Summary
Students complete this Beer's law activity in class by examining the attenuation of various thicknesses of transparencies. From this activity, they come to understand that different substances absorb light differently. This concept is transferred to xrays to explain that different substances absorb xrays differently, hence the need for dualenergy analysis. In looking at Beer's law, students use the properties associated with natural logarithms. To conclude the activity, students complete a series of questions and calculations.Engineering Connection
Light attenuation and Beer's law are concepts that are very important to many engineers. Environmental engineers must understand these concepts when designing solar panels as a means of alternative energy. Biomedical engineers apply these concepts to bone mineral density measurements using xray machines, as well as other broader applications such as the design of biomaterials.
PreReq Knowledge
Students should be familiar with either Microsoft Excel® or the use of graphing calculators.
Learning Objectives
After this activity, students should be able to:
 Derive the relationship between light and number of layer of attenuation.
 Perform experiments to illustrate the concept of attenuation.
More Curriculum Like This
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Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN),
a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics;
within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
NGSS: Next Generation Science Standards  Science

Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.
(Grades 9  12)
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This standard focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Use mathematical representations of phenomena or design solutions to describe and/or support claims and/or explanations. The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. Empirical evidence is required to differentiate between cause and correlation and make claims about specific causes and effects.
Common Core State Standards  Math

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
(Grades 9  12)
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(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
(Grades 9  12)
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For exponential models, express as a logarithm the solution to ab^{ct} = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
(Grades 9  12)
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International Technology and Engineering Educators Association  Technology

Telemedicine reflects the convergence of technological advances in a number of fields, including medicine, telecommunications, virtual presence, computer engineering, informatics, artificial intelligence, robotics, materials science, and perceptual psychology.
(Grades 9  12)
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Technology transfer occurs when a new user applies an existing innovation developed for one purpose in a different function.
(Grades 9  12)
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State Standards
Tennessee  Math

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
(Grades
9 
12)
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Tennessee  Science

Scientific Research
(Grades
9 
12)
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Materials List
Each group needs:
 lamp
 incandescent 60 W bulb (not a halogen lamp)
 aluminum foil, ~12 x 12 inch piece
 clean transparencies
 Light Attenuation Scale; individually print this light intensity scale because it loses the grayscale detail when photocopied
 masking tape, ~12 inches
 scissors
 access to Microsoft Excel® computer software or a graphing calculator
 Light Experiment Worksheet
Introduction/Motivation
Now that you have been introduced to the equation used to calculate intensity and completed a few practice problems, you are ready to use it in a realworld application.
Today we will complete a lab dealing with measuring light intensity through different numbers of sheets of transparencies.
I am passing out the worksheet now. Please get into groups of three and I will explain further once everyone has all the materials.
Procedure
Background
 Each group needs to be able to work at a table near a wall to shine the lamp onto and take intensity measurements.
 Experiments must be performed with classroom lights out and shades drawn.
 See additional comments on the Light Experiment Worksheet Answer Key.
Before the Activity
 Make copies of the Light Experiment Worksheet.
 Print out enough Light Attenuation Scales, one per group.
 Set materials out at each workstation.
With the Students
 Tape the light intensity scale to a wall and set up the lamp to shine on the scale (do not turn on the lamp yet).
 Cut a plastic transparency sheet into eight equalsized sections.
 Cut a 5 mmdiameter hole in the center of a piece of foil.
 Cover the face of the lamp by wrapping the foil around it, making sure that the hole is in the center of the face of the lamp and that the foil does not cover up any vents in the back of the lamp.
 Darken the room, turn on the lamp apparatus, and hold a piece of plastic transparency a few inches from the wall to cast a shadow near the scale (but not on the scale).
 Match the intensity of the resulting shadow with a square on the scale, as shown in Figure 1. Tip: It is easier to distinguish the shade of gray in the shadow by stepping back to look at it.
 Record the intensity in worksheet Table 1.
 Repeat the process with two sheets of the transparency stacked together, then three, and so on until the table is filled.
 Next, use Excel to plot the natural logarithm of the shadow's intensity versus the thickness of the attenuator.
Worksheets and Attachments
Safety Issues
Do not leave the lamp on for more than a minute at a time; the foil traps heat and can cause the bulb to burst.
Assessment
PostActivity Assessment: Collect and grade students' completed Light Experiment Worksheets. Review their answers and calculations to assess their depth of comprehension.
Contributors
Cynthia Paschal; Stacy Klein; Sean Brophy; Chris Garay; Hunt McKelvey; Stephen Schleicher; Rachael Shevin; Rebecca Zambon; Kristyn Shaffer; Megan JohnstonCopyright
© 2013 by Regents of the University of Colorado; original © 2004 Vanderbilt UniversitySupporting Program
VU Bioengineering RET Program, School of Engineering, Vanderbilt UniversityAcknowledgements
The contents of this digital library curriculum were developed under National Science Foundation RET grant nos. 0338092 and 0742871. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.
Last modified: July 20, 2017
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