Web Diffraction of Light

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Title: Diffraction of Light

Version: July 1, 2006

Authors: Gil Toombes, Andrew J. Telesca, Jr., James Overhiser, MartinAlderman

Appropriate Level: Grades 9-12

Abstract: The diffraction and interference of light are easily observedphenomena that give direct, tangible evidence of the wave

nature of light. Diffraction is at the root of many technologies,

scientific techniques, and common visual phenomena. Studentsexplore diffraction by shining a laser at a hair, a variable-width

slit made from pencils, wire meshes of various size and

diffraction gratings. After an introduction to single-slit and N-slit diffraction equations, students are faced with three

challenges: (1) to measure the track spacing in a CD and

DVD, (2) to determine the relative thickness of hairs, and (3) to

estimate the diameter of a lycopodium spore. In the last twochallenges, students design their own procedure.

Time Required: Two 40-minute periods

NY Standards Met: 4.3l Diffraction occurs when waves pass by obstacles orthrough openings. The wave-length of the incident wave

and the size of the obstacle or opening affect how the

wave spreads out.

4.3m When waves of a similar nature meet, the resulting

interference may be explained using the principle of

superposition. Standing waves are a special case of

interference.

Special Notes: Diffraction of Light is a kit available from the CIPT

Equipment Lending Library, www.cns.cornell.edu/cipt/.

Center for Nanoscale Systems Institute for Physics Teachers

632 Clark Hall, Cornell University, Ithaca, NY 14853

www.cns.cornell.edu/cipt/

[email protected]

7/06
http://www.cns.cornell.edu/cipt/http://www.cns.cornell.edu/cipt/


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Objectives:

To recognize that light is a wave with a small wavelength.

To learn that diffraction is the bending of waves around an obstacle, and todifferentiate this from projection.

To gain familiarity with single-slit and multi-slit diffraction patterns.

To learn that the dimensions of features in a diffraction pattern are inversely related tothe dimensions of the object causing diffraction for small angles.

To apply the diffraction equations to determine the size of features on some commonobjects, including CDs and DVDs, hairs, and lycopodium spores.

Class Time Required:

Two 40 minute periods

Teacher Preparation Time Required:

5 - 10 minutes to set out supplies

Materials Needed:

Diffraction of Light is a kit in the CIPT equipment lending library

Assumed Prior Knowledge of Students:

Students understand the definition of wavelength, interference, and diffraction

Background Information for Teachers:

History of the particle versus wave debate for light:

1. Isaac Newton (1642-1727) thought that light must be a particle

a. Light cast sharp shadows, and it was commonly thought that only particles wouldgo in perfectly straight lines in order to cast sharp shadows.

b. Water and sound waves were observed to bend around obstacles, not go instraight lines to cast sharp shadows. This wave behavior was clearly distinct fromparticle behavior, and light did not appear to exhibit such behavior.

c. Newton had incomparable status in the scientific community, so his viewdominated throughout the 1700s. (Youngs experiments in 1803 finally gave the

concept of light as a wave common acceptance.)

2. Christiaan Huygens (1629-1695) thought that light must be a wave

a. In ca. 1690, Huygens attempted to persuade Newton that light was a longitudinal

wave, like sound wavesb. Huygens observed that light reflects and refracts like sound and water waves do

c. He pointed out that if the wavelength of light were small enough, diffractionwould be minimal and sharp shadows should occur.

3. Francesco Maria Grimaldi (1618-1663) thought that light must be a wave

a. He passed a beam of light through two consecutive narrow slits and onto a surface

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Teacher Section Diffraction of Light


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i. The band of light on the surface was a bit larger than the band of light enteringthe first slit. The beam had bent slightly outward at the edges of the slit. BUT

his findings were neglected!

ii. Grimaldi called this bending of the light diffraction

iii. He observed colored bands of light towards the outside (different wavelengths

of light diffract at different angles), and it remained unexplained for 150 years4. Thomas Young (1773 - 1829)

a. Young [proved that light is a wave] in 1803 by sending light through very

narrow openings and showing that separate bands of light appeared where thereshould have been nothing but the sharply shadowed boundary of the edge of the

opening. These bands of light arose from the kind of diffraction around corners

that Grimaldi had noted, and it could not be explained by the particle theory.

Young had a more conclusive piece of evidence. From his study of sound he

grew interested in the phenomenon of beats, in which two different pitches of

sound produced periods of intensified sound separated by periods of silence. This

was easily explained, since the two pitches had different wavelengths andtherefore did not keep step.

Now, then, would two light waves add up to produce darkness? If they were

particles, they couldnt; if they were waves, they could. Young introduced lightbeams through two narrow orifices. They spread out and overlapped. The

overlapping region was not a simple area of intensified light but formed a striped

pattern of alternating light and darkness, a situation (interference) exactly

analogous to beats in sound.

From his diffraction experiment Young was able to calculate the wavelength of

visible light, for it was only necessary to figure out what wavelength would allow

the observed degree of small bending. --Isaac Asimov, fromIsaac Asimovs

Biographical Encyclopedia of Science & Technology, Avon Books, 1972b. Young used double refraction to show that light waves must be transverse

5. Einstein

a. In 1905 Einstein read Planks paper in which he calculated the electromagnetic

energy radiated by a hot body. Plank was only able to get theoretical agreement

with experiment by assuming that the energy emitted by the oscillating charges of

the hot body was quantized, = hf. Plank had since distanced himself from thisstrange conclusion, but Einstein realized that h was not just a mathematical patch.

Rather, it implied that electromagnetic radiation (light) was composed of discrete

particles, each with energy = hf, and he called these particles photons.

b. Einsteins particle theory of light offered a neat explanation for the photoelectriceffect, unexplained since its 1839 discovery in France. In 1921 Einstein won the

Nobel Prize for his theory of photons.

6. Confronted with undeniable evidence that light must be both a particle and a wave,

physicists of the 1920s developed the concept of wave-particle duality to describethe nature of light. This non-intuitive conclusion is one of many that illustrates the

fundamental weirdness of the quantum mechanical world.

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Christiaan Huygens Model of Diffraction(Diffraction through an opening in a barrier)

When one drops a pebble into the water, a series

of circular periodic waves travel outward from the

impact. Huygens generalized this result into a

principle which states each of the infinite number

of points on any wavefront acts as a source of

circular waves, called wavelets, like those from

a pebble dropped into the water.

The top diagram shows seven straight wavefronts.

At the third wavefront from the top, circular

wavelets generated from point sources along the

third wavefront are drawn. Note that the circular

wavelets have the same wavelength as the straight

wavefronts had. The wavelets superimpose and

only add constructively at the location of the next

wavefront, i.e. the second wavefront from the top.

(Note that since waves are assumed to travel in thedirection indicated by the velocity vector, the

other wavefront generated at the location of the

fourth line from the top is ignored.)

The second diagram from the top shows the same

straight wavefronts approaching a barrier that has

a large opening compared to the wavelength of the

wave. The wave energy that hits the barrier

simply reflects back (not shown here). The

wavefront in between the edges of the barrier

generates plenty of circular wavelets to add up to

a straight wavefront except at the edges of the

opening. At the edges of the opening, the circularwavelets created from the outer points do not have

other wavelets to the outside to interact with. The

overall result is a mostly straight wavefront

passing through the opening with just a bit of

curving at the edges, as only a bit of the wave

energy spreads out behind the barrier.

The bottom diagram shows the outcome if the size

of the opening in the barrier is comparable to the

wavelength of the wave. In this case, the

wavefront behind the barrier has a relatively short

segment that is straight and most of the

propagated wave is curved. The wavefrontsbehind the barrier appear nearly semi-circlar.

Summary: When the size of the opening in a

barrier is large compared to the wavelength of the

wave, relatively little diffraction occurs. When

the opening is comparable to or smaller than the

wavelength, much diffraction occurs, and the

waves appear circular.

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Christiaan Huygens Model of Diffraction(Diffraction around an obstacle)

The top diagram shows straight wavefronts

approaching an obstacle that is large compared to

the wavelength of the wave. The wave energy thathits the obstacle simply reflects back (not shown

here). The wavefronts on either side of the

obstacle generate plenty of circular wavelets to add

up to a straight wavefront except in the regiondirectly behind the obstacle. At the edges of the

obstacle, the circular wavelets created from the

outer points do not have other wavelets behind the

obstacle to interfere with. The overall result is a

straight wavefront on each side of the obstacle

with curved wavefronts around the edges, as some

of the wave energy spreads into the region behind

the obstacle.

The bottom diagram shows the outcome if the sizeof the obstacle is comparable to the wavelength of

the wave. In this case, the straight wavefronts

continue on either side of the obstacle; and the

outside edge points of the obstacle are so close to

each other that the associated circular wavelets on

the two sides overlap substantially. The wave fills

in almost completely behind the obstacle, there is

no shadow cast; however, the superposition of the

wavelets behind the obstacle creates an diffraction

pattern. In the limit that the obstacle is much

smaller than the wavelength, very little diffraction

occurs, and it is as though the obstacle isnt there

at all!

Summary: When the size of an obstacle is much

larger than the wavelength of a wave, relatively

little diffraction occurs and the obstacle effectively

blocks the wave energy from the region behind it.

When the size of an obstacle comparable to the

wavelength of a wave, the wave bends around each

side of the obstacle and creates a substantial

diffraction pattern. When the obstacle is much

smaller than the wavelength, it has very little

effect on the wave.

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Answers to Questions:

Exploration 1: The "shadow" from a strand of hair

1. Carefully sketch the pattern of the light on the screen with the laser aimed at the hair.

2. Does the pattern on the screen look like a shadow of the hair? Explain. No. There

are several bright and dark fringes, rather than one dark line like a shadow.

3. Why do you think the laser beam spreads out when you put the hair in the path of thelaser? The light bends, or diffracts, around each side of the hair and spreads out.

4. What direction does the laser beam spread relative to the orientation of the hair? The

beam spreads perpendicular to the direction of the hair.

Exploration 2: Light between two pencils

1. Carefully sketch the pattern of the light on the screen with the laser aimed through the

slit.

2. Does the pattern on the screen look like a shadow of the slit? Explain. No. There are

several bright and dark fringes, rather than one bright line with darkness on either

side like a shadow.

3. What happens to the pattern when you squeeze the pencils to make the slit narrower?

The pattern of bright and dark fringes becomes wider as the slit becomes narrower.4. How does the pattern of the slit compare to the pattern of the hair? The pattern of the

slit is the same as the pattern of the hair. This is an example of Babinets Principle,

named for the man who mathematically proved that an object and its inverse alwayshave the same diffraction pattern.

Exploration 3: Wire meshes

1. Record your data in the first two columns of the table. Calculate the distance d

between adjacent wires in the mesh and put your answers in the third column.

Mesh

Distance between

nearest bright dots in

diffraction pattern (x)

Number of wires

in one millimeter

(n)

Distance between

wires

(d =1/n)

Coarse 2.5 mm 2.0 0.50 mm

Medium 5.5 mm 4.0 0.25 mmFine 8.0 mm 6.0 0.17 mm

Finest 11 mm 8.0 0.13 mm

2. How does the diffraction pattern change as the wires get closer together? The

features of the diffraction pattern spread out, i.e. the distance between the dots grows.

3. What is the mathematical relationship betweenx and n? They are directly

proportional to each other.

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4. What is the mathematical relationship betweenx and d? They are inversely related to

each other.

5. Predict the distance between nearest bright dots in the diffraction pattern if you had a

mesh with 10 wires per mm. Show work. Since x and n are directly proportional,

wires/mm10wires/mm8.0

mm11

or2

2

2

1

1 x

n

x

n

x

==

Solving for x2 gives 14 mm.

Exploration 4: Diffraction gratings

1. Organize your data in the first two columns of the table. Calculate the ratiox/L.

x L x/L

8.8 cm 10. cm 0.88

7.0 cm 8.0 cm 0.88

10.5 cm 12 cm 0.882. Why did you have to move the display screen closer to see the diffraction pattern?

The lines in the diffraction grating are much closer together than the wires of the

mesh; therefore, the features in the diffraction pattern of the grating are much fartherapart.

3. As you changed the distance between the screen and the gratingL, what remained

constant? The ratio x/L remained constant.

4. What does your answer to question 3 imply about the angle (see diagram above)?

The angle also remains constant.

Challenge 1: Measure CD and DVD track spacing1. Fill in the data table with measured distancesx1 andL. Calculatex1/L and use this to

find the angle 1 with the formula ( )Lx11

1 tan= .

Media x1(cm) L (cm) x1/L 1

CD 6.75 14.50 0.466 25.0

DVD 11.20 8.20 1.37 53.9

2. The wavelength of the red laser is approximately 670 nm. Use the diffraction

formula to calculate the distance between tracks for a CD and a DVD. Show your

work. The diffraction equation is:ndn sin=

For the CD and DVD, n = 1, and solving for d gives:

1sin=d

Substituting the values of1 from the chart and= 670 nm, d is the track spacing:

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CD track spacing 1.610-6

m or 1.6m DVD track spacing 7.110-7

m or 0.71 m

3. Use the images below to measure the track spacing on a CD and a DVD. Write your

answer in the blanks provided.

CD track spacing __1.5 m____ DVD track spacing __0.73 m_

4. How do your answers for questions (2) and (3) compare? Can you explain anydiscrepancies? The values for the CD and DVD track spacings as determined by

diffraction and by SEM images are the same to within the uncertainty of these

measured values. The accepted values for track spacing are 1.6m on a CD and

0.74 m on a DVD.

5. A CD can store 0.65 gigabytes whereas a DVD can store 4.7 gigabytes of

information. How does the DVD store more information in the same size area? The

DVD tracks are closer together than a CD, so it has a greater total length of track inwhich to store information. The smaller track width of the DVD also implies that its

bits of information are more compact and that it can store more data per given length

of track.

Challenge 2: Is your hair thicker than mine?

1. Describe your experimental procedure (include diagrams): Place each hair in the

beam of the laser and measure the width of the central maximum (from dark fringe on

one edge to dark fringe on the other). The narrower the central maximum, the widerthe hair.

2. Record your data (neatly organized) and write any calculations: Answers will vary. If

students actually calculate the width of their hairs, answers will vary approximately

from 50 to 80 m.

3. Write your conclusion: Answers will vary depending on the results of calculations in

part (2).

Challenge 3: What is the diameter of a lycopodium spore?

1. Describe your experimental procedure (include diagrams): Shine the laser through

spores thinly dispersed on a glass slide and onto a display screen. Record thewavelength of the laser, the distance to the screen, and the width of the central

maximum (center of dark fringe on one side to center of dark fringe on the other

side).

2. Record your data (neatly organized) and write any calculations: The data are:

Diameter of central bright spot = 2x1 = 1.1 cm, so x1 = 0.55 cm

Distance of spores to screen = L = 23.5 cm

From Challenge 1,

( ) ( ) === 3.15.2355.0tantan 111

1 Lx

If students simply apply the diffraction formula for a single slit, they will get

( ) m293.1sinnm670sin 1 === d

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If students use the more accurate diffraction formula for a circular object

sin22.1 d=

where d is the diameter of the circular object and is the angle to the first minimum,

they will get

( ) m353.1sinnm67022.1sin22.1 === d Measured with a microscope, Lycopodium spores from various plants range from 25

to 40 m in diameter.

3. Write your conclusion: The diameter of a Lycopodium spore is 35 m.

Tips for Teachers:

Remind students to be careful handling the lasers, to keep them lower than eye level,and to block the beam with the display screen.

When students work with the wire meshes, check that the mesh is flat and orientedperpendicular to the laser beam. If the mesh has substantial curvature or deviates

significantly from perpendicular orientation, additional bright spots will occur in the

diffraction pattern that complicate interpretation.

When viewing the diffraction pattern of the lycopodium spores, make the room asdark as possible. The rings surrounding the central bright spot are much dimmer thanit and cannot easily be seen with a lot of background light falling on the viewing

screen. A green laser, which appears brighter than a red laser, can help with viewing

the diffraction pattern. However, only the teacher should handle the green laser due

to the greater potential for eye damage.

Special Notes:

Some of the original ideas for activities in this lab are taken from a lesson developed by

the Cornell Center for Materials Research entitled,Diffraction and Interference of Light.

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DIFFRACTION OF LIGHT

What is the nature of light? Is it a wave? Is it a particle? Isaac Newton (1642-1727)

thought that light must be a particle. He noticed that light makes sharp-looking shadowsof objects. This can be explained by particles of light that travel in straight lines until

they are stopped by some object that lies in their path.display

Waves, such as water wave and sound waves, can bend around obstacles in their path.

For example, you can hear someone talking around a corner. This bending is called

diffraction. When waves are diffracted (bent), they collide with other waves and interfereto form interesting patterns called diffraction patterns.

Christiaan Huygens (1629-1695) thought light must be a wave because it reflects andrefracts like sound and water waves do. He attempted to correct Newton and pointed out

that if wavelength of light were small enough, the diffraction or bending would be a verysmall effect and for most objects and sharp-looking shadows would occur.

Due to Newton's greater status within the scientific community, his particle theory of

light dominated through the 1700s. But was Newton right? You get to decide with theaid of a modern invention, the laser. The laser produces an intense, parallel beam of light

at a single wavelength, which is ideal for investigating the fundamental nature of light.

bent wavesinterfereand form adiffractionpattern

paths of wavefronts

waves comefrom a distantsource

displayscreen

light

dark(shadow)

light

screenpaths of light particles

light particlescome from adistant source

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Student Section Diffraction of Light


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Exploration 1: The "shadow" from a strand of hair

display

ree

sc n

aserpath of l

slide mountwith hair

laserbinderclip

sampleholder

~2 meters

(top view)

Instructions:

Take a piece of your hair and tape across the opening of an empty slide frame and

clip it with the binder clip of the sample holder.

Clip the two large binder clips on the sides of the display screen at the bottom andplace the display screen 2 meters from the hair.

Put the laser underneath the rubber bands on the mounting block, and aim the laser atthe hair and the screen.

Use the binder clip to clamp the laser on, and adjust the laser as necessary to strikethe hair directly.

Observe the laser light on the screen and answer the following questions.

Questions:

1. Carefully sketch the pattern of the light on the screen with the laser aimed at the hair.

2. Does the pattern on the screen look like a shadow of the hair? Explain.

3. Why do you think the laser beam spreads out when you put the hair in the path of the

laser?

4. What direction does the laser beam spread relative to the orientation of the hair?

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Exploration 2: Light between two pencils

pencils

Instructions:

Construct a narrow slit using two pencils and two rubber bands, as shown below:

Rest the erasers of the pencils on the table so that the laser shines through the narrowslit between them. Position the screen 2 meters behind the pencils.

Observe the pattern of the light that falls on the screen. Try squeezing the pencilsgently together to decrease the slit size. Observe any changes to the pattern of light

on the screen.

Questions:1. Carefully sketch the pattern of the light on the screen with the laser aimed through the

slit.

2. Does the pattern on the screen look like a shadow of the slit? Explain.

3. What happens to the pattern when you squeeze the pencils to make the slit narrower?

4. How does the pattern of the slit compare to the pattern of the hair?

loop each rubber band once aroundone pencil, then wrap tightly around both narrow slit

laser

binderdisplayclip

screen path of laser

2 meters

(side view)

lasermount

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Exploration 3: Wire meshes

binderclip

laser

display

screen

path of laser

wire mesh

~2 meters

(top view) sampleholder

Instructions:

Find the coarsest mesh and clamp it in the sample holder. Place the display screen 2meters from the mesh.

Aim the laser perpendicular to the mesh so that it shines through the mesh onto thescreen. Observe the pattern on the display screen.

Record the distancex between nearest bright dots on the display screen.

Place a clear plastic ruler on top of the mesh and use the handheld microscope tomeasure the number of wires n in one millimeter of the mesh. Record in the chart.

Repeat for the other wire meshes.

Questions:

1. Record your data in the first two columns of the table. Calculate the distance d

between adjacent wires in the mesh and put your answers in the third column.

Mesh

Distance between

nearest bright dots in

diffraction pattern (x)

Number of wires

in one millimeter

(n)

Distance between

wires

(d =1/n)

Coarse

Medium

Fine

Finest

2. How does the diffraction pattern change as the wires get closer together?

3. What is the mathematical relationship betweenx and n?

4. What is the mathematical relationship betweenx and d?

5. Predict the distance between nearest bright dots in the diffraction pattern if you had amesh with 10 wires per mm. Show work.

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Exploration 4: Diffraction gratings

Instructions:

Find the diffraction grating marked 1000 lines/mm and clamp it in the sampleholder. Place the display screen about 10 cm from the diffraction grating.

Aim the laser perpendicular to the grating so that it shines through the grating andonto the screen. Observe the pattern on the display screen.

Measure and record the distancex from the central bright spot to the nearest brightspot (either side is OK).

Measure and record the distanceL from the diffraction grating to the display screen.

Move the display screen two additional times and recordx andL for each newconfiguration.

Questions:

1. Organize your data in the first two columns of the table. Calculate the ratiox/L.

x L x/L

2. Why did you have to move the display screen closer to see the diffraction pattern?

3. As you changed the distance between the screen and the gratingL, what remained

constant?

4. What does your answer to question 3 imply about the angle (see diagram above)?

laser

displayscreen

diffractiongrating

L

x

(top view)

sampleholder

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The Diffraction Formula:

Approximation

(small angles only):

dxn n

For all angles:

ndn sin=

For two or more slits (identical, evenly spaced slits):

= wavelength

x = the distance between the center of the zero th order

antinode (bright fringe) and the n

th

order antinode,measured along the screen surfacen = the order of the antinode being viewedd= the distance between the centers of the slits

L = the perpendicular distance from the slits to the screen

n = the angular deviation from the 0th order antinode to the

nth

order antinode on the screen

For one slit:

x = distances as above, but measured to nodes (dark fringes)n = the order of the node being viewed

d= the width of the slit

n = the angular deviation as above, but measured to nodes

parallel light

wavelength

displayscreen

x11

Two or more slits

(top view)

object with

narrow slits

2

x2two ormore slits

d

parallel lightwavelength

displayscreen

x1 1

2

x2

dOne slit

(top view)

one slit

object withnarrow slit

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Challenge 1: Measure CD and DVD track spacing

The closely spaced, parallel tracks of a CD and DVD act just like a diffraction grating.

You can use the diffraction pattern to find the distance between the tracks.

displayscreen

CD/DVD1

1x1

sampleholder

(top view)

laser

Instructions:

Clamp the CD in the sample holder. Orient the bare section of the CD with thereflective coating removed so that it is opposite the binder clip.

Adjust the height of the CD so that the laser beam falls in the bare section. Seediagram below.

(side view)

bindercliplaser

beam

sampleholder

sector withaluminumremoved

Place the display screen about 20 cm from the CD. Adjust CD and screen so both areperpendicular to the laser beam and the diffraction pattern is symmetrical.

Measure and record the distancex1between the central bright dot and the nearestbright dot (either side) in the diffraction pattern.

Measure and record the distanceL from the CD to the display screen.

Repeat the same procedure for the DVD. You may need to move the display screencloser to observe the diffraction pattern.

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Questions:

1. Fill in the data table with measured distancesx1 andL. Calculatex1/L and use this to

find the angle 1 with the formula ( )Lx11

1 tan= .

Media x1(cm) L (cm) x1/L 1

CD

DVD

2. The wavelength of the red laser is approximately 670 nm. Use the diffraction

formula to calculate the distance between tracks for a CD and a DVD. Show your

work.

CD track spacing _______ DVD track spacing ______

3. Use the images below to measure the track spacing on a CD and a DVD. Write your

answer in the blanks provided.

DVDCD

Scanning Electron Microscope (SEM) images of a CD (left) and a DVD (right) taken at 2000X with 5 kV

beam voltage. The CD has been stamped with data, while the DVD is blank. Note the 20 m scale bar atthe bottom of both images. Images courtesy of Dr. David Tanenbaum, Pomona College.

CD track spacing _______ DVD track spacing ______

4. How do your answers for questions (2) and (3) compare? Can you explain any

discrepancies?

5. A CD can store 0.65 gigabytes whereas a DVD can store 4.7 gigabytes of

information. How does the DVD store more information in the same size area?

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Challenge 2: Is your hair thicker than mine?

Instructions:

Secure a few pieces of human hair (one of your own!).

Devise and write a procedure to determine which hair is thickest, which is thinnest,and order the hairs according to thickness.

Make measurements and record your data below. Then write your conclusion.

1. Describe your experimental procedure (include diagrams):

2. Record your data (neatly organized) and write any calculations:

3. Write your conclusion:

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Challenge 3: What is the diameter of a lycopodium spore?

Instructions:

Carefully open the container of lycopodium spores (from the lycopodium clubmoss)and sprinkle a small amount on the glass slide provided. The slide supports the

spores so that you can shine light at them.

Devise and write a procedure to estimate the diameter of the lycopodium spores,which are fairly uniform in size and roughly spherical.

Try to get the room as dark as possible to see the diffraction pattern of the spores.

Record your data and calculations below. Then write your answer.

1. Describe your experimental procedure (include diagrams):

2. Record your data (neatly organized) and write any calculations:

3. Write your conclusion:

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S d S i Diff i f Li h

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