Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Insert the batteries into the laser pointers.
2. Construct the measurement frames by cutting each index card into 2.5" x 3" pieces. Using scissors or a utility knife, cut a center rectangle out of each index card half, leaving a 1.5-cm border around each side (see Figure 9). One frame is needed per student group.
   {14019_Preparation_Figure_9}

Safety Precautions

Remind students to not aim the laser pointer directly into anyone’s eyes and not to look directly into the beam. The lowpower, coherent light can cause damage to the sensitive retina and may lead to permanent eye damage. Students should not aim the laser at any reflective surfaces such as mirrors or highly polished metal. Prevent stray laser light from projecting beyond the classroom to eliminate any unintentional exposure to the laser light. When refracting the laser light, it is best to do this on a low work surface to keep the refracted laser light below “normal” eye level. For people with sensitive eyes, it is recommended that dark, IR- protective safety glasses be worn. Follow all laboratory safety guidelines.

Disposal

Remove batteries from laser pens for long-term storage. Measurement frames with the fishing line, copper wire and hair may be disposed of in the regular trash.

Lab Hints

• Enough materials are provided in this kit for 6 groups of students. This laboratory activity can reasonably be completed in one 45- to 50-minute class period. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• Additional lasers are available from Flinn Scientific, Catalog No. AP8934. Laser pointers may also be purchased at some department stores or pet supply stores. Be sure to purchase lasers that are clearly labeled with the class, power and wavelength.
• The longer the distance, L, the more spread out the diffraction pattern, but the bands will also be less distinct. Distances from 1.5 to 3 meters are recommended for ease of measurement between bands. The distance between bands will be more difficult to measure at distances less than 1 meter.
• The diffraction pattern is more distinct in a dimly lit environment. Turning off classroom overhead lights should be sufficient for viewing the diffraction pattern if other sources of light enter the room. However, a completely dark classroom is not recommended for safety reasons.
• If sufficient wall space is not available for all student groups, a large book or notebook may be used instead. Students should place the setup on the floor, counter or lab table, stand a book up 1.5 to 3 meters from the object being measured, and tape a piece of white paper to the book. The cover of the book should be parallel to the measurement frame.
• The laser beam wavelength may vary on the order of ±30 nm from trial to trial because the wavelength depends on the condition of the transistor. Heat affects the transistor properties, and therefore the wavelength of the light. A laser that has been used continuously for several minutes may produce a light with a wavelength that is slightly different compared to when it was just turned on. Remind students to only turn on the laser when their set-up is ready and to release the power button as soon as they have placed the tape between two dark spots on the white paper.

Teacher Tips

• This activity may be used to develop the concepts of measurement, energy and the electromagnetic spectrum or properties of light. This experiment would also be a good supplementary activity to a microscope unit in life science.
• For more information on the laser principle, request Laser Theory, Flinn Publication No. 10427.
• If time permits, students may measure the width of a hair from each lab partner and compare results. Students may also bring in other samples to measure (e.g., sewing thread, pet hair, different fishing line).
• Students may continue to explore the properties of laser light with the Flinn Laser Pointer Education Kit, Catalog No. AP4507.

Further Extensions

Opportunities for Inquiry
Experimentally confirm the wavelength of the laser pointer. To do so, shine the laser through a pair of narrow slits separated by a measured distance. An equation can be derived to solve for the wavelength, based on the distance between interference maxima. Discuss reasons for any observed differences between your experimentally determined wavelength and that provided by the manufacturer.

Alignment to the Curriculum Framework for AP^® Physics 2

Enduring Understandings and Essential Knowledge
Only waves exhibit interference and diffraction. (6C)
6C2: When waves pass through an opening whose dimensions are comparable to the wavelength, a diffraction pattern can be observed.
6C3: When waves pass through a set of openings whose spacing is comparable to the wavelength, an interference pattern can be observed. Examples should include monochromatic double-slit interference.

Learning Objectives
6C2.1: The student is able to make claims about the diffraction pattern produced when a wave passes through a small opening and to qualitatively apply the wave model to quantities that describe the generation of a diffraction pattern when a wave passes through an opening whose dimensions are comparable to the wavelength of the wave.
6C3.1: The student is able to qualitatively apply the wave model to quantities that describe the generation of interference patterns to make predictions about interference patterns that form when waves pass through a set of openings whose spacing and widths are small, but larger than the wavelength.

Science Practices
1.4 The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively.
6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models.
7.2 The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understandings and/or big ideas.

Answers to Prelab Questions

1. Complete the following “If/then” hypothesis to explain how the width of the object being measured will influence the distance between the bands of the diffraction pattern.

   “If an object being measured with laser light is smaller than a previously measured object, then the distance from one band to the next will increase because the width of the object is inversely proportional to the distance between the bands.”

2. The wavelength of visible light is usually measured in nanometers and the width of human hair is usually measured in micrometers (1 μm = 1 • 10^–6 m). (a) How many nanometers are in a micrometer? (b) The light from a green laser pointer has a wavelength of 532 nm. Convert this wavelength to micrometers. Show your work.

   (a) 1 μm = 1000 nm
   (b) 532 nm x 1 μm /1000 nm = 0.532 μm

3. All the dimensions of Equation 1 from the Background section will be millimeters. (a) If 1 mm = 1000 μm, what is the wavelength from question 2(b) above in millimeters? (b) Suppose the distance, L, is 1.4 meters. How would that be expressed in millimeters?

   (a) 0.53 μm x 1 mm /1000 μm = 0.00053 mm
   (b) 1.4 m x 1000 mm /1 m = 1400 mm

4. What safety precautions must be taken when using a laser pointer?

   Do not aim the laser pointer directly into anyone’s eyes and never look directly into the laser beam. Do not aim the laser at any reflective surfaces. Prevent stray laser light from projecting beyond the classroom to eliminate any unintentional exposure to the laser light. When refracting the laser light, it is best to do this on a low work surface to keep the refracted laser light below “normal” eye level.

Sample Data

Introductory Activity

Guided-Inquiry

Analyze the Results

• Accuracy is a measure of an experimental value’s closeness to a known, accepted value. Why is it not possible for you to determine the accuracy of your width measurements of hair?

  Accuracy is a measure of an experimentally-determined value’s closeness to a known, or accepted value. We do not have known, or accepted values for the measured objects. Unlike the density of water or the salt content in a can of soup, there is no reported value associated with the width of a human hair, particularly given the fact that hair width varies from person to person. If such a value were provided, the accuracy of the measurements could be quantitatively assessed by calculating a percent error. The percent error is calculated by dividing the absolute value of the difference between the experimental value and the accepted value by the accepted value and subsequently multiplying the quotient by 100.

• Precision is a measure of the closeness of a data set’s values to each other. Describe how you can use your experimental setup to generate a data set to assess the experiment’s precision?

  Precision is a measure of an experiment’s reproducibility, or a measure of how closely the data points in a series are to one another. Precision may be quantitatively assessed by calculating a standard deviation for a data set. The higher the data set’s standard deviation, the lower the precision, and vice versa.
  
  An assessment of precision requires at least two data points since precision is a measure of an experiment’s reproducibility. As the number of data points increases, an experiment’s precision can be better assessed. Of course, practical concerns such as time and cost often limit the number of measurements that can be taken in an experiment. In this case, with respect to the hair, you might change the distance L between the hair and the screen to obtain a number of width measurements. Alternatively, each group could measure the same hair and compare results.
  
  There is no specific, universal standard deviation value correlated to very high precision or very low precision. Rather, assessments of precision are relative. For example, if six student groups carried out an experiment and calculated an average standard deviation of 0.005, a seventh student group’s value of 0.1016 would imply a lower level of precision, but not necessarily a “low” level of precision.

• The laser beam wavelength may vary on the order of ±30 nm from trial to trial because the wavelength depends on the condition of the transistor. Heat affects the transistor properties, and therefore the wavelength of the light. A laser that has been used continuously for several minutes may produce a light with a wavelength that is slightly different compared to when it was just turned on. Describe whether this is an example of a systematic or random error, and comment on sources of error present in this experiment.

  Random errors are statistical fluctuations in measured data attributable to instrument limitations. For example, a person measuring the time it takes a basketball to reach the floor when dropped from a constant height with a stopwatch will likely record slightly different values over ten trials. Or a person measuring the same distance with a meter stick may record slightly different values over a series of trials. These types of errors can be mitigated by collecting more data and analyzed by statistical means such as standard deviation calculations.
  
  Systematic errors are typically attributable to instrument flaws and are mitigated via calibration or application of a correction factor (e.g., the subtraction of four pounds from the weight displayed by a faulty bathroom scale). With respect to the variance of the laser beam’s wavelength and its impact on the experimental results in this laboratory, it is a systematic error because it describes something inherent to the instrument. Because all student groups are provided the same laser pointers, the systematic error might not present. That is, one group’s measurements may not stand out as erroneous when compared to classroom results if the inherent instrument limits are uniform across all groups. Because the wavelength variance is associated with the heat affects on the transistor, it is best to turn on the pointer for brief periods of time and only when ready to generate a diffraction pattern and record a measurement.

Answers to Questions

Answers to Guided-Inquiry Discussion Questions

1. Given Equation 1, what data do you need to measure or observe to calculate the width of an object by diffraction?

   To calculate the width of an object by diffraction, using Equation 1, you will the wavelength (λ) of the laser used, the distance (L) between the object and the screen, and the distance from the center of one dark band to the center of the next dark band (Δy). The wavelength will be given while the other two data points must be measured.

2. Write a step by step procedure describing how to collect the necessary data.

   Once a clear diffraction pattern is visible, one partner should quickly and carefully place the straight edge of a piece of masking tape on the screen at the center of a dark band near the middle bright spot, then place a second piece of tape at the center of the next dark band on the screen. The pieces of tape may be placed either to the right or the left of the middle spot, but not one on either side. The distance between the pieces of tape represent Δy (see Figure 8).

3. Carry out the necessary calculations to determine the width of the fishing line.

   d = λL/Δy = (0.00065 mm x 2000 mm) /4 = 0.33 mm

4. Apply the procedure you used to determine the width of the fishing line to determine the widths for a piece of Cu wire and a human hair.

   Cu wire: d = λL/Δy = (0.00065 mm x 2000 mm) /5 = 0.26 mm
   Hair: d = λL/Δy = (0.00065 mm x 2000 mm) /12 = 0.11 mm

Review Question for AP^® Physics 2 

1. List the measured objects from the data table in order from smallest width to largest. How did the diffraction pattern change from one object to the next?

   The human hair had the smallest width, followed by the copper wire and then the fishing line. The smaller the object, the greater the distance between the bands of the diffraction pattern.

2. The diameter of human hair varies, but is usually in the range of 20–180 μm. Did the experimental value obtained fall within this range? Compare your results with other groups. Does there seem to be a relationship between hair color and width? Explain.

   The hair measured 110 μm, within the accepted range. Lighter-colored hair appears to be thinner than darker hair.

3. The diameter of a 30-gauge copper wire is 0.255 mm. (a) How does the measured width of the copper wire compare to the accepted width? (b) Use Equation 2 to calculate the percent error between the measured and accepted values for the width of the wire. (c) What are some possible sources of error in this experiment?
   1. The measured value for the copper wire was very close to the accepted value.
   2. (0.26 mm – 0.255 mm)/0.255 mm x 100% = 2.0% error
   3. Possible sources of error include difficulty in marking the exact center of the dark bands with tape, variations in the wavelength of the laser light and precision of measuring instruments (meter stick and ruler).
4. Is it possible to measure the width of a wider object such as a cell phone by this process? Explain.

   No, because most cell phones are too wide to produce a measurable diffraction pattern under the circumstances in which this experiment is performed, i.e., the size of the room and the type of laser.

5. Consider an archer on a range. The archer fires ten arrows at a circular target. One of the arrows comes close to the bull’s eye but does not hit it. The other nine arrows contact the target in close proximity to each other but away from the bull’s eye. Describe the accuracy and precision associated with the archer’s shots.

   The single shot that hit the bull’s eye may be called accurate. However, the average location of the shots is inaccurate because the majority of the shots land far from the bull’s eye, or true value. This “experiment” is fairly precise as nine of the ten shots cluster near each other and the archer shows a high degree of reproducibility. A situation in which all ten shots struck the bull’s eye or in close proximity to the bull’s eye and each other would be called accurate and precise. Precision is a measure of the closeness of a data set’s values to each other.

References

AP^® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

PhysicsQuest. Physics Central. http://www.physicscentral.com (accessed April 2013).

Toombes, G. Diffraction. Cornell Center for Materials Research [Online] March 2003. http://www.ccmr.cornell.edu/education/ (accessed April 2013).

Introduction

A variety of methods are available for measuring objects, and using the appropriate instrument is important. For example, a ruler may be used to determine the thickness of a book, while a meter stick would be more reasonable for measuring the height of a table. What if the object is less than a millimeter wide? Discover how light can be used to measure the dimensions of very small objects such as the width of a wire or a human hair.

Concepts

• Measurement
• Interference
• Diffraction
• Wavelength

Background

Visible light, like all energy of the electromagnetic spectrum, travels in waves with crests and troughs. The height of the crest is the amplitude and the distance from one crest to the next is the wavelength (see Figure 1).

Each color of the visible spectrum has its own wavelength—measured in nanometers (1 nm = 10^–9 m)—ranging from 400 nm for violet light to 700 nm for red light (see Figure 2). When light strikes the edge of an object, the light bends and spreads out, much like water waves fan out when they strike a barrier. This bending of light is called diffraction. When an object is very small, the light waves bend around both sides of the object and overlap, creating an interference pattern. If the crests of two waves overlap, constructive interference results with the wave amplitude becoming greater, increasing the brightness of the light. If a crest of one wave meets a trough from another wave, the waves cancel out. This is known as destructive interference (see Figure 3). Unlike white light with a range of wavelengths, laser light is monochromatic light—light of one color—and is composed of a single wavelength. When the light of a single wavelength bends around a small object, a distinctive diffraction pattern of light and dark bands is observed. The light bands are a result of constructive interference and the dark bands are a result of destructive interference (see Figure 4). The distance between the bands is inversely proportional to the width of the object. When the diffraction pattern is projected onto a screen, the distance from one dark band to the next can be measured. By using Equation 1, the width of a very thin object can be calculated: where

d is the width of the object
λ is the wavelength of light
L is the distance between the object and the screen
Δy is the distance from the center of one dark band to the center of the next dark band

Experiment Overview

The purpose of this advanced inquiry investigation is to devise a method for measuring the width of very thin materials by taking advantage of the principles of diffraction. The introductory activity provides instructions for setting up an apparatus to create diffraction patterns by shining monochromatic red laser light at the edges of various materials. The guided-inquiry activity asks students to devise a means for calculating the widths of the various materials and assessing experimental error.

Materials

Prelab Questions

1. Complete the following “If/then” hypothesis to explain how the width of the object being measured will influence the distance between the bands of the diffraction pattern. “If the width of an object being measured with laser light is less than a previously measured object, then the distance from one band to the next will (increase/decrease) because ________________________________.”
2. The wavelength of visible light is usually measured in nanometers and the width of human hair is usually measured in micrometers (1 μm = 1 • 10^–6 m). (a) How many nanometers are in a micrometer? (b) The light from a green laser pointer has a wavelength of 532 nm. Convert this wavelength to micrometers. Show your work.
3. All the dimensions of Equation 1 from the Background section will be millimeters. (a) If 1 mm = 1000 μm, what is the wavelength from question 2(b) above in millimeters? (b) Suppose the distance, L, is 1.4 meters. How would that be expressed in millimeters?
4. What safety precautions must be taken when using a laser pointer?

Safety Precautions

Do not aim the laser pointer directly into anyone’s eyes and never look directly into the laser beam. The low-power, coherent light can cause damage to the sensitive retina and may lead to permanent eye damage. Do not aim the laser at any reflective surfaces such as mirrors or highly polished metal. Prevent stray laser light from projecting beyond the classroom to eliminate any unintentional exposure to the laser light. When refracting the laser light, it is best to do this on a low work surface to keep the refracted laser light below “normal” eye level. For people with sensitive eyes, it is recommended that dark, IR-protective safety glasses be worn. Follow all laboratory safety guidelines.

Procedure

Introductory Activity

1. Obtain a measurement frame (modified index card) and a 6-cm piece of fishing line.
2. Orient the frame so the longer sides are at the top and bottom. Stretch the fishing line vertically across the center of the frame opening.
3. Tape the fishing line to the top and bottom of the frame, making sure the line is vertical and taut (see Figure 5).
   {14019_Procedure_Figure_5}
4. Obtain a 6-cm piece of 30-gauge copper wire and tape the wire to the frame to the left of the fishing line, leaving about a centimeter of space between them.
5. Obtain a sample of human hair (one person in the group should carefully pull or cut one strand from his or her own head) and tape the hair to the frame to the right of the fishing line (see Figure 5). Cut off any excess length from the hair sample.
6. Attach a small binder clip to one bottom corner of the frame as shown in Figure 5 so the frame will stand up.
7. Obtain a laser pointer. Note: Make sure you have read the Safety Precautions regarding the use of lasers. Do not press the power button to turn on the laser until the set-up is complete. Leaving the light on too long will affect its wavelength, which in turn will affect the results.
8. Use the medium binder clip as a stand for the laser by placing the laser pointer inside the medium clip with the power button on top and visible beyond the edge of the clip (see Figure 6). The clip will help keep the laser steady during use.
   {14019_Procedure_Figure_6}
9. Place the frame on a level surface 1.5–3 meters away from a wall. Note: The farther away the laser is from the wall, the more spread out the diffraction pattern will be. Measurements will be easier, but the diffraction pattern will be dimmer.
10. Place a piece of masking tape on the level surface to mark the position of the measurement frame.
11. Place a 2- to 3-cm thick book or other flat object directly behind the frame and place the laser on the book. The lens of the laser should point at the fishing line across the opening of the frame (see Figure 7).
    {14019_Procedure_Figure_7}
12. Tape a piece of white paper to the wall as a screen where the laser beam will shine when it is on.
13. Place the tip of the laser pointer within 1 cm of the fishing line.
14. Holding the back of the binder clip, press the power button and hold it down to turn on the laser light. Caution: Never look directly into the beam of the laser—serious eye injury may result!
15. Aim the laser beam directly at the fishing line. When the laser is positioned correctly, a horizontal diffraction pattern of light and dark bands will be seen on the screen, with a brighter red spot in the middle (see Figure 8).
    {14019_Procedure_Figure_8}

Guided Inquiry Design and Procedure

1. Given Equation 1, what data do you need to measure or observe to calculate the width of an object by diffraction?
2. Write a step by step procedure describing how to collect the necessary data.
3. Carry out the necessary calculations to determine the width of the fishing line.
4. Apply the procedure you used to determine the width of the fishing line to determine the widths for a piece of Cu wire and a human hair.

Analyze the Results

• Accuracy is a measure of an experimental value’s closeness to a known, accepted value. Why is it not possible for you to determine the accuracy of your width measurements of hair?
• Precision is a measure of the closeness of a data set’s values to each other. Describe how you can use your experimental setup to generate a data set to assess the experiment’s precision?
• The laser beam wavelength may vary on the order of ±30 nm from trial to trial because the wavelength depends on the condition of the transistor. Heat affects the transistor properties, and therefore the wavelength of the light. A laser that has been used continuously for several minutes may produce a light with a wavelength that is slightly different compared to when it was just turned on. Describe whether this is an example of a systematic or random error, and comment on sources of error present in this experiment.

Student Worksheet PDF

14019_Student1.pdf