Polarization of light

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Darrell Norman
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1 Laboratory#8 Phys4480/5480 Dr. Cristian Bahrim Polarization of light Light is a transverse electromagnetic wave (EM) which travels due to an electric field and a magnetic field oscillating in phase and perpendicular to one another. Both fields also oscillate perpendicularly to the direction of motion, and therefore, the light is a transverse wave (see Figure 1). X Y The direction of propagation of an electromagnetic wave is given by the Poynting vector, r 1 S = E B µ Z Figure 1 An EM wave in vacuum. The electric and magnetic fields are traveling in the positive z_direction and oscillate perpendicularly to one another. where µ represents the magnetic characteristic of the material. The average value of S r is typically called the intensity of light. (1) I r = S (2) avg Two experiments are proposed for examining the transverse character of the light wave using different methods of polarization: (1) transmission of light through a polarizing sheet (with verification of Malus law) and (2) reflection of light by a dielectric surface (with identification of the Brewster angle). Due to the light wave s transverse character it is possible to re-orient the direction in which the electric field oscillates. This phenomenon is known as the polarization of light. Longitudinal waves (which are waves that oscillate parallel to the direction of propagation), like the sound wave, cannot be polarized. 1

2 Theoretical model Matter is a collection of atoms and molecules. The distribution of the electronic charge in molecules forms typically an ellipsoid of rotation. The electronic cloud has a positive end (where the charge of the nuclei dominates) and a negative end (where there is a concentration of the electronic charge). This separation of charges is indicated in figure 2. Unless the incident light matches one of the characteristic frequencies of the atoms, the electronic cloud will simply oscillate with respect to the positive nucleus at the same frequency as the incident light, oesonantly. At this point the energy of the light has been converted into the vibrational energy of the electronic cloud. Next, the oscillatory electric dipoles will induce another electric field which will propagate forward. In this way each atom acts as an antenna and passes the information about the incident light to the next atom. Figure 2 shows the interaction between the electric field component of light and the electric dipole moment of the atoms or molecules of a material. This process represents the propagation of light through a transparent material. E = Eo cos ( kz ωt) E = Eo cos ( kz ωt) p = po cos ( kz ωt) Figure 2 Propagation of light through a transparent dielectric. Electric dipoles oscillating under an incident E = Eo cos( kz ωt) field. The oscillation creates an oscillating dipole moment, p = po cos( kz ωt), which in turn induces an identical E = Eo cos kz ωt. electric field ( ) The light wave can be polarized linearly r E = ie ˆ ± ˆjE cos kz ωt, (3) ( ) ( ) ox Circularly, r E = Eo iˆcos kz ωt ± ˆj sin kz ωt oy [ ( ) ( )], (4) or even elliptically, which has a more complex formula than in equation (4). 2

3 a. Polarization by transmission A linear polarizer is a material with all the molecules lined up in a single file row. When an electric field is incident on it, only the component of the electric field parallel with the row of atoms will cause the atoms to oscillate. Therefore the electric field component is selectively absorbed (a phenomenon called dichroism ). The oscillations of these molecules re-radiate the light in the forward direction as explained above. Since all components of light contribute to its intensity eliminating all but one component will lessen the intensity given in equation (2). When unpolarized light travels through a polarizer, only 50% passes as shown figure 3. When linearly polarized light passes through a second polarizer (often called analyzer ) even less light is transmitted. Figure 3 Unpolarized light incident on two polarizers. The electric field of the incident light as well of the light transmitted through the first polarizer and the second polarizer (analyzer) are shown. Malus s law relates the intensity of the polarized light transmitted through a linear polarizer to the angle,θ, between the transmission axis of the linear polarizer and the polarization axis of the incident light, as seen in figure 3: 2 ( θ ) I( 0) cos θ I = (5) where I ( θ ) is the intensity of a linearly polarized light (3) after it passes through the analyzer and I ( 0) is the intensity of the light incident on the analyzer. In order to investigate the wave nature of light, we set up an experiment based on the polarization of light by transmission with the verification of Malus s law. Experimental procedure You will measure the intensity of the polarized light transmitted through a second polarizer using a setup similar with the one shown in figure 3. We use PASCO equipment composed by two linear polarizers, a diode laser, a high sensitivity light sensor, an aperture bracket, an optics bench, a rotary motion sensor, a PASCO interface, and the DataStudio software with the appropriate settings for sensors. By rotating smoothly and steady the analyzer connected to the rotary motion sensor, you will compare the theoretical value of the intensity of the transmitted light given in (5) with the experimental signal. When the appropriate calibration of the theoretical curve to the experimental signal is done, an excellent agreement will be found. 3

4 b. Polarization by reflection It is also possible to polarize light by reflection on a dielectric surface. Reflection is a kind of back scattering that will occur whenever light experiences a discontinuity in the medium. The principle of polarization by reflection on a dielectric surface is shown in figure 4. We define the plane of incidence as being the one which contains the incident, reflected and transmitted rays. The angle of reflection is always equal to the angle of incidence no matter what the polarization of the light is. However, for light polarized parallel to the plane of incidence there is an incident angle where no light is reflected. This angle of incidence is called Brewster angle. This phenomenon can be understood by using the electric dipole oscillator model. Incident Ray Reflected Ray E 0 I θ I θ R θ E 0 R n I Lets consider an incident wave ( E 0 I Due to the polarization of the incident wave, the reflected wave ( wave ( E 0 T ) polarized parallel to the plane of incidence. E 0 R ) and the transmitted ) will also be polarized as shown in figure 4. An electric dipole cannot radiate energy parallel to the direction of its own axis of oscillation (along the dashed line in figure 4). Since the electric dipoles always oscillate perpendicularly to the electric field s direction of travel, it is inferred that if the angle between the transmitted ray and the reflected ray is 90 there will be no radiation emitted by the electric dipole back into the initial medium. This can be seen from figure 4 when θ + θ + 90 = 180. Because θ = θ (law of reflection) then I R θ = 90. (6) T θ I No light wave is reflected if E 0. The particular angle of incidence at which the 0 R = reflected component disappears is called Brewster angle θ B = θ I and is related to the relative index of refraction by the Brewster law: n T tan θb =. (7) n I θ T E 0 T Figure 4 The principle of polarization by reflection considering only the parallel component of an incident light beam. Equation (7) allows to find the index of refraction of a material by measuring θ B. At any angles other thanθ B, the reflected light is partially polarized n T T R 4

5 Experimental procedure This experiment uses PASCO equipment and the setup is shown in figure 5. The light sources are diode lasers of wavelength 532 nm (green) or 650 nm (red). The laser beam is polarized by using two polarizers having their transmission axis oriented at 45 degrees to one another. Next, the polarized laser beam is reflected by the surface of a glass prism (flint or crown). The reflected light passes through a polarizer and next is detected by a high sensitivity light sensor. The rotary motion sensor measures the angle of incidence. The data is transferred to the DataStudio program through a PASCO interface. Figure 5 A top view of the setup. The setup lets us to measure the intensity of the laser beam parallel and perpendicular to the surface of a dielectric material. At each angle of incidence you should report three values: the intensity of the beam without a polarizer, the intensities of the polarized light parallel and perpendicular to the plane of incidence (shown in figure 4). By analyzing the data for the parallel component with respect to the plane of incidence we can find the Brewster angle (where the parallel component vanishes). The relationship between the Brewster angle and the index of refraction of the dielectric is given by equation (7). Record the times for various angular positions for the parallel and the perpendicular components of the reflected light by a dielectric surface and for the total reflected light. The times recorded correspond to a steady state of the setup at a fixed angular position and for the maximum intensity. 5

6 Procedure: I. Data acquisition: You need to consider two steps: 1. << Find the approximate location of the Brewster angle >>: Start at 90 degrees and rotate the light sensor arm clockwise (or counterclockwise) in steps of 5 degrees until you reach 45 degrees. You will collect 10 (ten) sets of 3 points each, which should contain the times for measurements of the total, the parallel and the perpendicular components. Once you finish this measurement you need to Export the data file from DataStudio. For each measurement, you need to collect data in your DataStudio file over an interval of 15 seconds. During this time you don t turn on the flashlight, orient the screen of the laptop toward the detector, push or skate the optics table. If one of these conditions are not carefully preserved then you need to restart counting the time again for another 15 seconds. Information about the files Exported from DataStudio is contained in Step II.1 below. The file with the times at various angular positions for the total, parallel and perpendicular component of the reflected light by a dielectric surface should be called input-brewster-team#...txt. While you are processing the data recorded as indicated below, please DON T stop DataStudio because you will RUIN your work, and have to start over the measurement from 90 degrees. For each chosen angle you need to type in the template file called input- Brewster-team#.txt the times for the Total intensity, and the Parallel and Perpendicular components. Do this recording as soon as your setup has the light sensor arm fixed at certain angle for which you can read a maximum value for the light intensity. DON T wait until you collect all 10 data points, but introduce the numbers in the input-brewster-team#.txt file one by one before you move to the next angle. Save the file as input-brewster-team#-zoom-out.txt. 2. << Precise determination of the Brewster angle >>: For this purpose move back the light sensor arm at 66 degrees (if you are using the flint glass) or 64 degrees( if you are using the crown glass). Next, go from 66 degrees down to 48 degrees for flint (or 64 degrees to 46 degrees for crown) in steps of 1 degree. You will collect about 19 points. Once you finish this set of measurements you need to Export the data file as indicated in Step II.1 below. While you are doing the saving of data, DON T stop DataStudio because you will RUIN your work and you have to restart the measurement. Be aware that you use the same filenames a.txt and i.txt as in the Step I.1 from above, so the information you have collected previously will be overwritten (but not lost!) because the first ten points from the zoom out are still in the new *.TXT files. Save the file as input-brewster-team#-zoom-in.txt. 6

7 II. Data processing: You need to access the Brewster-Optics.exe available on the jump drive (ask for it): 1. You need to export the data from your DataStudio file: use the name << i >> for Run#1 under Light Intensity and << a >> for Run#1 under angle. For exporting the data you have to use the Export Data feature. The two files should be saved on the Desktop, and next, should be copied on the jump drive for using the executable file. 2. You need to run the program called Brewster-Optics.exe (click on it). Open the file input-brewster-team#-zoom-out.txt. Once you did that, the program Brewster-Optics.exe processes the data and reports quickly (within one second!) the message *.txt file has created. The name of this file will reflect the header in the file called input-brewster-team#-zoom-in.txt. E.g. D_zoom_out_flint_red_5sec_ txt for using the 10 points from 90deg. to 45 deg., flint glass, red laser (650 nm), 5 seconds interval for intensities, and the current date. Similarly, you have to use the Zoom in version from the file called input- Brewster-team#-zoom-in.txt and to generate an output file. The output file generated with the Brewster-Optics.exe program will contain the intensities for total, parallel and perpendicular components of the reflected light by the surface for the times measured. III. Data analysis: 1. Open the files generated by the Brewster-Optics.exe program (for example, D_zoom_out_flint_red_5sec_ txt ) and copy all the information in the Zoom_out (sheet 1) and Zoom_in (sheet 2) spreadsheets of the Excel file called Template.xls. This file is ready to process your data and do the graphs for Zoom out (on sheet 1 Zoom_out ) and for Zoom in (on sheet 2 Zoom in ). 2. Check on the sheet no. 3 called Parabolic_Fit the result of a parabolic fit done with the LINEST command (provided by Excel). You will see two Brewster angle values for the Parallel and the Perpendicular components. 3. Compare youesults with the result found by the team that uses the same glass, but the other laser (for example, if you have used Red laser incident on flint glass, look for the result obtained with a Green laser incident on flint glass). The best case scenario is when you will see that the Brewster angle for the Green laser (of smaller wavelength) is larger than for the Red laser (of longer wavelength). θ ( λ = nm) = θ ( λ = nm) = B 532 B You can calculate your index of refraction using equation (7) taken n I (air) = 1: Report: n = 7

8 SETUP POLARIZATION OF LIGHT (a) by TRANSMISSION THROUGH A POLAROID. (b) by REFLECTION ON A DIELECTRIC SURFACE. 8

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