Activity P34: Polarization Verify Malus’ Law
What Do You Think?I f the transmitted light is at maximum intensity when the two polarizers are parallel, and minimum intensity when the two polarizers are perpendicular, what is the relationship of the intensity of transmitted light to the angle of the polarizers between 0 and 90 degrees? Take time to answer the ‘What Do You Think?’ question(s) in the Lab Report section. The purpose of this activity is to determine the relationship between the intensity of the transmitted light through two polarizers and the angle, Ø, of the axes of the two polarizers. BackgroundA polarizer only allows light that is vibrating in a particular plane to pass through it. This plane forms the “axis” of polarization. Unpolarized light vibrates in all planes perpendicular to the direction of propagation. If unpolarized light is incident upon an “ideal” polarizer, only half will be transmitted through the polarizer. Since in reality no polarizer is “ideal”, less than half the light will be transmitted.
However, if the second polarizer is oriented at an angle so that it is not perpendicular to the first polarizer, there will be some component of the electric field of the polarized light that lies in the same direction as the axis of the second polarizer, thus some light will be transmitted through the second polarizer (see the bottom figure). The component, E, of the polarized electric field, Eo, is found by: Since the intensity of the light varies as the square of the electric field, the light intensity transmitted through the second filter is given by: where Io is the intensity of the light passing through the first filter and Ø is the angle between the polarization axes of the two filters. Consider the two extreme cases illustrated by this equation: • If Ø is zero, the second polarizer is aligned with the first polarizer, and the value of cos2Ø is one. Thus the intensity transmitted by the second filter is equal to the light intensity that passes through the first filter. This case will allow maximum intensity to pass through. • If Ø is 90˚, the second polarizer is oriented perpendicular to the plane of polarization of the first filter, and the cos2(90˚) gives zero. Thus no light is transmitted through the second filter. This case will allow minimum intensity to pass through. • These results assume that the only absorption of light is due to polarizer effects. In fact most polarizing films are not clear and thus there is also some absorption of light due to the coloring of the Polaroid filters.
For You To DoUse the Light Sensor to measure the relative intensity of light that passes through two polarizers. Change the angle of the second polarizer relative to the first polarizer. Use the Rotary Motion Sensor to measure the angle of the second polarizer relative to the first polarizer. Use DataStudio or ScienceWorkshop to record and display the light intensity and the angle between the axes of the polarizers. Use the program’s built-in calculator to compare the relative intensity to the angle and the cosine2 of the angle. PART I: Computer Setup1. Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn on the computer. 2. Connect the Light Sensor into Analog Channel A on the interface. 3. Connect the Rotary Motion Sensor stereo phone plugs to Digital Channels 1 and 2. 4. Open the document titled as shown:
• The document opens with a Digits display of light intensity, a Graph display of light intensity versus the angle, and a Graph display of light intensity versus the cosine square of the angle.
• See the pages at the end of this activity for information about modifying a ScienceWorkshop file. PART II: Equipment Setup and Sensor CalibrationEquipment Setup1. Assemble the Polarization Analyzer as shown in the instructions that came with the analzyer. • Place the polarizer on the accessory holder. • Mount the Rotary Motion Sensor onto the bracket. • Loop the plastic belt over the Rotary Motion Sensor and the polarizer. 2. Mount the Polarization Analyzer on the Optics Bench. 3. Mount the Light Sensor on the Aperture Bracket and attach the Aperture Bracket to the Aperture Bracket Holder. Put the Aperture Bracket Holder onto the Optics Bench. 4. Rotate the Aperture Disk so the open circular aperture is in line with the opening to the Light Sensor 5 6. Turn on the Light Source. Move the Light Source and the Light Sensor so they are as close as possible to the polarizers. Sensor Calibration• Calibrate the Light Sensor so that it produces its maximum voltage when axes of the two polarizers are parallel (Ø = 0˚). 1. Set the GAIN select switch on the top of the sensor to 1. Move the Light Sensor so its port is as close as possible to the light source. 2. In the Experiment Setup window, double-click the Light Sensor icon. Result: The Sensor Properties window opens in DataStudio. The Light Sensor setup window opens in ScienceWorkshop. In DataStudio click the ‘Calibration’ tab.
3. Check the voltage from the Light Sensor.
4. Now adjust the polarizers so the light source shines as brightly as possible into the Light Sensor. For example, turn one polarizer so the zero degree mark is next to the reference peg on the accessory holder. Turn the second polarizer so it is parallel with the first polarizer (i.e., also at zero degrees). Adjust the second polarizer until the transmission is maximum as indicated by the voltage in the calibration window.
5. Keep this value of voltage as the maximum value (corresponding to 100% intensity). In DataStudio click ‘Take Reading’ below the ‘High Point’ column. In ScienceWorkshop, click the top Read button. 6. Now adjust the polarizers so the light transmission is as dim as possible. Turn the second polarizer to 90 degrees. Adjust the second polarizer so the transmission is minimum as indicated by the voltage in the calibration window. 7. Keep this value of voltage as the minimum value (corresponding to 0% intensity). In DataStudio click ‘Take Reading’ below the ‘Low Point’ column. In ScienceWorkshop, click the bottom Read button. Click ‘OK’ to return to the Experiment Setup window.
PART III: Data Recording1. Adjust the polarizers for maximum transmission of light. 2. When you are ready, start recording data. (Hint: Click the ‘Start’ button in DataStudio or the ‘REC’ button in ScienceWorkshop.) 3. Begin turning the Polarization Analyzer slowly and smoothly. Watch the results in the Graph display. Continue to turn the polarizer for at least one full rotation (360 degrees). 4. After at least one full rotation, stop recording data. 5. Turn off the light source.
Analyzing the DataUse the Graph displays to analyze your data. 1 2. Try to fit the data to a mathematical model. • Hint: In DataStudio, click the ‘Fit’ menu button and select ‘Polynomial’. In ScienceWorkshop, click the ‘Statistics’ button and then select ‘Curve Fit, Polynomial Fit’ from the Statistics menu. Note whether or not the ‘Polynomial’ model is a ‘good fit’. 3. Next, examine the Graph display for ‘Light Intensity versus cosine (angle)’. • In DataStudio, click the second graph to make it active. In ScienceWorkshop, select ‘Calculations, Cosine squared’ from the X-axis Input menu. 4. Try to fit the data to a new mathematical model. In DataStudio, click the ‘Fit’ menu button and select ‘Linear’. In ScienceWorkshop, click the ‘Statistics’ menu and select ‘Curve Fit, Linear Fit’.
Answer the questions in the Lab Report section.Lab Report - Activity P34: Polarization – Verify Malus’ LawWhat Do You Think?If the transmitted light is at maximum intensity when the two polarizers are parallel, and minimum intensity when the two polarizers are perpendicular, what is the relationship of the intensity of transmitted light to the angle of the polarizers between 0 and 90 degrees? Questions1. What is the shape of the graph of the Light Intensity versus the Angular Position? 2. What is the shape of the graph of the Light Intensity versus the square of the cosine of the angle? 3 Theoretically, what percentage of incident plane polarized light would be transmitted through three polarizers which each have their axes rotated 17 degrees from each other? Assume ideal polarizers and assume that the first polarizer’s axis is 17 degrees from the axis of the second polarizer. Appendix: Modify a ScienceWorkshop FileModify an existingScienceWorkshop file to add the Rotary Motion Sensor. Open the ScienceWorkshop FileOpen the file titled as shown:
Set Up the Rotary Motion SensorI n the Experiment Setup window, click and drag the digital sensor plug to Channel A. Select ‘Rotary Motion Sensor’ from the list of sensors. Click ‘OK’. Result: The Rotary Motion Sensor setup window opens. Click ‘1440’ under ‘Divisions/Rotation’ and then click ‘OK’ to return to the Experiment Setup window. Set the Sampling OptionsClick the ‘Sampling Options’ button in the Experiment Setup window or select ‘Sampling Options’ from the Experiment menu to open the Sampling Options window. Result: The Sampling Options window opens. De-select ‘Keyboard’ by clicking the checkmark. Under ‘Periodic Samples’ click the right arrow to set the sample rate at ‘20 Hz’ (20 measurements per second). Click ‘OK’ to return to the Experiment Setup window. |