"You know that stick in the water that looks bent when it isn't? That's why I don't take baths."
--Steven Wright, quoted in Amassed Hysteria!: A Collection of Great Comedy Sketches
from Hysteria!, Hysteria 2! and Hysteria 3!, edited by Lise Mayer and Rachel Swann,
Penguin (1991), p. 150.
Preparation
Due 12:00 AM before start of lab
Pre-lab assignment 1 (*.html)
Equipment
rulers (12")
semicircular water dish (*.gif)
protractor template (*.pdf)
cardboard scraps
craft pins
whiteboards, markers
laboratory laptop
Microsoft Excel
Big Ideas
Paths of light rays ("lines of sight") can be traced using the "method of parallax."
The sines of the angles of an incident light ray and a refracted light ray are proportional to the ratio of the refractive indices of the incident and refracted media.
Goals
Students build upon previous knowledge and best practices to execute a research task by taking and analyzing data, write a conclusion, and finally a descriptive abstract in a group lab report.
Students self-assess their own work, and receive immediate instructor feedback regarding expectations on content and format, and have time remaining to correct/supplement deficiencies before work is approved.
Tasks
(Only form groups of two students; a group of three students will be allowed at the instructor's discretion to handle an odd total number of students in a section. Record your lab partner's name on your worksheet for tasks 1-2, to be turned in at the end of today's lab for randomly selected grading for your group.)
1. Method of Parallax- Use craft pins to secure a protractor template sheet onto a stack of two cardboard scraps. Fill the semicircular water dish just a little more than half-full, and then center it on the protractor template with the rounded end below the "interface-interface" line, and the flat end aligned along the interface line. Trace the outline of the semicircular water dish on the protractor template, such that it can be always be placed back in the same position. Place a pin at the center (origin) of the protractor template. (Ignore the protractor markings on the bottom of the semicircular water dish.)
- For the initial sample data point, place a pin at the upper-left 45° mark of the protractor template (above the flat side of the semicircular water dish). Note that all angles will have an uncertainty taken to be ±2°, due to the width of the pins, placement errors, and the degree markings on the protractor template.
- Crouch down such that your eye level is at tabletop level, and look down along the 45° and the center pins such that they line up vertically. Then look through the flat surface of the semicircular water dish, and determine where a third pin should be placed behind the rounded surface of the semicircular water dish such that it also lines up vertically with the two other pins. This pin should wind up being placed somewhere around 30°-35°. (Ask your instructor for assistance if needed to make sure you are clear on this process, as this will be done for all other data points.)
- To clearly illustrate the path of the light ray that passes through the air-water interface of the semicircular water dish, remove it and the pins from the protractor template, and connect the dots from the 45° incident pin mark to the center pin mark, and then from the center pin mark to the refracted pin mark.
- Snell's law relates the incident angle θ1 of a light ray in initially traveling through a medium with an index of refraction n1 with the refracted angle θ2 of the light ray subsequently traveling through a new medium with an index of refraction n2:
n1⋅sinθ1 = n2⋅sinθ2.
Consider the following generalization:
"The index of refraction of water is greater than the index of refraction of air." Support or refute this generalization, based on the evidence you collected. Explain your reasoning and provide evidence by include specific relevant numbers in your concluding statement, such that it can be read (and cited) on its own in words.
Brief concluding statement:
2. Index of Refraction Ratio- For the range of 0° ≤ θ1 ≤ 90° incident angles in air, find the resulting refracted θ2 angles in water. Develop an experimental linear trendline equation of how sinθ2 (dependent variable) depends on sinθ1 (independent variable). Refer to the example data table below to create your spreadsheet. Do not enter the "A..." column headings and "1..." row headings, as those are just spreadsheet "coordinates." Sample cell formulas to be entered below are highlighted in yellow.
Note that the ±2° uncertainty for θ corresponds to an uncertainty of ±0.03 for sinθ, as sin(2°) = 0.034899..., or 0.03 to one significant figure. Also Excel trigonometric functions only work in radians, so a "PI()/180" factor must be included to convert degrees to radians; where "PI()" is the specific function to return a numerical value of π.
Incident (air) vs. refracted (water) angles and sines
| A | B | C | D | E | F |
| 1 |
Angle
θ1
(°) |
Angle
θ2
(°) |
θ uncer-
tainty
(°) |
sinθ1
(unitless) |
sinθ2
(unitless) |
sinθ
uncertainty
(unitless) |
| 2 |
00 |
|
2 |
=SIN(A2*PI()/180) |
=SIN(B2*PI()/180) |
0.03 |
| 3 |
10 |
|
2 |
⋮ |
⋮ |
0.03 |
| 4 |
20 |
|
2 |
⋮ |
⋮ |
0.03 |
| 5 |
30 |
|
2 |
⋮ |
⋮ |
0.03 |
| 6 |
40 |
|
2 |
⋮ |
⋮ |
0.03 |
| 7 |
45 |
|
2 |
⋮ |
⋮ |
0.03 |
| 8 |
50 |
|
2 |
⋮ |
⋮ |
0.03 |
| 9 |
60 |
|
2 |
⋮ |
⋮ |
0.03 |
| 10 |
70 |
|
2 |
⋮ |
⋮ |
0.03 |
| 11 |
80 |
|
2 |
⋮ |
⋮ |
0.03 |
Use a software package (such as Excel, instructions below, which may be slightly different depending on the version) to graph this data set, and to apply a linear trendline with vertical error bars.
- Select an unused blank cell anywhere else in the spreadsheet. Under "Insert" on the top bar menu, click on "Scatter," and in the pop-up window select "Scatter with only Markers" (plotting data points only, no connecting lines or curves). A (blank) graph should appear.
- Click on the graph. Under "Design" on the top bar menu, click on the "Select Data" button. In the pop-up window, click on the "Chart data range" box, and on the spreadsheet, click-drag-release to select the cells D2 through D11; and then while pressing the "Ctrl" key, click-drag-release to select the cells E2 through E11. (Check to see if "=Sheet1!$D$2:$D$11,Sheet1!$E$2:$E$11" is in the box; this is also how to select independent and dependent parameters that are not in adjacent columns.) Click on "OK" when done. You should now see the data points plotted on the graph.
- Right-click on any of the data points in the graph, then select "Add Trendline...," and in the pop-up window, select "Linear." Click on the "Options" tab, check both "Display Equation on chart" and "Display R-squared value on chart" options. Then click "OK" when done.
- Click on the graph. Just off to the upper right of the graph, click on the "[+]" icon, check the "Error Bars" box, and next to it, click on the triangle and select "More Options..." Right-click on any vertical error bar, select "Format Error Bars..." in the pop-up window, and in the "Format Error Bars" menu, and under "Error Amount" select "Custom" and click on "Specify Value." In the pop-up window, under "Positive Error Value" click-drag-release to select the cells F2 through F11, and under "Negative Error Value" click-drag-release to also select the cells F2 through F11, and then click "OK" when done. The vertical error bars should now correctly display for each data point.
- (Use similar steps as above to create and format horizontal error bars.)
- Print out one copy of this graph (to be attached to the one individual report from your group to be selected later for grading today).
- Since this graph has an independent parameter of x = sinθ1 and a dependent parameter of y = sinθ2, then Snell's law can be expressed in terms of a linear equation:
n1⋅sinθ1 = n2⋅sinθ2,
n1⋅x = n2⋅y,
y = (n1/n2)⋅x,
where the slope m of this graph would be the experimental value for the quantity (n1/n2).
linear slope of trendline = __________.
The percent error (or "percent approximation error") is used to compare the discrepancy between an experimental value (here, your calculation) with a theoretical, known, established, or accepted value:
% error = 100 × | experimental − theoretical | / theoretical.
(The percent error is a positive definite value, because of the absolute value operation.) Determine the percent error of the linear slope of your experimental trendline, compared to the known value for (n1/n2), where for air n1 = 1.0003, and for water n2 = 1.33.
experimental value of (n1/n2) = __________.
known value of (n1/n2) = __________.
% error = __________%.
- Consider the following generalization:
"The experimental value for the linear slope of our experimental trendline was essentially equivalent to the known value of (n1/n2), within an expected percent error of 3%." Support or refute this generalization, based on the evidence you collected. Explain your reasoning and provide evidence by include specific relevant numbers in your concluding statement, such that it can be read (and cited) on its own without referring to the above calculations and numbers.
Brief concluding statement:
3. Informal Whiteboard Lab Report (checklist: (*.pdf))
Write up an informal lab report on a whiteboard, to be presented to the instructor, which should include:- Descriptive abstract.
- Procedure (materials used and how the experiment was set up (diagrams)).
- Data table (printout), graph (printout), calculations and/or results.
- Evidence-based conclusion statement.
- For the descriptive abstract for your experiment (approximately 100 words, can be slightly shorter or longer), make sure that each of the following guidelines (if applicable) are followed:
- Describes measurement made, equipment and methods used.
- Describes data analysis and mathematical modeling.
- Describes how mathematical model is validated with experimental values (or what experimental results are compared to known/established values).
- Uses active voice and first-person pronouns ("we" or "I"), instead of passive voice.
- Written in past-tense, instead of present-, future-, or mixed-tense.
- Omits opinions and unnecessary facts.
- Avoids abbreviations, equations, and symbols.
- Omits specific numerical results, conclusions, and recommendations.
- For the procedure (materials used and how the experiment was set up (diagrams), instead of step-by-step instructions), make sure that each of the following guidelines (if applicable) are followed:
- Describes in general detail the materials and the methods of what/how things were measured, without being overly specific.
- Written in paragraph form with complete sentences, not as an ingredient list, step-by-step recipe, or recitation of the original lab instructions.
- Describes in just enough detail the materials and the methods of what/how things were measured, such that the results can be later replicated.
- Uses passive voice with no personal pronouns ("the heights were measured") instead of active voice and first-person pronouns ("we measured the heights").
- Written in past-tense, instead of present-, future-, or mixed-tense
- Omits specific numerical results and conclusions.
- For your data collection and graphical analysis, make sure that each of the following guidelines (if applicable) are followed:
- Minimum-maximum data range (spanning a factor of at least 5×, 10× is better).
- Has minimum number of data points (10).
Concentrated data in rapidly changing portions of graphs.
Variable data points should be an average of repeated measurements (3-5 maximum), with a standard deviation reported in the data tables, and represented with vertical error bars on the graphs.
- Outlying data points should be replaced/removed.
Proper choice of trendline fit types.
- Vertical and horizontal error bars are both displayed properly, or are instead explicitly noted to be too small to sufficiently display due to the scale of the graph.
- For your concluding statement, make sure that each of the following guidelines (if applicable) are followed:
- Uses active voice and first-person pronouns ("we" or "I"), instead of passive voice.
- Written in past-tense, instead of present-, future-, or mixed-tense.
- Conclusion can be read (and cited) on its own in words without referring to graphs, calculations and tables.
- All claims are backed up with evidence, with specific relevant numbers included.
- No unsupported claims are made.
- No extraneous evidence is included.
- Bring your individual written work, one copy of your graph, and your group whiteboard up to the front of the class for evaluation by your instructor.
- Documentation Rubric (tasks 1-2)
(Graded from randomly selected group member)
| Score | Description |
| 3 | Explanations complete and calculations correct, or very nearly so. |
| 2 | Essentially complete; few explanations/calculations missing or incorrect. |
| 1 | Substandard effort; substantive amount of explanations/calculations missing or incorrect. |
| 0 | Unacceptable or no significant effort. |
- Whiteboard Rubric (task 3)
(Graded as a group, evaluated by instructor during debrief session)
| Score | Description |
| 3 | Complete, thorough, understandable, with little or no clarification needed during verbal instructor critique (can be resubmitted and presented again with requested corrections/revisions made, and still receive full credit). |
| 2 | Minor problems; some corrections/revisions requested by instructor still needed, but not completed during time remaining in lab. |
| 1 | Minimally acceptable effort, essential/critical revisions still needed. |
| 0 | Unacceptable or no significant effort beyond experimental work. |
Follow-up
Complete this week's post-lab assignment, next week's pre-lab assignment, and review lab instructions.
Due 12:00 AM before start of next lab
Post-lab assignment 1 (*.html)
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