Brewster s Angle Accessory

Instruction Manual Manual No. 012-08489A Brewster s Angle Accessory

Table of Contents Equipment List... 3 Introduction... 4 Theory... 4-5 Setup Instructions... 5-8 Suggested Experiment: Discovering Brewster s Angle... 9-13 Further Investigation...11 I. Intensity of Reflected Light (without a polarizer)...11 II. Intensity of Transmitted Light...12 III. Snell s Law...13 Appendix A: Creating Equations in DataStudio... 14 Appendix B: Laser Safety Instructions...15-16 Appendix C: Technical Support... 17 Appendix D: Copyright and Warranty Information... 17 2

Equipment List 1 3 2 Included Equipment *Use Replacement Model Numbers to expedite replacement orders. Replacement Model Number* 1. Polarizer Assembly (1 lens holder and 2 polarizers) 003-08337 2. Acrylic Lens, semi-circular (1) 003-08545 3. Polarizer and Pivot Plate Assembly (1) 003-08332 Additional Equipment Required Model Number Educational Spectrophotometer* Laser Diode Aperture Bracket* OS-8537 or OS-8539* OS-8525A OS-8534 Collimating slits* 636-06566 Optics Bench* Light Sensor, High Sensitivity* Rotary Motion Sensor* DataStudio software (version 1.5 or higher) PASCO computer interface (ScienceWorkshop ) Experiment Setup (CD-ROM) *Indicates components included with the OS-8539 Educational Spectrophotometer OS-8541 CI-6604 CI-6538 Various (see catalog) Various (see catalog) EX-9922 3

Introduction The (OS-8170) is used in optics for studying the polarization of reflected light and for determining Brewster s angle. PASCO's Brewster's Angle Accessory (OS-8170) is designed to be used with the Educational Spectrophotometer System (OS- 8539). The Basic Optics Diode Figure 1: Brewster s Angle Accessory Setup for Experiments Laser (OS-8525A), a ScienceWorkshop interface, and DataStudio software are also required for the experiments. When light reflects off a nonconducting material, the reflected light is partially polarized. The amount of polarization depends on the incident angle and the index of refraction of the reflecting material. The incident angle that gives the maximum polarization is called Brewster's angle. Light from a Diode Laser is reflected off the flat side of an acrylic semicircular lens. The reflected light passes through a polarizer and is detected by a Light Sensor. The angle of incidence is measured by a Rotary Motion Sensor mounted on the Spectrophotometer Table. The intensity of the reflected polarized light versus the incident angle is graphed to determine the angle at which the light intensity is a minimum. This is Brewster's angle, which is used to calculate the refraction index of acrylic. NOTE: A complete experiment with a DataStudio setup file is available to purchase separately. All equipment and the complete experiment setup files are included in the Brewster's Angle experiment (EX-9919). Theory When unpolarized light reflects off a nonconducting surface, it is partially polarized parallel to the plane of the reflective surface. There is a specific angle called Brewster's angle at which the light is 100% polarized. This occurs when the reflected ray and the refracted ray are 90 degrees apart. 4

According to Snell's Law, n 1 sin θ 1 = n 2 sinθ 2 (1) where n is the index of refraction of the medium and θ is the angle of the ray from the normal. Figure 2: Polarization of Unpolarized light When the angle of incidence is equal to Brewster's angle, θp, n 1 sinθ P = n 2 sinθ 2 (2) and since θp + θ2 = 90o, θ2 = 90o - θp, and sinθ 2 = sin(90 o - θp ) = sin90o cosθ P - cos90 o sinθ P = cosθ P Substituting for sinθ 2 in Equation (2) gives n 1 sinθ P = n 2 cosθ P n Therefore, ----- 2 = tanθ (3) P n 1 Setup Instructions 1. Attach the Spectrophotometer table to the Optics Bench. (For instructions on setting up the Spectrophotometer, see the Educational Spectrophotometer Manual.) After attaching the Spectrophotometer, perform the following instructions for setup of the Brewster's Angle Accessory. 5

2. Put the Laser Diode, two polarizers, and the collimating slits on the bench as shown in Figure 3. Note: The polarizers snap onto the Lens Platform. Figure 3: Polarizers, Collimating Slits, and Laser Diode 3. Mount the Rotary Motion Sensor with the bigger diameter of the spindle against the Spectrophotometer Table (See Figure 4). Attach the Spectrophotometer Table base to an electrical ground, as instructed by your teacher. 4. Position the spectrophotometer disk backwards (with the 180- degree mark at the position where the zero mark is normally). Rotary Motion Sensor Figure 4: Mounting the Rotary Motion Sensor to the Spectrophotometer Table 5. Two round polarizers are used on the holder. Rotate the second polarizer (second from laser) to 45 degrees (the indicator is the bottom lip on the lens holder) and lock it in place by tightening the brass screw. The first polarizer (closest to the laser) is used throughout the experiment to adjust the light level. Since the ratio of reflected light to incident light is measured, better data will be obtained if the incident light level is kept above 50%. 6. The square analyzing polarizer (in Figure 5) has its transmission axis marked, and for normal use, position the polarizer with its label on top and with its axis horizontal and thus 90 degrees from Figure 5: Analyzing Polarizer with Axis 6

the polarization axis of the reflected light. This is finding the variation in the p (parallel) component of the reflected light and is used to determine Brewster s angle and to calculate the refraction index. By placing the analyzing polarizer with its transmission axis vertical, you can also look at the variation in the s (perpendicular) component of the reflected light as well. Note: The 45 degree polarizer is used to solve the problem that the laser light is already polarized. To make the relative intensities of the s and p components the same, the light is polarized at 45 degrees. 7. Using the thumbnut below the Spectrophotometer Table, attach the Brewster s angle disk to the spectrophotometer disk. The small metal Brewster's angle base disk should be screwed in and zeroed so that the mark at the top of the label above the N in the word ANGLE is aligned with the zero angle mark on the spectrophotometer disk. 8. Place the metal lens holder on the Brewster's angle base disk. It has two zero marks. For reflected light, use the mark that is on the side with the higher step. The D lens is placed with the magnet side down on the lower surface flush against the step. The other mark can be used for transmission studies in a Snell s Law experiment. 9. To prepare to align the laser beam with the Light Sensor, remove the polarizers, collimating slits, and the D lens. WARNING: Never look directly at the laser light source or reflected light, such as from a mirror. Although the laser used in this experiment is of low power, looking directly into the laser light source or its reflected light from a mirror could cause eye damage. To avoid eye injury, do not look directly into the laser beam and wear laser protective goggles. For more information about laser safety, see Appendix B of this manual. 10. Set the Spectrophotometer Arm on 180 degrees. Plug the Laser Diode into a grounded power outlet. Use the vertical adjust on the laser to get the laser beam at the center of the Light Sensor slit. The Light Sensor Bracket slit should be set on #4. Place the collimating slits on track and adjust the slit position so that the laser beam passes through the #4 slit. 11. Replace the D lens, and set the Brewster's angle base disk to zero. If the laser pattern is not still centered on the aperture 7

bracket, slide the D lens to center it on the base. Make sure the lens is firmly against the step. Software Setup Plug a Rotary Motion Sensor into Channels 1 and 2 of a ScienceWorkshop interface. Plug a Light Sensor into Channel A. In DataStudio, create the following equations. Angle = (180-abs(x)/15)/2 where x is the Angular Position (from Channels 1 and 2). Light Intensity = smooth(8,i) where I is the Light Intensity (from Channel A). Ratio=100 pol/tot, where pol is the polarized light and tot is the total light. Set up the table and graph as shown below. Note: The Experiment Resource CD-ROM provides the software setup files you need for your experiment. To order the Experiment Resource CD-ROM, use part no. EX-9922. Note: For instructions on creating equations in DataStudio, see Appendix A or the DataStudio online help. From the Data list, drag the angle, total light, polarized light, and ratio icons to a Table display. From the Data list, drag the Ratio equation icon over the y-axis in the display. Then drag the Angle equation icon over the x-axis. Note: Use Digits displays to monitor the angle and light intensity. 8

Suggested Experiment: Discovering Brewster s Angle Equipment Required (OS-8170) Laser Diode (OS-8525A) Rotary Motion Sensor (CI-2120) Spectrophotometer (OS-8537 or OS-8539) Light Sensor (CI-6604) DataStudio Software Optics Bench (OS-8541) Aperture Bracket (OS-8534) ScienceWorkshop interface Collimating Slits (636-06566) Experiment Setup: Follow the Experiment Setup instructions on pages 5-8 of this manual. Procedure: 1. With the D lens removed, zero the angle for Rotary Motion Sensor: Rotate Figure 1-1:Experiment Setup the Spectrophotometer Arm so the laser beam is centered on the Light Sensor slit. The spectrophotometer disk should be near 180 degrees, but it is okay if than angle is slightly off. 2. In DataStudio, click the Start button. Move the arm back and forth in front of the laser, watching the intensity on the computer. Stop at the position that gives the maximum intensity. Click on the Stop button. Note: Do not move the arm until the program is started to take the actual data run. This ensures that zero for the Rotary Motion Sensor is at the center of the beam. Place the D lens on the platform against the step. Note about angle measurement: The angle is computed by dividing the actual angle (recorded by the computer) by two. The best procedure is to move the spectrophotometer arm, read the angle on the Digits display, and then rotate the plastic Brewster's disk to match same angle. Thus the mark- 9

ings on Brewster's disk are only there for convenience (in this experiment) and are not directly used. However, to get the laser beam exactly on to the slit, you must make fine adjustments while watching the Digits display for the maximum light intensity. You can adjust either the disk or the spectrophotometer arm until the intensity is maximized. 3. Turn out the room lights. (A small light might be useful for seeing the computer keys to type in values and to put the analyzing polarizer on and off.) Click on the Start button. Do not click on the Stop button until all of the procedure steps are completed. Set the angle to the 85 degrees. The square analyzing polarizer should not be in place. Rotate the Brewster disk to about 85 degrees and, while watching the digits display of light intensity, fine tune the position to get into the beam. It doesn t have to be exact, just so that you get enough light. Rotate the first polarizer (nearest to the laser) to adjust the level to be as high as possible without exceeding 90%. The Light Sensor should be on a gain of 1 or 10. 4. Record the angle. Read the Digits display of the light intensity and record the value. Place the square analyzing polarizer (axis horizontal) on the arm just in front of slits. (Note: The square analyzing polarizes must sit level, flat on the arm.) Read the Digits display of light intensity and record the value. 5. Remove the analyzing polarizer and go to the next angle, in increments of 5 degrees. Since the results are live on the graph, you can see when the intensity is approaching the minimum. Take data points every 1 degree near the minimum. At low intensities (below 2%), it is useful to switch the gain on sensor up by a factor of 10. Note that you must divide the measured intensity by 10 to get the correct value, but this method gives much better results. 6. For each intensity data pair, calculate the ratio of the (light with polarizer)/(light without polarizer). 7. Under the "Experiment" pull-down menu in DataStudio, click on New Empty Data Table. Also make a graph of the Ratio of Light Intensities versus Angle. 8. Click on "Fit" at the top of the graph and choose the polynomial fit. Determine the angle at which the reflection is a minimum. This is Brewster's angle. Use Brewster's angle to calculate the index of n refraction of acrylic using Equation (3), tanθ p = 2 -----. n 1 10

Sample Data Polarized Light (%) vs. Angle (degrees) Further Investigation I. Intensity of reflected light (without polarizer) Note: This experiment uses the same setup except the analyzing polarizer is removed. 1. Reflect the laser beam off the outside plane side of the lens. 2. Make a graph of Light Intensity versus Angle where Angle is a calculation: Angle = (180-abs(x)/15)/2, where x is the Angular Position, from Channels 1 and 2. (For instructions on creating equations in DataStudio, see Appendix A of this manual.) 3. Repeat Step 1 of the procedure for the Brewster's Angle experiment. Then do Step 2, except this time, sweep the Light Sensor through the reflected laser beam. The result is an intensity peak. Do not stop recording data. Use a Smart Cursor to measure the angle to maximum intensity and the magnitude of the maximum intensity. It is useful to have the graph set on a sliding scale, but if the smart cursor is used, you will need to click on show live data in the pull down menu to resume the sliding scale. 4. Repeat the procedure or angles in increments of 5 degrees. 5. Under the "Experiment" pull-down menu in DataStudio, click on New Empty Data Table, enter the data, and make a graph of Light Intensity versus Angle. 11

6. Repeat the experiment with the laser beam entering the curved side of the lens and reflecting off the inside of the plane side of the lens. This will give the critical angle for total internal reflection. II. Intensity of Transmitted Light This experiment uses the same setup as part I Reflected Intensity, but the slits should both be set on #3. 1. The computer can measure the refracted angle, but not the incident angle. You must read the markings on Brewster's base and enter them manually. 2. Keep the curved part of the lens should be towards the laser. Set Brewster's base angle to 10 degrees. Sweep the Light Sensor through the reflected laser beam. The result is an intensity peak. Do not stop recording data. Use a Smart Cursor to measure the angle to maximum intensity and the magnitude of the maximum intensity 3. Repeat the procedure for angles in increments of 10 degrees. 4. In DataStudio, set up the displays as shown below. 12

5. Repeat this procedure with the lens turned around. Have the flat side of the D lens towards the laser. This will show total internal reflection above angles of about 40 degrees. Sample Data: Light Intensity vs. Incident Angle III. Snell s Law For the data from the first part of part II, graph Sin (incident angle) vs. Sin(refracted angle). The slope of the line is the refraction index of the plastic. Sample Data: Incident Angle vs. Refracted Angle In DataStudio, create the following equations: a) refracted angle=oi-x(deg), where Oi is the incident angle, and x is the arm angle in degrees. b) sin incident=sin(x), where x is the incident angle (degrees). c) sin refracted = sin(x), where x is refracted angle (degrees). For instructions on creating equations, see Appendix A or the DataStudio online help. 13

Appendix A: Creating Equations in DataStudio Step 2: Type in and/or build the equation. (Use the Scientific, Statistical, and Special menus, and the trigonometric functions to build the equation.) Click the Accept button. Step 3: Define the dependent variables. Under Variables, use the down arrow to select a variable or constant, etc. and click OK. (Example: For x, select Data Measurement. In the pop-up, select Angular Position, and click OK. Step 1: Create a new equation. On the main toolbar, click the Calculate button to open the Calculator dialog. In the Calculator dialog, click the New button. Step 4: Enter any experiment constants (optional). Use the (+) button to create an experiment constant. Click New, then enter the name, value and units for the constant. Click the Accept button. Go back to the Variables menu and select experiment constant. Click OK. Step 6: Save the equation. Click the Accept button. Step 5: Label the units. Click on the Properties button to open the Data Properties dialog and enter the name and units. (Example: In the Data Properties dialog, type Angle in the name box and degrees in the units box.) Note: Each time you build a new equation, click the New button. To edit a completed equation, double click on the equation in the Data list, make your changes, and click the Accept button to save your changes. 14

Appendix B: Laser Safety Information The OS-8525A Laser Diode is a low power, Class 2 laser. When Class 2 lasers are used in accordance with Occupational Health and Safety Administration (OSHA) standards, Class 2 lasers are not harmful. However, when appropriate safety precautions are not taken, Class 2 lasers can cause permanent, irreversible damage to the eyes. As an instructor, you should always inform your students of the hazards of lasers and the necessary preventative, safety measures. PASCO cannot be held liable for negligent use in the classroom. As a courtesy, we are providing you with the following laser safety instructions. These reminders are not a comprehensive list of all possible safety measures or hazards. For more information, see the OSHA web site (http://www.osha.gov). Also see http:// www.safetymanual.com or www.laserinstitute.org Safety Reminders: Never look directly into the laser or at any reflection from the laser at eye level (see Figure 6 below.). Figure 6 laser light source DO NOT LOOK DIRECTLY INTO THE BEAM! Do not point a laser at your own eye, through glass, mirrors or transparent objects in your surroundings, or at the eyes of other individuals. Never remove any of the covering or components of the OS-8525A Diode Laser. If the laser is defective, return the defective laser immediately to PASCO scientific. If you are uncomfortable or unsure about working around lasers, wear protective laser goggles or spectacles. 15

About Laser Protective Eyewear The eyewear must be designed for use with lasers and meet OSHA standards specific to the type and class of laser you are using. You can tell if the type of goggle or spectacle you are using meets laser standards by looking at the insignia on the side of the frame. Any type of plastic chemical protective goggle will not suffice. Also, you need to select protective eyewear with the correct filter for the wavelength range of the laser (For a Class 2 laser, you need a 400-780 nm filter.) Example: Laser goggles designed to protect for Class 1 lasers do not provide maximum protection when using Class 2 lasers. For more information, see the OSHA web site (www.osha.gov). Laser Injuries Severe corneal injuries or eye burns may or may not present with pain at the surface of the eye. In retinal injuries, the individual may see red spots, or have blurred vision or altered color perception. Less severe injuries may not show up immediately and are more hazardous when they occur repetitively. If you believe you have a laser injury, report the injury immediately to your instructor/supervisor, school health department and/or safety officer. If necessary, go to an emergency health facility or contact a medical doctor or opthalmologist. 16

Appendix C: Technical Support For assistance with the OS-8170 or any other PASCO products, contact PASCO as follows: Address: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95747-7100 Phone: (916) 786-3800 FAX: (916) 786-3292 Web: www.pasco.com Email: techsupp@pasco.com Appendix D: Copyright and Warranty Information Copyright Notice The PASCO scientific 012-08489A Manual is copyrighted and all rights reserved. However, permission is granted to non-profit educational institutions for reproduction of any part of the 012-08489A Manual, providing the reproductions are used only for their laboratories and are not sold for profit. Reproduction under any other circumstances, without the written consent of PASCO scientific, is prohibited. Limited Warranty PASCO scientific warrants the product to be free from defects in materials and workmanship for a period of one year from the date of shipment to the customer. PASCO will repair or replace, at its option, any part of the product which is deemed to be defective in material or workmanship. The warranty does not cover damage to the product caused by abuse or improper use. Determination of whether a product failure is the result of a manufacturing defect or improper use by the customer shall be made solely by PASCO scientific. Responsibility for the return of equipment for warranty repair belongs to the customer. Equipment must be properly packed to prevent damage and shipped postage or freight prepaid. (Damage caused by improper packing of the equipment for return shipment will not be covered by the warranty.) Shipping costs for returning the equipment after repair will be paid by PASCO scientific. 17