PASCO Specialty & Mfg. OS8170A User's Manual
Contents
1. 1 3 mange deg 08 10 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 E L 10 T5 20 25 30 35 40 45 50 55 60 65 TU 75 8D Incident Angler deg PASC C a Brewster s Angle Accessory Model No OS 8170A Ill 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 acrylic plastic Sample Data Incident Angle vs Refracted Angle 1 00 i 0 80 mt Slope 150 4 0 60 amp 040 0 20 030 0 20 0 30 0 40 0 50 0 50 sin refracted In DataStudio create the following equations a refracted angle2Oi 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 Acknowledgements The Brewster s Angle experiment was developed using original ideas from P J Ouseph Professor of Physics at University of Louisville KY from an American Journal of Physics article titled Polarization of Light by Reflection and the Brewster Angle Vol 69 page 1166 2001 by P J O2. PRE LA LLLA H a N NU O gt Quadratic Fit 0 00127 3 0E 5 in T Root MSE 0 00514 E o ux E L3 zZ E o 0 142 0 0035 a m Squared Error 2 54E 5 ERAN LLLA ALL SJ lx li Normalized reflected light N E intensity perpendicular Co Angle Editable deg s PASC OG Model No OS 8170A Brewster s Angle Accessory The Curve Fit dialog box for the green laser shows the coefficients of the quadratic formula of the curve fit Quadratic Fit na i x Remove Acce Quadratic Fit Ax Bx C Automatic Manual Input Norm Il s Angle Editable Data Fitwith first selected data point at X D CurveFit ly Display standard deviations Properties Coefficient Value Initial Guess Display A 0 00127 3 0E 5 1 00 iv B 0142 00035 10 v e 38940098 0p v Mean Squared Error 2 64E 5 Root MSE 0 00514 Curve Fit dialog box for green laser Questions 1 From the curve fit how do you determine the minimum of the function To find the minimum set dy dx equal to zero ERE for the quadratic formula BS SIM HE CI OC RI Ald E oe Be dy zx 2Ax B 2 0 00127 0 142 0 Solving for x gives 55 9 omi To estimate the error use the cursor in the Graph display to select a different set of data points see the Graph E li z E z The different set of data points gives an angle of 56 1 The er
3. blurred vision or altered color perception Less severe injuries may not show up immediately and are more hazardous when they occur repetitively ee PASCOR Model No OS 8170A Brewster s Angle Accessory 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 PASCCE 25 Brewster s Angle Accessory Model No OS 8170A Technical Support For assistance with the OS 8170A Brewster s Angle Accessory 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 Copyright and Warranty Information Copyright Notice The PASCO scientific 012 08489B Brewster s Angle Accessory Manual is copyrighted and all rights reserved However permission is granted to non profit educational institutions for reproduction of any part of the 012 08489B Brewster s Angle Accessory 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
4. to use PASPORT sensors PASCO s Brewster s Angle Accessory is designed to be used with the Educational Spectrophotometer System OS 8539 In addition to the Educational Spectrophotometer System the experiments need the Basic Optics Diode Laser OS 8525A and one or more of each of the following Optics Bench OS 8541 Aperture Bracket OS 8534A and High Sensitivity Light Sensor A PASCO computer interface and PASCO data acquisition software are also required for the experiments NOTE A folder for the Brewster s Angle experiment is available as a ZIP file to download from the PASCO web site Go to the page that shows the EX 9919A or EX 9965A Brewster s Angle Experiment and click Download The folder contains DataStudio setup files and sample data files for ScienceWorkshop and PASPORT sensors and Microsoft Word DOC files for the experiment procedure PASCOR Model No OS 8170A Brewster s Angle Accessory Introduction The Brewster s Angle Accessory OS 8170A is used in optics for studying the polarization of reflected light and for determining Brewster s angle The accessory consists of a lens holder with two polarizers a rotating platform Pivot Plate Assembly with a semi circular D lens an analyzing polarizer and a beam splitter High Sensitivity Light Sensor PEIUS DIaeKel lc N a Analyzing Polarizer We Ae D Lens on Lens Mount Beam Lens Holder with Polarizers oplitter Colli
5. Instruction Manual 012 08489B Brewster s Angle Accessory Model No OS 8170A ll oy Ul e 0 10101 Foothills Blvd o Roseville CA 95747 7100 zm Phone 916 786 3800 FAX 916 786 8905 www pasco com Brewster s Angle Accessory Model No OS 8170A Table of Contents e Ue age a MERE TT 3 PTI CUS OVA eree TREES 5 TUNG aln e A E E A E A EE E E 5 n 0 om TOS TUO eae E E E E E E A 6 e e EL o E E IRR Tm 10 FOC CCI Casta soca tases aE EEE EE E E E E AEE 11 ARNAN SIS e EE E E E EE 13 IBI OAS NN A sd coca E E 14 Teacher s Guide Discovering Brewster s Angle 15 POR INVEST m 20 l Intensity of Reflected Light without a polarizer Il Intensity of Transmitted Light Il Snell s Law ACKDoWIedgemerlls uude secu tu co pee iesia qudm cose o natus detecta EEEN 22 Appendix A Creating Equations in DataStudio 23 Appendix B Laser Safety Instructions eeeeseeeeeeeeeesss 24 Tecnica SO OO iN ERR E E m ET 26 Copyright and Warranty Information esses 26 2 E 2 169 Model No OS 8170A Brewster s Angle Accessory Brewster s Angle Accessory Model No OS 8170A Equipment Analyzing Polarizer Beam Splitter p i p Lens Holder Polarizers P inc e amp d w Semi circular Acrylic D
6. Lens 9 lens Mount Pivot Plate Assembly Included Equipment 1 Polarizer Assembly 1 lens holder and 2 round polarizers 2 Analyzing Polarizer 1 Lens Mount 1 and Pivot Plate Assembly 1 003 08332 3 Beam Splitter 1 OS 8171 4 Semi circular Acrylic Lens 1 D Lens 003 08545 Additional Equipment Required Option 1 Model Number Educational Spectrophotometer Accessory OS 8537 Spectrophotometer Base EE High Sensitivity Light Sensor 2 PS 2176 or Cl 6604 Rotary Motion Sensor 1 PS 2120 or Cl 6538 Aperture Bracket 2 OS 8534A Optics Bench 60 cm 2 OS 8541 Basic Optics Diode Laser 1 OS 8525A OR see next page The Accessory includes unlisted items that are not used for the experiments PASCCE 3 Brewster s Angle Accessory Model No OS 8170A Educational Spectrophotometer System OS 8539 Educational Spectrophotometer Accessory OS 8537 Optics Bench 60 cm OS 8541 High Sensitivity Light Sensor Cl 6604 Additional Equipment Required Option 2 Model Number High Sensitivity Light Sensor See PASCO web site or catalog See PASCO web site or catalog PASCO data acquisition software See PASCO web site or catalog WWW pasco com Complete packages of all the equipment and sensors are available from PASCO Choose the EX 9919A Brewster s Angle Experiment ScienceWorkshop if you want to use Science Workshop sensors or choose the EX 9965A Brewster s Angle Experiment PASPORT if you want
7. Plate almost all the way down and then tighten the wing nut under the Spectrophometer Base 4 Place the Lens Mount on the Pivot Plate so that the hole in the bottom of the lens mount matches the post on the pivot plate 5 The Lens Mount has two vertical index marks For reflected light use the mark that 1s on the side with the higher step Line up the index mark with the zero degree angle on the edge of the Pivot Plate that 1s closest to the laser Note The other mark can be used for transmission studies in a Snell s Law experiment PASCCE 7 Brewster s Angle Accessory Model No OS 8170A Align the Laser Beam 1 Put a Laser Diode on the end of the bench opposite to the Spectrophotometer Base Connect the laser s power supply to a grounded electrical outlet and plug the power cord into the laser cotimating Turn on the laser the ON OFF switch is on the back of the Slits laser Laser N WARNING Do not look directly into the beam of the laser light source or reflected light from the laser light source 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 2 Set the Spectrophotometer Arm so that 180 degr
8. Workshop sensor set the GAIN switch on the top of the sensor to 100 2 In the data acquisition program click Start and rotate the first round polarizer nearest to the laser to allow the light level to be as high as possible without exceeding 95 on the Digits display of the Reflected Light Intensity measured by the sensor on the Spectrophotometer Arm and the Reference Light Intensity measured by the sensor on the second optics bench Click Stop PASC Che Model No OS 8170A Brewster s Angle Accessory Note If the Reflected Light Intensity is as high as possible without exceeding 95 but the Reference Light Intensity is above 95 try one of the following to reduce the Reference Light Intensity e Slightly adjust the second optics bench from side to side so that only part of the laser beam enters through slit 5 of the Aperture Disk Rotate the Aperture Disk in front of the second light sensor so that the laser beam enters slit 4 instead of slit 5 Zero the Rotary Motion Sensor 1 To zero the Rotary Motion Sensor first remove the D Lens Adjust the Spectrophotometer Arm if needed so that the laser beam is centered on slit 5 on the Aperture Bracket disk The 180 mark on the Spectrophotometer Degree Plate should be near the index line 2 Click Start and slowly move the arm back and forth so that the slit moves through the width of the laser beam Stop at the position where the Digits display sh
9. at surface of the D lens Thus when the incident angle is such that the reflected light is 100 polarized parallel to the flat surface of the D lens Brewster s Angle the horizontal component will be zero During the experiment both the horizontal and vertical components of the reflected light are measured so the horizontal component of interest can be normalized by dividing by the sum of the two components This gives a percentage of the total reflected light that is horizontally perpendicularly polarized Each measurement must also be divided by the reference light intensity to account for momentary changes in intensity of the laser light source NOTE The laser light is already polarized but the round polarizer set at 45 solves the problem To make the relative intensities of the p parallel and s perpendicular components the same the light is polarized at 45 Sensor Setup 1 Connect the PASCO interface to the computer and start the data acquisition software 2 If you are using DataStudio open the DataStudio setup file titled Brewsters PASPORT ds for PASPORT or Brewsters ds for ScienceWorkshop 3 Plug the Rotary Motion Sensor and the two High Sensitivity Light Sensors into the interface Set the Light Sensor Range 10 1 To get full use of the Light Sensor range set the light sensor range for a PASPORT sensor press the light bulb button on the side of the sensor and for a Science
10. crements of 5 degrees 5 Under the Experiment pull down menu in DataStudio click New Empty Data Table Enter the data and make a graph of Light Intensity versus Angle 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 ll 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 Arrange the curved part of the lens so it is towards the laser Set the Pivot Plates 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 20 1 VrYee Model No OS 8170A Brewster s Angle Accessory 4 In DataStudio set up the displays as shown below a Light Intensity ws Angle E E a So El e Date ij 130 o xi amp Zll Ea 7 Sef 39 Data x Or A Arm Angle m x 100 Data x a
11. curs when the reflected ray and the refracted ray are 90 degrees apart According to Snell s Law njsin0 m sin 1 PASCCE 5 Brewster s Angle Accessory Model No OS 8170A where n is the index of refraction of the medium and 0 is the angle of the ray from the normal Normal Incident Ray Reflected Ray When the angle of the incident ray is equal to Brewster s angle Op n sinOp nsin 0 2 and since 9p 0 90 sin sin 90 95 Refracted Ray sin90 cos 0 p cos90 sin Op cos Op Figure 2 Polarization of Unpolarized light Substituting for sinO in Equation 2 gives n4sin0 p nycos Op n Therefore 2 _ tan 0 3 n 1 Setup Instructions p Index E line Line up the 180 Assemble the Spectrophotometer Base degree mark g 1 Attach the Spectrophotometer Base at one end of an Optics Bench 2 Attach the Spectrophotometer Degree a Plate to the Base but align the Degree Plate backwards that is line up the 180 degree mark on the Degree Plate with the index line on the Base Spectrophotometer 2 Base 3 Attach the Spectrophotometer Arm to Hos the Degree Plate IE 4p For instructions on setting up the gross dd Pp Spectrophotometer parts see the 5 Educational Spectrophotometer Manual Youcan downloada PDE file Figure 3 Assemble the Spectrophotometer Base of the manual from the PASCO web Bega TAE ANA site Go to the page t
12. e that the laser beam is still aligned with the first High Sensitivity Light Sensor 6 Snap the round Polarizers into both sides of the Lens Holder and mount the Lens Holder on the bench between the Collimating Slits and the Beam Splitter The Polarizers help control laser intensity een aera Z Adjustment Screws 7 Rotate the second polarizer farthest from the laser to 45 Figure 8 Adjust the Beam degrees the indicator is the bottom lip on the lens holder Splitter as needed 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 being measured better data will be obtained 1f the incident light level is kept above 50 co PASC C Brewster s Angle Accessory Model No OS 8170A 8 The square Analyzing Polarizer see Figure 9 has its transmission axis marked Position the Analyzing Polarizer with its label on top and with its axis horizontal NOTE When the Analyzing Polarizer is horizontal the light passing through the polarizer is the horizontal component perpendicular to the D lens surface of the P ith Spectrophotometer Arm light reflected from the flat surface of the D Spectrophotometer Degree Plate lens In this orientation the Analyzing Figure 9 Analyzing Polarizer and D Lens Polarizer is blocking the light that is polarized parallel to the fl
13. ees on the Degree Plate is next to the index mark Set the Aperture Bracket disk to slit 5 Use the x y adjustment knobs on the back of the laser to aim the laser beam at the center of Aperture Bracket slit 5 Figure 5 Laser and Collimating Slits on bench 3 Place the Collimating Slits on the optics bench and adjust the slit position on the Collimating Slits so that the laser beam passes through slit 5 and also still shines on slit 5 on the Aperture Bracket disk see Figure 5 4 Adjust the Brewster s Lens Mount so that the index line on the higher step of the Lens Mount is aligned with the zero mark on the Pivot Plate 5 Place the D Lens on the lower step of the Lens Mount with the flat side of the lens against the edge of the higher step If the laser beam is not still centered on slit 5 of the Aperture Bracket adjust the D Lens side to side until the laser beam shines on slit 5 Make sure the D Lens is firmly against the step t Beam Splitter 6 Mount he Beam Splitter on the bench near the center of the bench Check that the transmitted laser beam still illuminates the 5 slit on the Aperture Bracket on the Spectrophotometer Arm If necessary loosen the adjustment screws on the Beam Splitter holder and move the holder to align the laser beam with slit 5 on the Aperture Bracket disk Figure 6 Mount the Beam Splitter PASC Che Model No OS 8170A Brewster s Angle Accessory Controlling the Laser I
14. eflected light intensity is approaching the minimum record data press Keep every one degree When you reach 50 change the angle by five degrees each time until you reach about 25 13 Click Stop to end data recording Entering the Data It is helpful to enter data in the table as it is collected so you can see the progression of the data towards the minimum There will be two sets of data for each angle The first set 1s for the perpendicular reflected light when the Analyzing Polarizer s axis was horizontal and the second set 1s for the parallel reflected light when the Analyzing Polarizer s axis was vertical For each angle read the Reflected Light Intensity and the Reference Light Intensity and enter the values into the Data Entry Table B Data Entry Table i El Ea ae Z Data x m MAngie Editable Polarized Light sk Polarized Light 4 Reference Light deg 96 of scale 96 of scale 96 of scale 96 of scale 1 For the first set type the value of the Reflected Light Intensity into the Polarized Light column Press Enter and then type the Reference Light Intensity into the Reference column Press Enter after typing the value 2 For the second set type the value of the Reflected Light Intensity into the II Polarized Light column Press Enter and then type the Reference Light Intensity into the II Reference column Press Enter afte
15. hat shows the OS 8539 and click the Manual tab PASC O Model No OS 8170A Brewster s Angle Accessory 4 Mount a High Sensitivity Light Sensor to an Aperture Bracket and attach the Aperture Bracket Light Sensorto ii the Spectrophotometer Arm md Degree Plate 5 Mount the Rotary Motion Sensor to the upper holes on the hinge of the Spectrophotometer Base Mount the Spindle on the shaft of the Rotary Motion Sensor so that the bigger diameter of the spindle 1s against the edge of the Spectrophotometer Degree Plate see Figure 4 otary Motion Sensor 6 Connect a patch cord from an electrical ground to a bare EV piece of metal on the Spectrophotometer Base as Figure 4 Mount the Rotary instructed by your teacher Motion Sensor to the Base Attach the Pivot Plate and Lens Mount 1 Screw the Pivot Plate into the threaded hole in the center of the Spectrophotometer Degree Plate 2 Screw a wing nut onto the threaded post of the Pivot Plate that extends below the Spectrophotometer Base 3 Turn the Pivot Plate so that the index mark at the edge of the plate above the N in the word ANGLE is aligned with the zero degree mark on the Spectrophotometer Degree Plate Note Make sure that the Pivot Plate 1s not screwed down too tightly against the Degree Plate The Spectrophotometer Arm should be able to rotate freely and the Pivot Plate should remain stationary as the Spectrophotometer Arm is moved Screw the Pivot
16. hich direction is the axis of polarization of the light reflected from the D Lens The axis of polarization of the light reflected off the D Lens is parallel to the surface which in this case 1s vertical 7 How is the index of refraction affected by a change in the wavelength of the laser In general the index of refraction increases as the frequency increases wavelength decreases PASC Che Model No OS 8170A Brewster s Angle Accessory Sample Data Blue Laser The following Graph display shows polarized light intensity versus angle for blue laser light having a wavelength of 405 nm M Blue Laser a i 7 Fit e Al 4 x e Data x Ej co ATAT NL LA aU aN DE ua Fit 0 00154 2 4E 5 B 0 188 x 0 0028 538 0 080 Y Ti Squared Error 3 04E 6 Root MSE 0 00174 TA aN as aun ee TO OT 35 40 45 CH 8 amp 0 65 70 75 Angle Editable deg Morm Il Norm Norm Il The Curve Fit dialog box for the blue laser shows the coefficients of the quadratic formula of the curve fit uereiFk SSC amp New x Remove v Acce To find the minimum set dy dx equal Quadratic Fi Ei n to zero for the quadratic formula Automate Manuel Input NamlvsAnge Edtsble Dets cy 2Ax B 2 0 00164 0 188 0 dain ee Curve Fit Fit with first selected data point at D Solving for X gives 51 39 Di
17. mating gt arf C M Pivot Plate Assembly Spectrophotometer Degree Plate gt ws e E Interface Rotary Motion r ILE Sensor Laser Aperture High AM Bracket Sensitivity RE Light Sensor E Optics Bench Items included in the Brewster s Angle Accessory Figure 1 Brewster s Angle Accessory Setup for 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 semi circular D lens The reflected light passes through an analyzing polarizer and is detected by a Light Sensor The angle of incidence is measured by a Rotary Motion Sensor mounted on the Spectrophotometer Base 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 1s Brewster s angle which is used to calculate the refraction index of acrylic Theory When unpolarized light reflects off a nonconducting surface it is partially polarized parallel to the plane of the reflective surface There 1s a specific angle called Brewster s angle at which the light is 100 polarized This oc
18. ntensity 1 Place the second optics bench at right angles to the first optics bench at the spot where the Beam Splitter is mounted 2 Mount the second High Sensitivity Light Sensor on an Aperture Bracket and attach the Aperture Bracket to a Lens Holder Set the disk on the Aperture Bracket to slit 5 3 Mount the Light Sensor Aperture Bracket at the far end of the second optics bench see Figure 1 Connect a patch cord between an electrical ground and a piece of bare metal on the Aperture Bracket NOTE The second High Sensitivity Light Sensor is used to compensate for the variability of the incident laser beam intensity see Figure 7 The second light sensor on the optics bench measures the relative incident light intensity from the Beam Splitter while the light sensor on the Spectrophotometer Arm simultaneously measures the reflected light intensity from the D Lens through the Analyzing Polarizer ez Light Intensity of scale max I2 Any fluctuations in intensity can be normalized by dividing the reflected light intensity by the relative incident light intensity Figure 7 Variability of Green Laser 4 Adjust the position of the second optics bench as Reflected needed until the reflected laser beam from the Beam p TRI Splitter travels to slit 5 on the Aperture Bracket disk in front of the second Light Sensor 5 If you need to re adjust the Beam Splitter make sur
19. 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 Written by Ann Hanks 26 E86 Z7 1Iee
20. ows maximum intensity 3 Click Stop and do not move the arm until you use the program to take the actual data run This insures that the zero for the Rotary Motion Sensor 1s at the center of the laser beam 4 Replace the D Lens on the lens mount against the step centering it so the laser beam still shines on slit 5 Note about angle measurement The angle of reflection from the D Lens is calculated by dividing the actual angle measured by the Rotary Motion Sensor by two The best procedure is to set the index line on the high side of the Lens Mount to a particular angle such as 85 and then move the Spectrophotometer Arm so that the angle shown on the Digits display is the same as the angle of the Lens Mount Note that to get the laser beam exactly on the 5 slit in front of the Light Sensor you must make fine adjustments while watching the Digits display for the maximum light intensity You can adjust either the Lens Mount or the Spectrophotometer Arm until the intensity is maximized Procedure Taking Measurements 1 Lighting Turn off the room lights when making a measurement A small light might be useful for seeing the computer keyboard and for putting the Analyzing Polarizer on and off 2 Click Start The Start button in the toolbar will change to Keep Li Do not click the red square Stop on the Keep button until all of the procedure steps are completed PASC C 3 Remove
21. r typing the value Repeat the Procedure Repeat the procedure for a different wavelength color laser Analysis The DataStudio file that is set up for Brewster s Angle has several built in calculations that use the perpendicular reflected light intensity the parallel reflected light intensity the reference light intensity and the angle of reflection The file also has Table displays for recorded data and entered data and a Graph display for determining Brewster s Angle PASC C s Brewster s Angle Accessory Model No OS 8170A Questions 14 1 To determine Brewster s Angle use the Graph display Norm versus Angle In the Graph select a group of data points on both sides of the apparent minimum 2 Click the Fit menu in the toolbar of the Graph Quadratic Fit S l M A 0 00127 3 0E 5 and select Quadratic Fit Note Double click the legend box B g 044200035 Quadratic Fit legend box to open the Curve Fit Mean Squared Error 2 64E 5 Root MSE 0 00514 dialog box Make sure that Fit with first selected data point at X 0 is NOT selected Curve Fit Quadratic Fit i X Remove Quadratic Fit M n Ax Bx C Automatic Manual Input Norm vs Angle Editable Data Fit with first selected data point at 0 Iv Display standard deviations Properties Coefficient Value Initial Guess Display 1 From the curve fit how do you dete
22. rmine the minimum of the function 2 Use Brewster s Angle to calculate the index of refraction of the acrylic D Lens using n Equation 3 tan 0p7 _2 What value should you use for n n 1 3 Would Brewster s Angle be larger or smaller for light in air reflecting off water 4 Would Brewster s Angle be larger or smaller for light in water reflecting from the D Lens that 1s 1f the D Lens were submerged in water 5 How do polarized sunglasses reduce glare Which direction is the axis of polarization in a pair of polarized glasses How would you check this 6 Which direction is the axis of polarization of the light reflected from the D Lens 7 How is the index of refraction affected by a change in the wavelength of the laser PASC Che Model No OS 8170A Brewster s Angle Accessory Teacher s Guide Discovering Brewster s Angle Sample Data The Table display Green Data Collection shows sample data of Angle Reflected Light Intensity and Reference Light Intensity for a green 532 nanometer diode laser A Green Data Collection m OX Ej Ea 2 2 2 amp Data x m Run 1 Run 1 Run 1 deg 96 of scale max of scale max 64 5030 5 0813 73 0380 63 7140 1 5787 73 5902 63 7140 46118 73 4854 53 5050 0 0664 57 0954 53 5050 2 4929 67 6626 EMEN S 5 U 54 3930 2 5502 66 5876 PASC C m Brewster s Angle Accessory Model No OS 8170A The Table display Da
23. ror estimate 1s 55 9 0 2 2 Use Brewster s Angle to calculate the index of refraction of the acrylic D Lens using n Equation 3 tan 0p7 _2 What value should you use for n n 1 The value of n 1 00 for air n n tanO 1 00 tan 55 9 1 481 0 01 for the green laser wavelength 532 nm n n tanO 1 00 tan 57 3 1 56 0 01 for a blue diode laser wavelength 405 nm See the sample data at the end of this section PASC C i 18 Brewster s Angle Accessory Model No OS 8170A 3 Would Brewster s Angle be larger or smaller for light in air reflecting off water The Brewster s Angle would be smaller for light in air reflecting off water 485 1 33 m tan n 7 9p 53 4 Would Brewster s Angle be larger or smaller for light in water reflecting from the D Lens that 1s 1f the D Lens were submerged in water The Brewster s Angle would be smaller for light in water reflecting from the D Lens 5 How do polarized sunglasses reduce glare Which direction 1s the axis of polarization in a pair of polarized glasses How would you check this Glare is polarized reflected light Since glare is often reflected off horizontal surfaces such as water the sunglasses are polarized vertically to extinguish the horizontally polarized reflected light To check this you could text the sunglasses with the Analyzing Polarizer since it has a known axis of polarization 6 W
24. see http www safetymanual com or www laserinstitute org Safety Reminders e Never look directly into the laser or at any reflection from the laser at eye level 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 eNever 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 elf you are uncomfortable or unsure about working around lasers wear protective laser goggles or spectacles 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 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
25. splay standard deviations Properties Coefficient Value Initial Guess Display A 0 00164 2 4E 5 1 00 v 0 188 0 0028 100 v E 5 38 0 080 00 jw Mean Squared Error 3 04E 5 Root MSE 0 00174 Curve Fit dialog box for blue laser PASC C Brewster s Angle Accessory Model No OS 8170A Further Investigation I Intensity of reflected light without polarizer Note This experiment uses the same setup except the Analyzing Polarizer is removed and you do not need the second optics bench aperture bracket and High Sensitivity Light Sensor 1 Reflect the laser beam off the outside plane side of the D 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 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 on the Spectrophotometer Arm through the reflected laser beam The result 1s an intensity peak Do not stop recording data Use a Smart Cursor to measure the angle at maximum intensity and the magnitude of the maximum intensity It 1s 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 for angles in in
26. t is helpful to enter data in the table as it is collected so you can see the progression of data towards the minimum When the polarizer is horizontal the light passing through the polarizer is polarized perpendicular to the surface of the D Lens This is the polarized light that is a minimum at Brewster s Angle 8 Rotate the square Analyzing Polarizer so its axis is vertical and set it on the Spectrophotometer Arm just in front of the Aperture Bracket 9 Press Keep to record the Angle the Reflected Light Intensity and the Reference Light Intensity When the polarizer is vertical the light passing through the polarizer is polarized parallel to the surface of the D Lens This is the polarized light that is a maximum at Brewster s Angle Both the horizontal and vertical components are measured so the perpendicularly polarized light can be normalized by dividing by the sum of the two components 10 Remove the Analyzing Polarizer and set up for the next angle Rotate the Lens Mount so the index mark lines up with 80 and move the Spectrophotometer Arm so that the angle in the PASC Che Model No OS 8170A Brewster s Angle Accessory Digits display is the same or close to it Adjust the Spectrophotometer Arm so the Digits display of Reflected Light Intensity is a maximum 11 Repeat steps 6 through 9 12 Continue to repeat the procedure reducing the angle of the Lens Mount by five degrees until you reach 65 When the r
27. ta Entry shows sample data entered into the table and calculated values for Norm and Norm ll I Data Entry EIE l Ej Ea 7 3 e Data x mi E ea o 09 S aas 09 o d 4E one mem nan sss ar oom o oom mus nes 0 2mm 5mm o 9 wo casos nen noa ome so 0 o mo ow m nem ones ose se om oss m nn mas ce mmo or 093 mss nan nme 0 omm o m 05s om 60 762 71 2533 70 3818 0 2075 3 5018 0 055 0 045 seoa omamr seexs oos saa os omr os owe owes 003 2945 oom 090 56 337 67 8027 67 3425 0 0498 2 9807 0 016 0 984 54333 J rome 6650 say 2002 000 O00 sss emm wmm 2m o mem o mr o or sw over mens 00m x S oso sem sasrsr anm zaa ooo oso e 60000 serrr ame 216 SO eno 0 9 67 5813 67 2832 1 8138 0 173 0 827 40 527 67 9849 67 9635 0 5900 1 4931 0 283 0 717 wem vm wams ommo o me se oet 66 9200 66 8478 The Graph display Green Laser shows normalized reflected light intensity for parallel and perpendicular polarized light versus angle a Green Laser z Fit e Al x e Data x HAH Vo Normalized reflected light intensity parallel AU T
28. ter any experiment constants optional Use the button to create an experiment constant Click New then enter the units Example In the Data Properties dialog type Angle in the name box and degrees in the units box name value and units for the constant Click the Accept button Go back to the Variables menu and select experiment constant Click OK 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 PASCCE 23 Brewster s Angle Accessory Model No OS 8170A 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
29. the Analyzing Polarizer from the Pivot Brewster s Angle Accessory Model No OS 8170A Spectrophotometer Arm Turn the Lens Mount so that the e index mark on the high step is at 85 on the Pivot Plate measured from the zero mark closest to the Beam Splitter 4 Rotate the Spectrophotometer Arm to about 85 as shown on the Digits display of the Angle and while watching the Digits display of the Reflected Light Intensity adjust the angle of the arm so that the laser beam reflected by the D Lens shines on the 5 slit on the Aperture Bracket The angle does not have to be exact just close enough that you get enough light 5 If the maximum light intensity drops below 50 adjust the round Polarizer nearest the laser to increase the light intensity above 50 Do not allow the reference intensity to exceed 95 This will make the measurement as precise as possible Since you are plotting the ratio of polarized intensity over total intensity changing the total intensity will not affect the ratio As you proceed it will eventually be impossible to make the maximum intensity above 50 6 Place the square Analyzing Polarizer with its axis horizontal just in front of the Aperture Bracket on the Spectrophotometer Arm Note The Analyzing Polarizer must sit flat on the arm 7 Press Keep to record the Angle the Reflected Light Intensity and the Reference Light Intensity See Entering the Data next page 12 I
30. useph Kevin Driver and John Conklin Modifications to the Brewster s Angle experiment were suggested by Cristian Bahrim and Wei Tai Hsu in an American Journal of Physics article titled Precise measurement of the reflective indices for dielectrics using an improved Brewster Angle method Vol 77 page 337 2009 x PASCOR Model No OS 8170A Brewster s Angle Accessory Appendix A Creating Equations in DataStudio Step 2 Type in and or build the equation Use the Scientific Statistical and Special 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 menus and the trigonometric functions to build the equation z Step 6 Save the Calculator Ix Click the Accept button equation Click X Remove Accept 4 the Accept Step 3 Define the qe button dependent variables Angle 180 abs x 15 2 Under Variables use Scientific Statistical Special DEG RAD Properties B Variables the down arrow to select B4 x Angular Position Ch 1 amp 2 Step 5 L abel the a variable or constant Experiment Constants units Click on the etc and click OK Properties button to open the Data Properties dialog and enter the name and Example For x select Data Measurement In the pop up select Angular Position and click OK Step 4 En
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