"Class 2: Lasers in this class emit visible light only. They are only capable of producing eye damage if the beam is stared at directly for longer than the normal human aversion response time to bright light (0.25 second). This means a person would naturally turn away from the beam before any damage is done."
--Laser Safety Manual, Caltech Safety Office (1998), p. 3.
Preparation
Due 12:00 AM before start of lab
Pre-lab assignment 2 (*.html)
Equipment
rulers (12")
glass semicircular prism (*.gif)
protractor template (*.pdf)
cardboard scraps
He-Ne laser (class 2)
adjustable lab jacks (2)
glass stirring rod, wire hanger
whiteboards, markers
laboratory laptop
Microsoft Excel
Big Ideas
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.
Total internal reflection occurs when a ray of light travels from a higher refractive index material to a lower refractive index material with an incident angle greater than the "critical angle."
Goals
Students learn how to handle data subject to experimental uncertainty, and to display these using error bars on graphs.
Students build upon previous best practices to independently write an individual lab report, which can be submitted early, on time, or late depending on their personal initiative.
Tasks
(Optimally form groups of two students, three only if necessary. 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. Data Collection- On top of an adjustable lab jack, center the semicircular prism on the protractor template with the rounded end below the "interface-ǝɔɐɟɹǝʇuᴉ" line, and the flat end aligned along the interface line. (Use the fact that the semicircular prism has a diameter of 9.0 cm.) Trace the outline of the prism on the protractor template, such that it can be always be placed back in the same position.
- Place a laser on another adjustable lab jack, and tape a wire hanger such that it holds a stirring rod horizontally in front of the laser beam. Verify that when the laser is turned on, the stirring rod is able to spread the beam out from a dot into a vertical line. Note: read the safety precautions for avoiding eye exposure to the laser beam.
- Place the laser and prism lab jacks approximately 50 cm apart, such that a straight laser line is projected onto the protractor template. You may need to make fine adjustments to the placement of the stirring rod in front of the laser.
For the range of 0° ≤ θ1 ≤ 90° incident angles in glass, find the resulting refracted θ2 angles (if any) in air. Align the laser beam and protractor template by having the laser beam pass through the center of the protractor template, and have the same angle on either side of the protractor circle. Then place the semicircular prism on the protractor, making sure it is centered. You will need to do these two alignments for each different measurement.
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°) = 0.0348994967..., 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 (glass) vs. refracted (air) angles and sines
(Incident and reflected angles in glass assumed to be identical)
| 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 |
05 |
|
2 |
⋮ |
⋮ |
0.03 |
| 4 |
10 |
|
2 |
⋮ |
⋮ |
0.03 |
| 5 |
15 |
|
2 |
⋮ |
⋮ |
0.03 |
| 6 |
20 |
|
2 |
⋮ |
⋮ |
0.03 |
| 7 |
25 |
|
2 |
⋮ |
⋮ |
0.03 |
| 8 |
30 |
|
2 |
⋮ |
⋮ |
0.03 |
| 9 |
35 |
|
2 |
⋮ |
⋮ |
0.03 |
| 10 |
40 |
|
2 |
⋮ |
⋮ |
0.03 |
| 11 |
45 |
|
2 |
⋮ |
⋮ |
0.03 |
| 12 |
50 |
|
2 |
⋮ |
⋮ |
0.03 |
| 13 |
60 |
|
2 |
⋮ |
⋮ |
0.03 |
| 14 |
70 |
|
2 |
⋮ |
⋮ |
0.03 |
| 15 |
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 D15; and then while pressing the "Ctrl" key, click-drag-release to select the cells E2 through E15. (Check to see if "=Sheet1!$D$2:$D$15,Sheet1!$E$2:$E$15" 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 F15, and under "Negative Error Value" click-drag-release to also select the cells F2 through F15, 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). Determine the index of refraction for glass, given that air has an index of refraction of 1.0003, with the appropriate number of significant figures.
index of refraction for glass = __________.
- Calculate the critical angle θc for the glass-air interface, with the appropriate number of significant figures.
glass-air θc = __________.
2. Critical Angle Behavior- Set up your apparatus to make and record quantitative measurements and qualitative, descriptive observations of the laser beam when:
- the incident angle θ1 in glass just below than the critical angle θc;
- the incident angle θ1 in glass is exactly equal to the critical angle θc;
- the the incident angle θ1 in glass is just above the critical angle θc.
- Consider the following question:
"When the critical angle in glass is reached, does the 90° ray in air exist?" Answer this question, based on the evidence you collected. Provide evidence by describing your observations of the behavior of the laser beam, and include specific relevant numbers in your concluding statement(s), such that it can be read (and cited) on its own without referring to the above calculations and numbers.
Brief concluding statement(s):
- Print out one copy of your data table and graph (with trendline equation and error bars) for review by your instructor, who will check off this off for your in-class work. Then print out more data tables and graphs (and an *.xlsx spreadsheet transferred via USB drive, e-mail, cloud, etc.) for each person in your group to use to independently write an individual lab report to be completed at the end of this lab.
- Documentation Rubric (task 2)
(Graded for the entire group)
| Score | Description |
| 3 | Sufficient amount of data points, graph/trendline and validation calculations complete, or very nearly so. |
2 | (No intermediate score possible.) |
| 1 | Substandard effort; insufficient data, problematic graph/trendline, validation calculations missing or incorrect. |
| 0 | Unacceptable or no significant effort. |
3. Independent, Individual Lab Report
(Due at the end of lab today)Independently work on writing an individual lab report during the rest of the time allotted in lab, which should include:- A descriptive abstract.
- Procedure section ("materials and methods").
- Data table, calculations and/or results (show work in calculating the critical angle).
- Evidence-based concluding paragraph (interpret your observations of what happens to the laser beam for each of the cases when the incident angle in glass is less than, equal to, and greater than the critical angle).
Suggested best-practice guidelines for each of these sections: (*.pdf). - Lab Report Rubric
(Due next lab; each student works on their individual write-up individually)
| Score | Description |
| 3 | (Essentially) complete, thorough, understandable, with very few or no corrections. |
| 2 | Minor problems; some corrections/revisions needed. |
| 1 | Minimally acceptable effort, essential/critical revisions needed. |
| 0 | Unacceptable or no significant effort beyond original experimental work. |
Follow-up
Complete this week's post-lab assignment, next week's pre-lab assignment, and review lab instructions. (You may complete and turn in your lab report today if you want to be assured of the "early" +1 submission modifier point.)
Due 12:00 PM before start of next lab
Post-lab assignment 2 (*.html)
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