURORA LIPPER ∙ SUPERCHARGED SCIENCE 2017

© 2017 Supercharged Science

TABLE OF CONTENTS

Materials ................................................................................................................................................................................................................... 3

introduction ............................................................................................................................................................................................................. 4

Light is a Wave ........................................................................................................................................................................................................ 5

Light Reflection ...................................................................................................................................................................................................... 6

Does Light Travel in a Straight Line? ............................................................................................................................................................ 7

Light Refraction...................................................................................................................................................................................................... 8

Light Refraction using Two Lasers ................................................................................................................................................................. 9

Diffraction .............................................................................................................................................................................................................. 10

Useful Diffraction................................................................................................................................................................................................ 16

Introduction to Lasers ...................................................................................................................................................................................... 17

Light Interference .............................................................................................................................................................................................. 18

More on Light Interference ............................................................................................................................................................................ 19

Thin Film Interference ..................................................................................................................................................................................... 20

Polarization ........................................................................................................................................................................................................... 21

Shadows ................................................................................................................................................................................................................. 23

Color and Vision .................................................................................................................................................................................................. 24

Visible Light .......................................................................................................................................................................................................... 30

Cold Light Mixing ................................................................................................................................................................................................ 36

What is Color? ...................................................................................................................................................................................................... 41

Where do different colors come from? ...................................................................................................................................................... 42

Pigments................................................................................................................................................................................................................. 43

Color Filters .......................................................................................................................................................................................................... 44

Paint and Light..................................................................................................................................................................................................... 49

How to Paint with Light ................................................................................................................................................................................... 50

Rods and Cones ................................................................................................................................................................................................... 51

Light Absorption ................................................................................................................................................................................................. 56

How does light get absorbed? ....................................................................................................................................................................... 57

Martian Sunsets .................................................................................................................................................................................................. 58

Two-Point Source Interference .................................................................................................................................................................... 63

Path Difference .................................................................................................................................................................................................... 64

When Path Difference Matters ...................................................................................................................................................................... 65

Measure the Track Spacing of a DVD and CD .......................................................................................................................................... 66

Wave-Particle Duality ....................................................................................................................................................................................... 67

Easy Light Wave-Particle Demonstration ................................................................................................................................................ 68

Homework Problems with Solutions ......................................................................................................................................................... 69


MATERIALS

While you can do the entire course entirely on paper, it’s not really recommended since physicsis based in real-world observations and experiments! Here’s the list of materials you need inorder to complete all the experiments in this unit.Please note: you do not have to do ALL the experiments in the course to have an outstandingscience education. Simply pick and choose the ones you have the interest, time and budget for.

2 hand

held magnifiers

dollar bill

penny

red laser pointer

green laser pointer

paper clip (2)

pliers

rubber band (2)

pond water (just a little bit)

two pairs of polarized sunglasses

tape (the 3/4″ glossy clear kind works best –

watch video for details)

index card

glass of water

feather

old CD and DVD

diffraction grating

strand of hair

calculator

ruler

paper

clothespin

flashlight (3 is best, but you use 2)

red, green, and blue fingernail polish

polarized sunglasses (2 pair)

metal frying pan or cookie sheet

TV remote control

plastic sheet

UV beads

sunblock

sunglasses

clear plastic bag

disposable clear plastic cup or glass jar

one of each: red, green, and blue true-

colorlight sticks

scissors with adult help

white wall space

dark room

pencil

cut-crystal (wine glasses, fancy vases, etc)

microscope slide or window

feather

frosted incandescent light bulb

red and green gummy bear

glass jar

few drops of milk

protractor

scissors

cardboard box

stack of books

marker

clothespin

brass fastener

hot glue gun

piece of grid

paper


INTRODUCTION

Energy can take one of two forms: matter and light (called electromagnetic radiation). Light is energy in the form of either a particle or a wave that can travel through space and some kinds of matter, like glass. We’re going to investigate the wild world of the photon that has baffled scientists for over a century.

Low electromagnetic radiation (called radio waves) can have wavelengths longer than a football field, while high energy gamma rays can destroy living tissue. We’re going to have a look at the nutty fellow called the ‘photon’ and its very odd behavior during two important experiments that, at first glance, seem to be in conflict with each other. The behavior of light is so strange that scientists are still trying to work out the details.

Imagine tossing a rock into a still pond and watching the circles of ripples form and spread out into rings. Now look at the ripples in the water and notice how they spread out. What makes the ripples move outward is energy, and there are different kinds of energy, such as electrical (like the stuff from your wall socket), mechanical (a bicycle), chemical (a campfire) and others.

The ripples are like light. Notice the waves are not really moving the water from one side of the pond to the other, but rather move energy across the surface of the water. To put it another way, energy travels across the pond in a wave. Light works the same way – light travels as energy waves. Only light doesn’t need water to travel through the way the water waves do – it can travel through a vacuum (like outer space).


LIGHT IS A WAVE

Energy can take one of two forms: matter and light (called electromagnetic radiation). Light is energy

that can travel through space. When you feel the warmth of the sun on your arm, that’s energy from the

sun that traveled through space as infrared radiation (heat).When you see a tree or a bird, that’s light

from the sun that traveled as visible light (red, orange… the whole rainbow) reflecting and bouncing off

objects to get to your eye. Light can travel through objects sometimes… like the glass in a window.

Light can take the form of either a wave or a particle, depending on what you’re doing with it. It’s like a reversible coat – fleece on the inside, windbreaker on the outside. It can adapt to whatever environment you put it in. This actually baffled scientists for years – they wanted it to be either ONE or the other, not both! “You can either wear your sweater or your jacket…” but light wanted to wear both, so it does! When light decides to be a particle, like a marble, it’s called a photon. You can think of photons as packets of light, just like M&Ms are little packets of chocolate. Photons are little packets of light.

In the sun, there are zillions of photons. In total darkness of the furthers reaches of outer space, there’s only a single photon or two. There are certain behaviors of light that you just can’t explain if you were to look at it just as a photon particle. Interference, reflection, refraction, diffraction, Doppler shifts are some of these behaviors. Particles like marbles don’t interfere with each other the way that waves do!


LIGHT REFLECTION

You can see objects because light from that object travels to your eyes. Sometimes light is reflected off objects before it reaches our eyes, and sometimes it comes straight from the source itself.

A candle is a light source. So is a campfire, a light bulb, and the sun. An apple, however, reflects light. It doesn’t give off any light on its own but you can see it because light waves bounce off the apple into your eye. If you shut off the light, then you can’t see the apple. In this same way, the sun is a light source, and the moon is a light reflector. You see objects because light reflections because light reflects off them into your eye. The angle that the

light wave approaches it equal to the angle that the wave leaves the surface, which is not only true for

light but also sound waves.


DOES LIGHT TRAVEL IN A STRAIGHT LINE?

Does light travel in a straight line? Let’s find out…


LIGHT REFRACTION

Light also bends as it passes from one medium to another, like going from the air to a glass window. But

why does that happen?

You can imagine a toy car going from a wood floor to carpeting. One wheel hits the carpet first and slows down before the other, causing the toy to turn. The direction of the wave changes in addition to the speed. The slower speed must also shorten its wavelength since the frequency of the wave doesn’t change. The bottom line is that bending is caused by the change in speed of light when it crosses a boundary. This is true everywhere, even in the vacuum of space if it’s going from space to our atmosphere.


LIGHT REFRACTION USING TWO LASERS

Here’s a cool experiment that uses two different colored lasers to show you how light refracts when it

moves from one medium to another:


DIFFRACTION

Diffraction happens when light goes around obstacles in its path. Sound waves diffract bend around

obstacles, so if you’re stuck behind a pillar at a concert, you can still hear just fine.

When light passes through a diffraction grating, it splits (diffracts) the light into several beams traveling

at different directions. If you’ve ever seen the ‘iridescence’ of a soap bubble, an insect shell, or on a pearl,

you’ve seen nature’s diffraction gratings.


Diffraction Overview:When light passes through diffraction gratings, it splits (diffracts) the light into several beams travelingat different directions. If you've ever seen the “iridescence” of a soap bubble, an insect shell, or on a pearl, you've seen nature's diffraction gratings.

What to Learn:Ever play with a prism? When sunlight strikes the prism, it gets split into a rainbow of

colors.Prisms un-mix the light into its different wavelengths (which you see as different colors). Diffraction

gratings are tiny prisms stacked together. The direction that the beam gets split and diffracted depends on the

spacing of the diffraction grating and also the wavelength of the incoming light.

Materials

feather

CD or DVD

diffraction grating

Experiment

1. Take a feather and put it over an eye.

2. Stare at a light source through the feather, like an incandescent light.

3. You should see two or three lights and a rainbow X.

4. Aim the CD so the light hits the CD and makes rainbows.

5. Look at the light source through the diffraction grating.

6. Draw what you see for all three. Were they the same?

7. Take this on a “light treasure hunt” to find different light sources. Good choices are candles, incandescent bulbs, fluorescent bulbs, non signs, halogen lamps, streetlights, stoplights, and anything else you can

think of that gives off light (except the sun).

8. Complete the table as you view the different light sources through your diffraction gratings.


Diffraction Data Table


Reading

Ever play with a prism? When sunlight strikes the prism, it gets split into a rainbow of colors. Prisms un-mix the

light into its different wavelengths (which you see as different colors). Diffraction gratings are tiny prisms stacked

together. The direction that the beam gets split and diffracted depends on the spacing of the diffraction grating

and also the wavelength of the incoming light.

The feather works because there are tiny “hairs” on the feather that are acting like tiny prisms.

Diffraction gratings were first discovered by James Gregory, right around the time Newton performed his

famous prism experiments with bird feathers. The first diffraction gratings took a long time to construct, as they

were individual hairs strung between screws.

A diffraction grating bends the light and splits it into different beams. You can see this very well when you use a monochromatic light source, like a laser, instead of a multi-wavelength light source.

Exercises

1. Which light source gave the most interesting results?

2. What happens when you aim a laser beam through the diffraction grating?


3. How is a CD different and the same as a diffraction grating?

4. Why does the feather work?

Answers to Exercises: Diffraction

1. Which light source gave the most interesting results? (This varies with data.)

2. What happens when you aim a laser beam through the diffraction grating? (It splits into three beams of light, as shown in the second video.)

3. How is a CD different and the same as a diffraction grating? (A CD has a spiral of finely‐spaced data tracks

while the diffraction grating has a series of parallel lines. The CD splits the light the same way as the

diffraction grating. The CD splits the beam into more than three beams.)

4. Why does the feather work? (There are tiny “hairs” on the feather that are acting like tiny prisms.)


USEFUL DIFFRACTION

Diffraction is very useful to measure things, because we can predict how much light will bend

around particular obstacles. Here’s how you can measure the width of your hair using a laser

diffracting around the hair:


INTRODUCTION TO LASERS

Since we’re starting to use lasers, let’s take a quick detour and see how lasers are different from

flashlights…

Lasers are optical light that is amplified, which means that you start with a single particle of light (called a photon) and you end up with a lot more than one after the laser process.

Stimulated emission means that the atom you’re working with, which normally hangs out at lower energy levels, gets excited by the extra energy you’re pumping in, so the electrons jump into a higher energy level. When a photon interacts with this atom, if the photon as the same exact energy as the jump the electron made to get to the higher level, the photon will cause the electron to jump back down to the lower level and simultaneously give off a photon in the same exact color of the photon that hit the atom in the first place.

The end result is that you have photons that are the same color (monochromatic) and in synch with each other. This is different from how a light bulb creates light, which generates photons that are scattered, multi-colored, and out of phase. The difference is how the light was generated in the first place.

Radiation refers to the incoming photon. It’s a word that has a bad connotation to it (people tend to think all radiation is dangerous, when really it’s only a small percentage that is). So in this case, it just means light in the laser. The incoming photon radiation that starts the process of stimulated emission (when the electron jumps between energy levels and generates another photon), and the light amplification means that you started with one photon, and you ended up with two. Put it all together and you have a LASER!


LIGHT INTERFERENCE

Laser light is coherent, which means that all the light waves peaks and valleys line up. The dark

areas are destructive interference, where the waves cancel each other out. The areas of brightness

are constructive interference, where the light adds, or amplifies together. LED light is not coherent

because the light waves are not in phase.


MORE ON LIGHT INTERFERENCE

Let’s take a closer look at the interference patterns of light:


THIN FILM INTERFERENCE

Ever noticed a rainbow on top of a water puddle where there is oil floating on top?The oil is spread in a very thin layer on top of the water, and when light hits this thin layer, it interferes and causes a rainbow to be seen.


POLARIZATION

Polarized glasses filter out any light that’s not coming from a certain direction. It allows some of the light to go through, but not all. So polarized lenses are light filters. Because it varies in brightness depending on its stage, astronomers use polarizing filters to look at the moon. They can use rotating polarizing filters to adjust the amount of light entering the eye. White light, like from the sun, vibrates in all directions. Polarizers are special kinds of filters that block out all light except for the ones that are vibrating in the vertical plane.

Polarization has to do with the direction of the light. Think of a white picket fence – the kind that has space between each board. The light can pass through the gaps in the fence but is blocked by the boards. That’s exactly what a polarizer does. It filters the light depending on its direction.

When you have two polarizers, you can rotate one of the “fences” a quarter turn so that virtually no light can get through – only little bits here and there where the gaps line up. Most of the way is blocked, though, which is what happens when you rotate the two pairs of sunglasses. Your sunglasses are polarizing filters, meaning that they only let light of a certain direction in. The view through the sunglasses is a bit dimmer, as less photons reach your eyeball.

You use the “filter” principle in the kitchen. When you cook pasta, you use a filter (a strainer) to get the pasta out of the water. That’s what the sunglasses are doing – they are filtering out certain types of light. Rotating the lenses 90° to block out all light is like trying to strain your pasta with two strainers that don’t have their holes lined up, so it’s more like a mixing bowl. Nothing is allowed to pass through. To understand polarization, we have to have a deeper look into what light really is. Have you wondered by scientists call light electromagnetic radiation? What does electricity and magnetism have to do with light?

Energy in the form of electromagnetic (EM) radiation is one of the two forms of energy in the universe (matter being the other). This type of energy is made when electrically charged particles (like electrons) move. One of the most important discoveries in science was that electricity and magnetism are linked. A moving electrical charge creates a magnetic field. Moving charges (electric fields) create magnetic fields.

Also – moving magnetic fields create electric fields. If you wrap a nail with wire and rub a magnet vigorously along its length, you can measure a voltage.

So a moving electrical charge creates a magnetic field, and the creation of the magnetic field creates an electric field, which then creates a magnetic field, which in turn created as electric field… and soon you have a wave leapfrogging through space just like a wave on the ocean. That wave is light. The kind of light wave you have (radio, visible, x-ray) depends on how much energy your wave has.


Polarization has to do with the direction of the electric field. Your sunglasses are polarizing filters, meaning that they only let light of a certain direction in. The view through the sunglasses is a bit dimmer.

Polarizing sunglasses also reduce darken the sky, which gives you more contrast between light and dark, sharpening the images.

Astronomers use polarizing filters to look at the moon. Ever notice how bright the moon is during a full moon, and how dim it is near new moon? Using a rotating polarizing filter, astronomer can adjust the amount of light that enters into their eye so they can see more detail on the surface without being blinded with too much light.


SHADOWS

Here’s a neat experiment you can do with shadows…


COLOR AND VISION

The electromagnetic spectrum shows the different energies of light and how the energy relates to different frequencies. The wavelength (λ) equals the speed of light (c) divided by the frequency (ν), or λ = c / ν. The speed of light is: c = 3 x 108 m/s (300,000,000 meters per second). You and I don’t detect most electromagnetic waves. Our eyeballs can only ‘see’ in the 400-700 nm (nanometer) range, which is only a small part of the entire spectrum, so we need special detectors to find the rest of the photons zipping around. Radio signals are picked up using an antenna (similar to your satellite dish in the backyard). These waves have the longest wavelengths and lowest energy in the electromagnetic spectrum. X-rays are more difficult to detect, because they would rather go through the detector than bounce off of it, so we use complicated mathematics and the shadows of the photons to “see” x-rays. Gamma rays are the toughest to detect – they are very highly energized packets of light that would rather zoom through mirrors than be detected. Gamma radiation has the highest energy and highest frequency in the electromagnetic spectrum.


Infrared Light

Overview: Infra-red light is in the part of the electromagnetic spectrum that isn’t usually visible to

human eyes, but using this nifty trick, you will easily be able to see the IR signal from your TV remote,

remote-controller for an RC car, and more!

What to Learn: When you press the button on your remote control to your TV, you’re using infrared light

(IR) to control your TV. Infrared light is invisible to our eyes. However, snakes can detect IR and see the

redder hues that we can’t. Every warm body gives off light in the IR, so snakes use this to find mice in the

cool night.

Materials :

You will need these items:

remote control for TV or stereo

camera (video or still camera)

This is just a suggested list of objects. Feel free to find your own!

metal frying pan or cookie sheet

plastic sheet

plastic baggie

trash bag (white or black, or both)

wooden cutting board

Experiment

1. Grab a remote control and verify that it is indeed working. Turn the device on and off using the remote.

2. Grab a sheet of plastic, like a cutting board, and place it between your remote and the device. Does it turn on when you aim the beam at it? Does the plastic block the beam?

3. Open up a trash bag and place one side of the bag between your remote and the device. Did that block the beam, or did the remote turn on the device?

4. What else can you try? How about a clear bag? 5. A clear bag filled with water? 6. A sheet of paper? 7. What about a metal pan? Find something that’s not coated with Teflon. Does infrared go through

metal?


8. What if you point it at a white wall behind you, pretending the white wall is a mirror and aiming it so it will reflect it back to the device?

9. Complete the table. 10. Now let’s make the invisible infrared light visible. Take your camera (either still or video camera

will work) and turn it on. Put it on a mode where you can see through the view screen. Aim the infrared camera right at the emitter for the remote (usually near the top) and press a button. Point the remote right at the camera and watch through the camera. Our eyes normally can’t see the infrared light, but the camera can!

11. The camera can also see the otherwise dark end of the remote! If your camera has a special night vision mode, where it’s especially sensitive to infrared light? If so, try it!

Infrared Data Table

Item/Object Tested Guess FIRST! What Happened?

Will the Infrared Light (Did it pass through or not?)

Pass Through?

Reading

Different detectors are sensitive to different colors. Your eyeballs are sensitive to specific colors in the 400-700 nm (nanometer) range which is how long one wavelength is. A nanometer is extremely tiny!

The frequency of red light is around 430 trillion Hz (Hertz, which is one wave cycle per second). If you

were to count the number of waves passing a certain point in one second, you’d count 430 trillion

waves. If you counted 750 trillion waves, the light would be violet. Different colors have different

frequencies.


Light energy (also called electromagnetic radiation) with the lowest amounts of energy and longest

wavelengths (1mm to 1km) are radio waves. These are emitted by radio galaxies like quasars,

supernova leftovers, and the radio tower at the top of the hill. Radio waves from space with a

wavelength greater than 100 meters are reflected back into space by our atmosphere. Radio waves are

detected in space by the COBE satellite, the VLA in New Mexico, and the Arecibo Observatory in South

America.

The next step down in wave size is microwaves, which have more energy than radio waves but are a shorter wavelength. These are the ones inside your microwave that excite the water molecules inside

your food so that your food heats up.

Infrared (IR) has slightly more energy and an even smaller wavelength (700 nanometers, or nm to 1mm), and you can feel this light as warmth on your skin when you step into the sun. There’s a lot of infrared radiation in space

around the star-forming clouds and objects with a temperature above 1000°C. SOFIA and the Infrared Observatory both detect infrared from various stars in space.

Visible light or optical light waves are the visible rainbow you can see with your eyes after a rainy

day. These wavelengths have more energy and shorter wavelengths (300 to 700 nm) than infrared. The

Hubble Space Telescope and Earth-bound optical telescopes look at stars, galaxies, and planets.

Ultraviolet (UV) light has more energy and shorter wavelengths (10nm to 390nm) than visible light, and

you’ll find hot stars emit largely in this region of the spectrum. The ozone layer protects us from most of the

UV, but not all. That’s why you get a sunburn if you don’t wear sun block, and why colors fade in sunlight.

SkyLab, Astrotelescope and SOHO all search for UV. SOHO looks directly at the sun’s corona to get amazing

images in UV.

X-rays have even more energy and short wavelengths (0.01nm to 10 nm) than UV light, and you’ll find

these are emitted by active black holes, supernova remnants, and very hot stars (we’re talking 1 million to

100 million° C). Fortunately for us, these are quickly absorbed in the upper atmosphere and most never

make it to the surface of Earth. X-rays generated on earth are emitted by electrons outside the nucleus of

an atom. ROSAT looked at cluster galaxies to detect X-ray sources.

Deadly gamma rays have the most amount of energy and the shortest frequency (less than 0.01 nm), and

you’ll find these in areas of superflares from pulsars, supernovas, and radioactive atoms. Gamma rays are

like X-rays, in that they both can go through thick materials, and would rather go through your detector

than into it to be detected. Gamma rays on Earth are generated inside the nucleus of an atom. The

Compton Observatory looked at quasars to detect gamma rays.


Exercises

1 Look over your data table. What kinds of objects (plastic, metal, natural, etc.) allow infrared light to pass through them?

2 Why does the camera work in making the infrared light visible?


Answers to Exercises: Infrared Light

1. What kinds of objects allow infrared light to pass through them? (Check data.)

2. Why does the camera work in making the infrared light visible? (The camera is a viewer that lets us

see this special frequency of light. Light is technically what we call electromagnetic radiation.

Radio waves, infrared, microwaves, X‐rays, and gamma rays are all electromagnetic radiation. If

you could see the radio waves, then you could see radio towers as they transmit. They would

appear to light up. If you could see all forms of light, then not only could you see the radio towers,

but also your cell phone, the doctor’s X‐ray cameras, and your car radio would all be lit up as they

operated. It’s all made out of the same stuff, just not all of it is visible to our eyes.)


VISIBLE LIGHT

Do you see where the “visible light” rainbow section is in the electromagnetic spectrum image below? This small area shows the light that you can actually see with your eyeballs. Note that the “rainbow of colors” that make up our entire visible world only make up a small part of all the light, from 400-700 nm (nanometers (nm), or 10-9 meters). Each color corresponds to a particular wavelength within the visible light spectrum. When that wavelength hits your eye, you perceive a particular color. Red has the longest wavelengths (closer to 400 nm) and violet has the highest frequencies (closer to 700nm). UV (ultra-violet) light is invisible, which means you can’t see it with just your eyes. Our sun gives off light in the UV. Too much exposure to the sun and you’ll get a sunburn from the UV rays. UV sensitive materials have a pigment inside that changes color when exposed to UV light from either the sun or lights that emit in the 350nm – 300nm wavelength. If you have fluorescent black lights, use them. (Do regular incandescent bulbs work? If not, you know they emit light outside the range of the beads!) UVA waves are the longest of the UV waves, and you’ll find them in black lights. These are not absorbed by the ozone layer. Their frequency wavelength ranges from 315-400nm. UVB waves are is medium energy waves, mostly absorbed by the ozone layer and have a range between 315-280nm). UVC are the shortest, highest energy UV waves that are used to kill germs, and they are completely absorbed by the atmosphere and the ozone layers. On the other end of the visible spectrum of visible light is infrared light. Infra-red light is in the part of the electromagnetic spectrum that isn’t usually visible to human eyes, but using this nifty trick, you will easily be able to see the IR signal from your TV remote, remote-controller for an RC car.


Ultraviolet Light

Overview: Stars, including our sun, produce all kinds of wavelengths of light, including UV (ultra-violet). That’s the wavelength that gives you sunburns. We’re going to find out the best way to protect you from the harmful rays.

What to Learn: The UV beads we’re going to use in our experiment are made from a chemical that reacts with light. It takes the UV light from the sun and then re-emits it in a different wavelength that’s visible to us.

Materials

5 UV beads (these change colors when exposed to the sun) tape (double-sided is easier) sun block sunglasses (ask the kids to bring a pair) sunny day water piece of fabric clear plastic bag

Experiment

1. Place a piece of tape on the data table, and stick your beads to the tape, one in each box.

2. Walk outside with your data table and record your observations.

UV Light Data Table 1


3. Walk back indoors and cover the beads, blocking out all light. Peek at them every minute or two to find out when they’ve returned to their unexposed color.

4. Now prepare your second round of testing by doing the following before exposing the beads to the sun:

a. Place a bead inside a baggie.

b. Place a second bead inside a baggie filled with water.

c. Smear a clean baggie with sun block and place a third bead inside.

d. Place a pair of sunglasses over a fourth bead.

e. Place a fifth bead under a piece of fabric.

5. Walk your five beads outside and record your observations in the data table.


6. Bring your beads back inside and return them to their unexposed color.

7. Prepare your third round of testing by exposing your beads to some of the following:

f. a fluorescent lamp

g. an incandescent lamp

h. flashlight

i. glow stick

j. computer screen

k. reflected sunlight using a mirror


l. candle flame (please be careful with this!)

m. any other light source you have access to

8. Record your observations in the data table.


Light Color Inside Color When Exposed How Long Did It Take to

Source Change Color when Exposed?

Reading

Stars, including our sun, produce all kinds of wavelengths of light, even UV. The UV beads we’re going to

use in our experiment are made from a chemical that reacts with light. It takes the UV light from the sun

and then re-emits it in a different wavelength that’s visible to us.

When a particle of UV light smacks into an atom, it collides with an electron and makes the electron jump

to a higher, more energetic state that is a bit further from the center of the atom than it’s comfortable

being. That’s how energy gets absorbed by an atom. The amount of energy an electron has determines how

far from the atom it has to be. The electron prefers being in its lower state, so it relaxes and jumps back

down, transferring a blip of energy away as it does. This blip of energy is the light we see emitted from the

UV beads. This process continues as long as we see a color coming from the UV beads.

UV sensitive materials have a pigment inside that changes color when exposed to UV light from either the

sun or lights that emit in the 350nm – 300nm wavelength. (UVA is high-energy: 400-320nm, and UVB is

low energy: 320-280nm). If you have fluorescent black lights, use them. (Do regular incandescent bulbs

work? If not, you know they emit light outside the range of the beads!)

When light hits the pigment molecule, it absorbs the energy and actually expands asymmetrically (one end

of the molecule expands more than the other). Different expansion amounts will give you a different color.

Although it’s a bit more complicated than that, you now have the basic idea. Your beads will change colors

thousands of times before they wear out, so enjoy these super-inexpensive UV detectors.


A note about sun block: You can test different SPF levels of sun block, but here’s the main idea behind the

ratings: the number for SPF is the number of minutes it takes to get the same sun exposure than if you

weren’t wearing any for one minute. For example, SPF 30 will give you the same sun exposure after 30

minutes that you would normally get if you weren’t wearing any after just one minute.

Exercises

1. What kinds of light sources didn’t work with the UV beads?

2. Did your sun block really block out the UV rays?

3. Which was the best protection against UV rays?


Answers to Exercises: Ultraviolet Light

1. What kinds of light sources didn’t work with the UV beads? (Check data.)

2. Did your sun block really block out the UV rays? (Check data.)

3. Which was the best protection against UV rays? (Check data.)


COLD LIGHT MIXING

You can demonstrate the primary colors of light using glow sticks! When red, green, and blue cold

light are mixed, you get white light. Simply activate the light stick (bend it until you hear a *crack*

– that’s the little glass capsule inside breaking) and while wearing gloves, carefully slice off one

end of the tube with strong cutters, being careful not to splash (do this over a sink).

Sometimes the chemical light sticks contain a glowing green liquid encapsulated within a red or

blue plastic tube, so when you slice it open to combine it with the other colors, it isn’t a true red.

Be sure that your chemical light sticks contain a glowing RED LIQUID and BLUE LIQUID in a clear,

colorless plastic tube, or this experiment won’t work.


Mixing Cold Light

Overview: You can demonstrate how the primary colors of light mix together using glow sticks. The glow

stick gives off its own light through a chemical reaction called chemiluminescence, which isn’t the same as

mixing paint together, since cups of paint are reflecting light, not generating it. It’s like the difference

between the sun (which gives off its own light) and the moon (which you see only when sunlight bounces

off it to your eyeballs).

What to Learn This

Materials

disposable test tubes

red, green, and blue true-color light sticks (one of each)

scissors (with adult help)

gloves

goggles

strainer, such as a coffee filter or bit of cheesecloth

Experiment

1. Bend the light sticks to break the glass inside the container (you’ll hear a little “crack”). Do this for all three light sticks. This will activate the sticks.

2. Slap your gloves on your hands and goggles on your eyes. No exceptions.

3. Stand over a sink and carefully cut one end off of the light sticks. Get an adult to help, as the plastic can be stiff to cut through.

4. Carefully pour a tiny amount of one of the colors into your test tube. If bits of glass come out also, use the cheesecloth as a strainer to catch the pieces of glass from inside the tube.

5. Now add a second color and swirl gently to mix. Record your observations in the data table.

6. Repeat steps 4 and 5 for your data table.

7. Note: You may not need all of the red, due to its level of color concentration. Only add about half of the red and swirl until the colors are completely mixed. Add more red if needed to adjust the color.

8. When you are done with this lab, discard the bits of glass in the trash and flush the liquid down the sink with plenty of water.


9. Mixing Cold Light Data Table

Color #1 Color #2 Color #3 (optional) Resulting Color

Reading

When we talk about light, its three primary colors are actually red, green, and blue. As a painter, you

already know that mixing these three colors together would get a muddy brown. But as a scientist, when

you mix together three cups of cold light, you will get something different. You’d get white light.

The key is that we would be mixing light, not paint. Mixing the three primary colors of light gives white

light. If you took three light bulbs (red, green, and blue) and shined them on the ceiling so they overlap,

you’d see a white spot where the three converge. And if you could magically un-mix the white colors,

you’d get the rainbow (which is exactly what prisms do).

If you’re thinking yellow should be a primary color – it is a primary color, but only in the artist’s world.

Yellow paint is a primary color for painters, but yellow light is actually made from red and green light.

There’s an easy way to remember this: think of Christmas colors – red and green merge to make the

yellow star on top of the tree.

The cold light is giving off its own light through a chemical reaction called chemiluminescence, whereas

the cups of paint are only reflecting nearby light. It’s like the difference between the sun (which gives off

its own light) and the moon (which you see only when sunlight bounces off it to your eyeballs).

Note: If you’re wondering if the real primary colors for painters are cyan, magenta, and yellow, you’re

right… but some folks still prefer to think of the primary colors as red-yellow-blue… either way, it’s

really not important to this experiment which primary set you choose, since the experiment deals with

light, not paint.


Exercises

1. What color do you get when you mix blue and green liquid lights?

2. What happens when you start to add the red light?

3. What is your final color result when mixing red, blue, and green lights?

4. How would your result differ if you instead mixed red, blue and green paints?


Answers to Exercises: Mixing Cold Light

1. What color do you get when you mix blue and green liquid lights? (answers vary – green to blue)

2. What happens when you start to add the red light? (the color starts to pale)

3. What is you final color result when mixing red, blue, and green lights? (white)

4. How would your result differ if you instead mixed red, blue and green paints? (it would be a brown color)


WHAT IS COLOR?

Is white or black a color? No and no. White is the mixture of all the colors (red, orange, yellow,

green, blue indigo, and violet), so technically white isn’t a color of light but rather the combination

of colors. Black is also not technically a color. In outer space, it’s pitch-black dark because there’s

no light. In a room with the lights off, it’s also black. Black is the absence of color.

Wasn’t that amazing how you can make objects change color just by changing the color light you

hit it with?


WHERE DO DIFFERENT COLORS COME FROM?

Have you ever wondered where different colors come from? Here’s the physics behind why apples

are red and grass is green…


PIGMENTS

A pigment takes incoming light, absorbs certain wavelengths, and reflects the rest so you see a

particular color. Pigments change the color of reflected light (or transmitted light, which we’ll get

to soon when we cover colored filters.)

Pigments are used in fabrics, paints, ink, make-up, food, and many other materials. A pigment is

different from a dye in that a dye is usually a liquid or can be made into a liquid by mixing in

solution, whereas a pigment is a powder.


COLOR FILTERS

When you change the wavelength, you change the color of the light. If you pass a beam white light

through a glass filled with water that’s been dyed red, you’ve now got red light coming out the

other side. The glass of red water is your filter. But what happens when you try to mix the

different colors together?


Rainbow Shadows

Overview: Imagine you’re a painter. What three colors do you need to make up any color in the universe?

(You should be thinking: red, yellow, and blue… and yes, you are right if you’re thinking that the real

primary colors are cyan, magenta, and yellow, but some folks still prefer to think of the primary colors as

red-yellow-blue… either way, it’s really not important to this experiment which primary set you choose.)

Here’s a trick question – can you make the color “yellow” with only red, green, and blue as your color palette? If you’re a scientist, it’s not a problem. But if you’re an artist, you’re in trouble already. The key is mixing light, not paint.

What to Learn: The three primary colors of light are red, blue, and green. Red and green light mixed together make yellow light. Sunlight can be blocked to make shadows.

Materials

flashlights (3)

fingernail polish ( red, green, and blue)

clear tape (NOT translucent)

a white wall (or another large white surface)

Experiment

1. Make your room as dark as possible for this experiment to work.

2. Cover each flashlight lens completely with the clear tape. Be sure to get the edges and around the rim.

3. Paint one flashlight’s tape layer red, one blue, and one green. Make sure there are no unpainted spots.

4. Allow the nail polish to dry.

5. Turn off all the lights.

6. Shine the flashlights together onto a white wall. What color is the wall? Record it on your chart

7. Now turn off the red flashlight. What color do you see now? Record your observation.

8. Place your hand, a pencil, or another object in front of the flashlight. Wave it around a bit. What color shadows do you see on the wall?

9. Experiment with the different color combinations while filling out the chart with your observations.


Rainbow Shadows Data Table

Lens #1 Color Lens #2 Color Shadow Color

Reading

Mixing the three primary colors of light gives white light. If you took three light bulbs (red, green, and blue)

and shined them on the ceiling, you’d see white. And if you could magically un-mix the white colors, you’d

get the rainbow (which is exactly what prisms do).

If you’re thinking yellow should be a primary color – it is a primary color, but only in the artist’s world.

Yellow paint is a primary color for painters, but yellow light is actually made from red and green light.

(Easy way to remember this: think of Christmas colors – red and green merge to make the yellow star on

top of the tree.)

Troubleshooting: This experiment has a few things to be aware of. If you’re not getting the colored shadows,

check to be sure that the flashlight is bright enough to illuminate a wall in the dark. Be sure to shut the

doors, shades, windows, and drapes. In the dark, when you shine your red flashlight on the wall, the wall

should glow red. Beware of using off-color nail polish – make sure it’s really red, not hot pink. Alternately,

you could use brightly-colored cellophane.

If you still need help making this experiment work, you can visit your local hardware store and find three flood

lamp holders (the cheap clamp-style ones made from aluminum work well – you’ll need three) and screw in

colored “party lights” (make one red, one green, and one blue), which are colored incandescent bulbs.

These will provide a lot more light! You can also add a fourth yellow light to further illustrate how yellow

light isn’t a primary color. Try using only red, yellow, and blue… you’ll quickly find that you can’t obtain

all the colors as you could with the original red-green-blue lights.


Exercises

1. What are the three primary colors of light?

2. What color do you get when mixing the primary colors of light?

3. How do you mix the primary colors of light to get yellow?

4. Use crayons or colored pencils to draw what you saw when all three lights were shining on the wall and you waved your hand in front of the light.


Answers to Exercises: Rainbow Shadows

1. What are the three primary colors of light? (red, blue, and green)

2. What color do you get when mixing the primary colors of light? (white)

3. How do you mix the primary colors of light to get yellow? (green and red light make yellow light)

4. Use crayons or colored pencils to draw what you saw when all three lights were shining on the wall and you waved your hand in front of the light.


PAINT AND LIGHT

Imagine you’re a painter and you’ve only got three colors to paint with. Which colors do you have on your palette?

You should be thinking: red, yellow, and blue. (And yes, you are right if you’re thinking that the real primary colors are cyan, magenta, and yellow, but some folks still prefer to think of the primary colors as red-yellow-blue, but either way, it’s really not important which primary set you choose for this particular lesson. We’ll get more specific and use the right colors in the next lesson, so stick with me for now…)

Here’s a trick question – can you make the color “yellow” with only red, green, and blue as your color palette? If you’re a scientist, it’s not a problem. But if you’re an artist, you’re in trouble already. The key is that we would be mixing light, not paint. Mixing the three primary colors of light gives white light. If you took three light bulbs (red, green, and blue) and shined them on the ceiling, you’d see white. And if you could magically un-mix the white colors, you’d get the rainbow (which is exactly what prisms do.)

If you’re thinking yellow should be a primary color – it is a primary color, but only in the artist’s world. Yellow paint is a primary color for painters, but yellow light is actually made from red and green light.


HOW TO PAINT WITH LIGHT

It’s true that the primary colors of paint are cyan, yellow, and magenta. The question is, why? It

has to do with how pigments reflect light.

Your brain doesn’t know the difference between yellow light and two lights overlapping to make

yellow light. To the brain, these are the same thing.


RODS AND CONES

Your eyes have two different light receptors located on the back of the eyeball. These are the rods, which see black, white and grays can detect different intensities. The cones can detect color when the light strikes the cells that have a color-sensing chemical reaction that gets activated and sends a pulse to the brain. There are three cones: red, which can detect red wavelengths and some orange and yellow, green cones (which can also detect blue and yellow) are the most sensitive to light, and blue cones.

So when white light hits your retina, all three cones are activated, and all three cones send signals to the brain, which puts these messages together to see white light. In order to adapt to the dark, our eyes make a chemical called visual purple. This helps the rods to see and transmit what you see in situations where there is little light. Your pupils also increase in diameter in the darkness. This allows for a slight increase in the amount of light entering your eye. This combination of visual purple and more light makes it possible for you to see in darker situations. We’ll talk more about this later when we look at The Eye.


Camera Eyes

Overview: Your eyes have two different light receptors located on the back of the eyeball. These are the

rods, which see black, white and grays, and the cones, which see color. In order to adapt to the dark, our

eyes make a chemical called visual purple. This helps the rods to see and transmit what you see in

situations where there is little light.

Your pupils also increase in diameter in the darkness. This allows for a slight increase in the amount of

light entering your eye. This combination of visual purple and more light makes it possible for you to

see in darker situations.

Materials

dark room

light switch

partner

pencil

Experiment

1. Turn out the light in a darkened room and give your eyes about 5 minutes to get used to the darkness.

2. After your eyes have had a chance to acclimate to the low-light conditions, it’s time to get to work. Try to draw a picture of your assistant’s eye. Pay particular attention to how the pupil looks in the darkness.

3. Now turn on the light while still observing your partner’s eye. What happens to their pupil?

4. Draw another picture of your partner’s eye with the lights on. Again, pay special attention to the diameter pupil of the eye.

5. Complete the data table by trying different lighting conditions.


Camera Eyes Data Table

Light Conditions Draw a Diagram of the Eye

Reading

As you flip the light switch on, your partner’s brain realizes that there is a lot of light entering the rods and

cones, so it restricts the size of the opening (your partner’s pupil) in order to limit the light. You might

notice this on a sunny day if you go from a dark movie theater into the bright sun. It can actually hurt for

moment, and makes you squint until your eyes have a chance to adjust to the brightness by reducing the

size of your pupils.


Exercises

1. How does the pupil adapt to light conditions?

2. What are the two special photoreceptors called and where are they located?

3. Which photoreceptor is used to help us see in the dark?


Answers to Exercises: Camera Eyes

1. How does the pupil adapt to light conditions? (Its diameter increases in the dark to allow in more light and decreases in bright light.)

2. What are the two special photoreceptors called and where are they located? (Rods and cones are located in our eye’s retina.)

3. Which photoreceptor is used to help us see in the dark? (rods)


LIGHT ABSORPTION

When light hits an object, it can do a number of things: it can transform into heat, be completely

absorbed by the object, be reflected and bounce off the object, or be transmitted through the

object.

The electrons inside of atoms vibrate at different frequencies. When light at the same natural frequency as the electrons in the atom, the electrons absorb the light wave energy and turn it into vibrational motion, which gets transformed into thermal energy (and not reflected or transmitted).

If the frequency of the incoming light matches that of the electrons in the object that the light is striking, then the wavelengths are absorbed. If they don’t match, then reflection and transmission happen.


HOW DOES LIGHT GET ABSORBED?

When light hits an object, the electrons begin vibrating (but not at resonance as with absorption) and energy is emitted at smaller amplitudes. If the object is transparent like a window, then the vibrations can pass through the other side. If the object is opaque, then the vibrations aren’t passed through the object stay on the surface and get reflected.

Here’s a cool way to play with your food and learn about absorption, transmittance, and reflection…


MARTIAN SUNSETS

Have you ever wondered why the sky is blue? Or why the sunset is red? Or what color our sunset would be if we had a blue giant instead of a white star? This lab will answer those questions by showing how light is scattered by the atmosphere.

Particles in the atmosphere determine the color of the planet and the colors we see on its surface. The color of the star also affects the color of the sunset and of the planet. The colors you see in the sky depends on how light bounces around. The red/orange colors of sunset and sunrise happen because of the low angle the Sun makes with the atmosphere, skipping the light off dust and dirt (not to mention solid aerosols, soot, and smog). Sunsets are usually more spectacular than sunrises, as more “stuff” floats around at the end of the day (there are less particles present in the mornings). Sometimes just after sunset, a green flash can be seen ejecting from the setting Sun. The Earth appears blue to the astronauts in space because the shorter, faster wavelengths are reflected off the upper atmosphere. The sunsets appear red because the slower, longer wavelengths bounce off the clouds.

Sunsets on other planets are different because they are farther (or closer) to the Sun, and also because they have a different atmosphere than planet Earth. The image shown here is a sunset on Mars. Uranus and Neptune appear blue because the methane in the upper atmosphere reflects the Sun’s light and the methane absorbs the red light, allowing blue to bounce back out.


Sky in a Jar

Overview: Have you ever wondered why the sky is blue? Or why the sunset is red? Or what color our

sunset would be if we had a blue giant instead of a white star? This lab will answer those questions by

showing how light is scattered by the atmosphere.

What to Learn: Particles in the atmosphere determine the color of the planet and the colors we see on its

surface. The color of the star also affects the color of the sunset and of the planet. The color of light striking

an object affects how our eyes see it.

Materials

glass jar

flashlight

fingernail polish (red, yellow, green, blue)

clear tape

water

dark room

few drops of milk

Experiment

1. Make your room as dark as possible for this experiment to work. 2. Make sure your label is removed from the glass jar or you won’t be able to see what’s going on. 3. Fill the clear glass jar with water. 4. Add a teaspoon or two of milk (or cornstarch) and swirl. 5. Shine the flashlight down from the top and look from the side – the water should have a bluish

hue. The small milk droplets scatter the light the same way our atmosphere’s dust particles scatter sunlight.

6. Try shining the light up from the base – where do you need to look in order to see a faint red/pink

tint? If not, it’s because you are looking for hues that match our real atmosphere, and the jar just

isn’t that big, nor is your flashlight strong enough! Instead, look for a very slight color shift. If you

do this experiment after being in the dark for about 10 minutes (letting your eyes adjust to the lack

of light), it is easier to see the subtle color changes. Just be careful that you don’t let the brilliant

flashlight ruin your newly acquired night-vision, or you’ll have to start the 10 minutes all over

again.


7. If you are still having trouble seeing the color changes, shine your light through the jar and onto an index card on the other side. You should see slight color changes on the white card.

8. Cover the flashlight lens with clear tape. 9. Paint on the tape (not the lens) the fingernail polish you need to complete the table. 10. Repeat steps 7-9 and record your data.

Sky in a Jar Data Table

Flashlight Color Location Color(s)

White Side of jar

White Bottom of Jar

Red Side of jar

Red Bottom of Jar

Yellow Side of jar

Yellow Bottom of Jar

Green Side of jar

Green Bottom of Jar

Blue Side of jar

Blue Bottom of Jar


Reading

Why is the sunset red? The colors you see in the sky depend on how light bounces around. The

red/orange colors of sunset and sunrise happen because of the low angle the sun makes with the

atmosphere, skipping the light off dust and dirt (not to mention solid aerosols, soot, and smog).

Sunsets are usually more spectacular than sunrises, as more “stuff” floats around at the end of the day

(there are less particles present in the mornings). Sometimes just after sunset, a green flash can be

seen ejecting from the setting sun.

The Earth appears blue to the astronauts in space because the shorter, faster wavelengths are

reflected off the upper atmosphere. The sunsets appear red because the slower, longer wavelengths

bounce off the clouds.

Sunsets on other planets are different because they are farther (or closer) to the sun, and also because

they have a different atmosphere than planet Earth. The image shown here is a sunset on Mars.

Exercises

1. What colors does the sunset go through?

2. Does the color of the light source matter?


Answers to Exercises: Sky in a Jar

1. What colors does the sunset go through? (The sunset goes through the colors of the rainbow as the sun sets lower in the sky, starting with yellow, then orange, and then red as it sets.)

2. Does the color of the light source matter? (Yes. White light gives the best results.)


TWO-POINT SOURCE INTERFERENCE

Lasers light is different from light from a flashlight in a couple of different ways. Laser light is

monochromatic, meaning that it’s only one color.

Laser light is also coherent, which means that the light is all in synch with each other, like soldiers

marching in step together. Since laser light is coherent, which means that all the light waves peaks

and valleys line up. The dark areas are destructive interference, where the waves cancel each

other out. The areas of brightness are constructive interference, where the light adds, or amplifies

together. LED light is not coherent because the light waves are not in phase.

Light travels in waves, and when those waves are in phase (coherent) they interfere with each

other in a special way. They cancel each other out (destructive interference) or amplify

(constructive interference). This pattern isn’t found with sunlight or light from a bulb because that

kind of light all out of phase and doesn’t have this kind of distinct interference pattern.


PATH DIFFERENCE

Imagine you have a coherent light in a shoebox, and you cut two narrow slits out the side and

shine the light on the far wall. The distance from one slit to the wall isn’t going to be exactly the

same as the other, so there’s a “path difference”.

The path difference refers to the difference in distance two waves from the same light source will

travel to reach the same point. At this point, their crests line up in such a way as to interfere with

each other. Here’s a more complicated approach to using it. (HINT: if you get lost, skip to the next

lesson.. it’s much easier and niftier because it involves airplanes…)


WHEN PATH DIFFERENCE MATTERS

Here’s a neat way to calculate the height of an airplane in flight using the interference from a radio

transmitter…


MEASURE THE TRACK SPACING OF A DVD AND CD

We’re going to use a laser pointer and a protractor to measure the microscopic spacing of the data tracks on a DVD and a CD. The really cool part is that you’re going to use an interference pattern to measure the spacing of the tracks, something that you can’t normally see with your eyes.

We’re going to measure the data track spacing using a diffraction pattern and a little math. The equation to determine the distance is:

dm = m λ / (sin θm – sin θi)

where λ is the wavelength of the laser, m = the order of the refraction ray, and d is the track spacing.

Watch the video to see how to do the calculations!


WAVE-PARTICLE DUALITY

This experiment is also known as Young’s Experiment, and it demonstrates how the photon (little

packet of light) is both a particle and a wave, and you really can’t separate the two properties from

each other. If the idea of a ‘photon’ is new to you, don’t worry – we’ll be covering light in an

upcoming unit soon. Just think of it as tiny little packets or particles of light. I know the movie is a

little goofy, but the physics is dead-on. Everything that “Captain Quantum” describes is really what

occurred during the experiment. Here’s what happened…

So basically, any modification of the experiment setup actually determines which slit the electrons go through. This experiment was originally done with light, not electrons. and the interference pattern was completely destroyed (as shown in the end of the video) by an ‘observer’. This shows you that light can either be a wave or a particle, but not both at the same time, and it has the ability to flip between one and the other very quickly.

So, both light and electrons have wave-particle characteristics. Now, take your brain this last final step… it’s easier to see how this could be true for light, you can imagine as a massless photon. But an electron has mass. Which means that matter can also act as a wave. (Twilight zone anyone?)


EASY LIGHT WAVE-PARTICLE DEMONSTRATION

To show how light acts like a wave, you can pass light through a glass of water and watch the

rainbow reflections on the wall. Why does this happen? We’ve already covered this in a previous

lesson, but basically when the light passes through the glass and the water, it bends to give

different frequencies of light and therefore different colors.

Imagine dipping your fingers in a bathtub of water. Can you see the ripples traveling along the top

surface? Light travels just like the waves on the surface of the water.

What what about light acting like a particle? Use a camera flash to quickly charge a glow-in-the-

dark toy in a dark closet. The light particles (photons) hit the electrons in the toy and transfer

energy to the electron. The result is that the electron emits another light particle of a different

wavelength, which is why glow-in-the-dark toys don’t reflect back the same color light they were

charged with.

Yay! You completed this section! Now it’s time for you to solve physics problems on your own:


HOMEWORK PROBLEMS WITH SOLUTIONS

On the following pages is the homework assignment for this unit. When you’ve completed all the videos

from this unit, turn to the next page for the homework assignment. Do your best to work through as

many problems as you can. When you finish, grade your own assignment so you can see how much

you’ve learned and feel confident and proud of your achievement!

If there are any holes in your understanding, go back and watch the videos again to make sure you’re

comfortable with the content before moving onto the next unit. Don’t worry too much about mistakes at

this point. Just work through the problems again and be totally amazed at how much you’re learning.

If you’re scoring or keeping a grade-type of record for homework assignments, here’s my personal

philosophy on using such a scoring mechanism for a course like this:

It’s more advantageous to assign a “pass” or “incomplete” score to yourself when scoring your

homework assignment instead of a grade or “percent correct” score (like a 85%, or B) simply because

students learn faster and more effectively when they build on their successes instead of focusing on their

failures.

While working through the course, ask a friend or parent to point to three questions you solved correctly

and ask you why or how you solved it.

Any problems you didn’t solve correctly simply mean that you’ll need to go back and work on them

until you feel confident you could handle them when they pop up again in the future.

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a = acceleration A = amplitude d = distance E = energy f = frequency F = force I = rotational inertia K = kinetic energy k = spring constant L = angular momentum � = lengthm = mass P = power p = momentum r = radius or separation T = period t = time U = potential energy V = volume v = speed W = work done on a system x = position y = height a = angular acceleration

m = coefficient of friction q = angle r = density t = torque w = angular speed

gU mg yD � D

2Tf

pw

� � 1

2smTk

p�

2pTg

p� �

1 22g

m mF G

r�

�

gFg

m��

�

1 2G

Gm mU

r� �

1 22E

q qF k

r�

�

qI

tDD

�

RAr� �

VIRD�

P I VD�

si

R R� i

1 1

p iiR R

�

A = area F = force I = current � = lengthP = power q = charge R = resistance r = separation t = time V = electric potential r = resistivity

WAVES

vf

l � f = frequency v = speed l = wavelength

GEOMETRY AND TRIGONOMETRY

Rectangle A bh�

Triangle 12

A bh�

Circle 2A p�

2C p�r

r

Rectangular solid V wh� �

Cylinder

V rp� �2

2 2S r rp p� �� 2

Sphere 3

3V rp� 4

24S rp�

A = area C = circumference V = volume S = surface area b = base h = height � = lengthw = width r = radius

Right triangle

2 2 2c a b� �

sin ac

q �

cos bc

q �

tan ab

q �

c a

b90�q

CONSTANTS AND CONVERSION FACTORS

Proton mass, 271.67 10 kgpm ��

Neutron mass, 271.67 10 kgnm ��

Electron mass, 319.11 10 kgem ��

Avogadro’s number, 23 -10 6.02 10 molN � �

Universal gas constant, 8.31 J (mol K)R � �

Boltzmann’s constant, 231.38 10 J KBk ��

Electron charge magnitude, 191.60 10 Ce ��

1 electron volt, 191 eV 1.60 10 J�� Speed of light, 83.00 10 m sc � �

Universal gravitational constant,

11 3 26.67 10 m kg sG ��

Acceleration due to gravityat Earth’s surface,

29.8 m sg �

1 unified atomic mass unit, 27 21 u 1.66 10 kg 931 MeV c�� Planck’s constant, 34 156.63 10 J s 4.14 10 eV sh ��

25 31.99 10 J m 1.24 10 eV nmhc ��

Vacuum permittivity, 12 2 20 8.85 10 C N me ��

Coulomb’s law constant, 9 201 4 9.0 10 N m Ck pe� � � �

AVacuum permeability, 70 4 10 (T m)m p ��

Magnetic constant, 70 4 1 10 (T m)k m p ��

5 1 atmosphere pressure, 5 21 atm 1.0 10 N m 1.0 10 Pa� � � �

UNIT SYMBOLS

meter, m kilogram, kgsecond, sampere, Akelvin, K

mole, mol hertz, Hz

newton, Npascal, Pajoule, J

watt, W coulomb, C

volt, Vohm,

henry, H

farad, F tesla, T

degree Celsius, C� W electron volt, eV

2

A

�

�

PREFIXES Factor Prefix Symbol

1012 tera T

109 giga G

106 mega M

103 kilo k

10�2 centi c

10�3 milli m

10�6 micro m

10�9 nano n

10�12 pico p

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q �0

�30

�37 45� �

53 60� 90�

sinq 0 1 2 3 5 2 2 4 5 3 2 1

cosq 1 3 2 4 5 2 2 3 5 1 2 0

tanq 0 3 3 3 4 1 4 3 3 �

The following conventions are used in this exam. I. The frame of reference of any problem is assumed to be inertial unless

otherwise stated. II. In all situations, positive work is defined as work done on a system.

III. The direction of current is conventional current: the direction in whichpositive charge would drift.

IV. Assume all batteries and meters are ideal unless otherwise stated.V. Assume edge effects for the electric field of a parallel plate capacitor

unless otherwise stated.

VI. For any isolated electrically charged object, the electric potential isdefined as zero at infinite distance from the charged object.

MECHANICS ELECTRICITY AND MAGNETISM

0x x xa tÃ Ã� �

x x� � 20 0Ãx t � a t

21

x

�2 20 2x x xa x xÃ Ã� � � 0

netFFa

m m� ��

��

f nF Fm��

2

carÃ�

p mv��

p F tD D��

212

K mv�

cosE W F d Fd qD � � ��

EPt

DD

�

20 0

12

t tq q w a� � �

0 tw w a� �

� � cos cos 2x A t A fw� � tp

i icm

i

m xx

m�

net

I Itt

a � ��

sinr F rFt �� q

L Iw�

L ttD D�

212

K Iw�

sF k x� ��

a = acceleration A = amplitude d = distance E = energy F = force f = frequency I = rotational inertia K = kinetic energy k = spring constant L = angular momentum � = lengthm = mass P = power p = momentum r = radius or separation T = period t = time U = potential energy v = speed W = work done on a system x = position y = height a = angular acceleration m = coefficient of friction q = angle t = torque w = angular speed

212sU kx�

gU mg yD D�

2 1Tf

pw

� �

2smTk

p�

2pTg

p� �

1 22g

m mF G

r�

�

gFg

m��

�

1 2G

Gm mU

r� �

1 22

0

14E

q qF

rpe�

�

EFE

q�

� �

20

14

qE

rpe�

�

EU q VD D�

0

14

qV

rpe�

VEr

DD

��

QV

CD �

0ACd

ke�

0

QE

Ae�

� 21 12 2CU Q V CD� � VD

QI

tDD

�

RAr� �

P I VD�

VIRD�

si

R R� i

1 1

p iiR R

�

pi

C C� i

1

s iC

� 1

iC

0

2IBr

mp

�

A = area B = magnetic field C = capacitance d = distance E = electric field e = emfF = force I = current � = lengthP = power Q = charge q = point charge R = resistance r = separation t = time U = potential (stored)

energy V = electric potential v = speed k = dielectric constant r = resistivity

q = angle F = flux

MF qv B� ��

�

sinMF qv q��

B

MF I B� ��

�

sinMF I Bq��

�

B B AF � � ��

cosB B AqF ��

B

te DF

D� �

B ve � �

�

FLUID MECHANICS AND THERMAL PHYSICS

A = areaF = force h = depth k = thermal conductivity K = kinetic energy L = thickness m = mass n = number of moles N = number of molecules P = pressure Q = energy transferred to a

system by heating T = temperature t = time U = internal energy V = volume v = speed W = work done on a system y = height�r = density

mV

r �

FPA

�

0P P gr� � �h

bF Vgr�

1 1 2 2A v A v�

21 1

12

P gy vr� �

22 2

12

P gy vr r� � �

1r

2

kA TQt L

DD

�

BPV nRT Nk T� �

32 BK k� T

VW PD� �

U Q WD � �

MODERN PHYSICS

E = energy f = frequency K = kinetic energy � = mass p = momentum l = wavelength f = work function�

E hf�

maxK hf f� �

hp

l �

2E mc�

WAVES AND OPTICS

d = separation f = frequency or

focal lengthh = height L = distance M = magnification m = an integer n = index of

refraction s = distance � = speed l = wavelength q = angle�

vf

l �

cnÃ

�

1 1 2sin sinn nq � 2q

1 1

i os s f� � 1

i

o

hM

h� � i

o

ss

L mlD �sind mq l�

GEOMETRY AND TRIGONOMETRY

A = area C = circumference V = volume S = surface area b = base h = height � = length w = width r = radius

Rectangle A � bh

Triangle 12

A b� h

Circle 2A rp�

2C rp�

Rectangular solid V w� � h

r

Cylinder 2V rp� �

22S rp p� �� 2

Sphere 34

3V p� r

24S rp�

Right triangle 2 2c a� � b2

sin ac

q �

cos bc

q �

tan ab

q �

c a

b90�q

advanced physics course chapter 12: light waves · advanced physics course chapter 12: light waves...

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