PHYSICS 116 POLARIZATION AND LIGHT MEASUREMENTS

Name Date Lab Time Lab TA PHYSICS 116 POLARIZATION AND LIGHT MEASUREMENTS I. POLARIZATION Natural unpolarized light is made up of waves vibrating in all directions. When a beam of unpolarized light is passed through a polarizing material, only waves that are vibrating in one specific direction are allowed to pass. The direction of vibration is determined by the polarization axis of the filter. (See Fig. 1.) Figure 1. Polarization and Transmission of Light by Aligned Filters. R. Feinberg 9/98 M. R. Knittel 10/13

If a second piece of polarizing material is held in the beam of light, the beam will easily pass through both if their polarization axes are aligned. If the axis of the second piece of polarizing material is placed at right angles to the axis of the first piece, most of the light will be absorbed and very little will pass through. (See Fig. 2) Figure 2. Polarization and Absorption of Light by Crossed Filters. 1. Variation of Transmitted Intensity With Angle For any value of angle between the polarization axes, the intensity of the light transmitted varies as I = I 0 cos 2 where I 0 is the transmitted intensity with the polarizer axes aligned, and is the angle between the axes of the polarizers. This relationship is known as Malus' Law. In this part we will attempt to check Malus' Law by measuring the transmitted intensity as a function of angle between the two polarizers Insert two polarizing disks into the grooved holder with their polarization axes aligned. Line up the 0 marker on each polarizer to coincide with the center of the vee groove or the edge of the circular groove. (See Fig. 3.) One disk frame is metal and will remain fixed; the other disk frame is plastic with degree marks and will be rotated. 2 Polarization and Light Measurements

Figure 3. Reading Degree Divisions on the Filter Rings. Attached to the holder is a bright red light emitting diode (LED) on one side and a light sensor on the other side. Leaving the metal-framed polarizer fixed, we will be measuring the light intensity as a function of the plastic-framed polarizer angle from 0 to 180. Mount the light sensor detector on the threaded stud, making sure that the detector is on-axis with the LED source. Also make sure that the GAIN switch on the detector is set to 1. Plug in the DIN connector from the light sensor into the ANALOG CHANNELS A socket in the Science Workshop 750 Interface. The LED is powered from a common 5VDC lab supply in the front of the room. Your LED is plugged into the back side of the lab table, which is connected to the room power supply. Figure 4. Polarization Apparatus with LED and Detector. Polarization and Light Measurements 3

Setting Up Capstone 1. Log on to the computer. 2. Double click on the Capstone icon near the left side of the desktop. 3. Click on the Open Experiment button, second from the left on the toolbar. 4. In the left pane, select k-drive (\\msfs-class1\class1) (K:) Browse to Physics\P116\Polarization and Light Measurements Select Polarization.cap and click on <Open> 5. Your display should look like: 6. There are two windows of interest: 1) Table This is filled in with the rotation angles and the light sensor output percent of maximum possible intensity as you take data. 2) Graph This will display a constantly-updated graph of Light Sensor Intensity (%) vs. Rotation Angle (degrees) as you take data. 4 Polarization and Light Measurements

Taking Data 1. Dim down the room lights!! 2. Click on the Preview button at the bottom of the screen. Verify that you have the axes of the two polarizers parallel (the intensity reading shown in the table is at the largest value you can get). Try rotating the metal-ring polarizer slightly with the plastic ring fixed at 0 until you get the highest reading. This ensures that the two polarizers are exactly parallel. 3. Click on Keep Sample to lock in the current light sensor intensity. 4. Rotate the plastic-ring polarizer to 5, and click on Keep Sample. Notice that both the table and the graph are automatically being updated. 5. Continue to enter into the table the light intensity at every 5 from 0 to 180. If you make an error, you can easily fix it by clicking on the Intensity value that you want to correct and, making sure that the polarizer angle matches that for the table entry, and click on Keep Sample. 6. After keeping the intensity for 180, click on Stop. Fit the Experimental Data 1. Click anywhere on the Graph to make it active. 2. From the drop down Curve Fits menu select User Defined: f(x). Click on the User Defined box that has now appeared in the graph to make it active (it may be behind the menu), and then click on the Curve Fit Editor button way over on the left of the screen. The equation should be the definition of Malus Lawy: y=i0*cos(x)^2 If not, edit it and click on <Apply>. The graph will now display the theoretical curve on top of your experimental data points. Polarization and Light Measurements 5

Analysis 1. To print the graph, select File Print Page Setup, and then select Landscape. Click on <OK>. Now select File Print and click on <Print> Include this graph with your report. 2. Examine the graph and explain any observed differences between the theoretical curve and your experimental data points. Why does your experimental data not drop to zero at 90, as Malus Law predicts? Try an addition to the User Defined curve fit function to take this into account and get a better fit. Show your improved equation. 6 Polarization and Light Measurements

2. Birefringence in Calcite Calcite (also called Iceland Spar) is a naturally occurring mineral which exhibits birefringence, or double refraction. This means that the crystal has two different values for its index of refraction depending on how the light is polarized. Light polarized perpendicular to the crystal s optic axis (a line joining the blunt corners) is called an ordinary ray because it obeys the ordinary laws of refraction. Light polarized parallel to the crystal's optic axis is called an extraordinary ray because it does not obey Snell's law. Place a calcite crystal on top of a printed page and examine the print. What do you see? What happens when you rotate the crystal around? The image that stands still is formed by the ordinary ray and the image that rotates is formed by the extraordinary ray. View the crystal and print through a polarizer. Slowly rotate the polarizer and describe what you see. What does this tell you about the relative polarization of each print image? How many degrees do you have to rotate the polarizer to go from the maximum intensity of one image to the maximum of the other? Polarization and Light Measurements 7

3. Stress and Strain Analysis with Polarized Light When a normally uniform material (like clear plastic) is stressed it becomes birefringent like calcite. When viewed between crossed polarizers, the light passing through the object isn't completely extinguished. Instead, patterns of light, dark and color appear corresponding to the locations of the greatest stress. Engineers sometimes build scale models of structures like bridges or teeth and use this photoelastic effect to find potential failure points. Sometimes these stresses can be frozen in to the object if it cooled unevenly during manufacture. Look at some of the plastic objects provided as shown in Fig. 5. Also try squeezing the stress specimen provided. Where do the greatest stress points appear to be? Figure 5. Stress Analysis with Polarized Lighting. 4. Polarization by Reflection Another way that light can be polarized is by reflection from a non-metallic surface. When light reflects off of a surface, the incident ray, the normal and the reflected ray all fall in the same plane. This plane is called the plane of incidence. The amount of light reflected by a surface is different, depending on whether the light is polarized parallel or perpendicular to the plane of incidence. The amount of reflected light for each polarization also depends on the angle of incidence. At one special angle of incidence called the polarizing angle p, or Brewster's angle, 100% of the light reflected from a surface will be polarized perpendicular to the plane of incidence. So if the incoming light is unpolarized and reflects in a vertical plane, the outgoing light will be horizontally polarized. This is why polarizing sunglasses are manufactured to pass only vertically polarized light. They absorb most of the reflected glare which is horizontally polarized. The polarizing angle is found from the expression 8 Polarization and Light Measurements

tan p n where n is the index of refraction of the reflecting surface. Set up the apparatus shown in Fig. 6. Figure 6. Polarization by Reflection Horizontal Surfaces. What is the polarizing angle for reflection off the black plastic square if it has an index of refraction n = 1.491? Look at the reflected image of the drawing on the cardboard disk at about this angle of incidence. Using the polarizer, determine the direction of the polarization of light reflected from the black plastic square. The polarization direction is found to be because (describe how you determined this): Place the black plastic square on a table almost directly underneath a ceiling light. Hold a polarizer up to your eye and view the reflection of the ceiling light from directly above the square. Is the reflected light polarized now? Why or why not? Polarization and Light Measurements 9

5. Polarization by Scattering When a beam of light strikes scattering particles it causes them to vibrate and re-emit the light in new directions. But light is also a transverse wave, which means that its electric field can only vibrate perpendicular to the direction that the beam travels. Imagine an unpolarized light beam that is incident vertically on a suspension of scattering particles. (See Fig. 7). Figure 7. Polarization by Scattering. The direction of the incident light s vibration is in the horizontal plane, perpendicular to the beam's direction. This light is not polarized since it is vibrating in all directions in the horizontal plane. When the light scatters off particles in the solution, it continues to vibrate in its original direction, but travels in a new direction (toward your eye). The scattered light must therefore be vibrating in a horizontal plane too. But since it must vibrate in a direction perpendicular to the direction that it is traveling, only one horizontal direction is allowed for each direction of observation. The scattered light must therefore be horizontally polarized. Using your polarizer, confirm this prediction. Write your observations here: 10 Polarization and Light Measurements

II. LIGHT MEASUREMENTS Imagine a point source of light like a small light bulb sitting at the center of an imaginary transparent sphere. Let's assume that the transparent sphere neither reflects nor absorbs any of the light striking it. All of the energy leaving the bulb each second must pass through the surface of the sphere. If it didn't, energy would have to appear from somewhere or disappear, a violation of the law of conservation of energy. Figure 8. Inverse Square Law. The same amount of energy passes through each of the surfaces 1, 2, 3 and 4 every second. If the sphere were made larger, the same amount of energy must still pass through its surface each second. But since a larger sphere has a larger surface area, the amount of energy falling on each unit area of the surface must now be less. Since the surface area of a sphere is proportional to the square of its radius, the energy falling on each unit area of its surface must decrease in proportion to the inverse square of its radius to keep the product of the two constant. In optics, this is commonly called the inverse square law. It states the energy per unit area per unit time falling on a surface decreases as 1/(the distance from the source) 2. (See Fig. 8.) I = I 0 ( D 0 D ) 2 where I is the intensity of the source measured at a distance D and I 0 is the intensity of the source measured at a different distance D 0 When you have finished taking data, we will try to fit an inverse n th power function to your experimental data to see if the n is really two i.e., does the intensity really decrease as the inverse square of the distance. Polarization and Light Measurements 11

Setting up Capstone 1. Click on the Open Experiment icon in the top toolbar. Reply <Discard> to not save changes to the last experiment. In the left pane, select k-drive (\\msfs-class1\class1) (K:) Browse to Physics\P116\Polarization and Light Measurements Select Light Measurements.cap and click on <Open> 2. Your display should look like: 3. There are two windows of interest: 1) Table This is filled in with Distances and the Light Sensor Output Intensity (%) as you take data. 2) Graph This will display a constantly-updated graph of light sensor Intensity (%) vs. Distance (m) as you take data. 4. Remove the LED light source from the grooved polarizer stand. Rotate the light sensor 180 so that it faces away from the light source s previous position. 12 Polarization and Light Measurements

5. Insert a meter stick into the slot in the light sensor base. 6. Place the halogen bulb holder on the meter stick at the 0.1 m point. This is a critical distance. Note that the light sensor element is 0.015 m inside the tip of the light sensor opening. You want the light source filament to be 0.1 m from the light sensor element. Figure 9 shows a suggested arrangement, with the meter stick extending 0.018 m into the base. Tighten the meter stick locking bolt. 7. Adjust the height of the sensor so that the opening is centered at the same height as the vertical center of the light filament, about 0.11 m above the table top. 8. Fully turn down the power supply voltage (counterclockwise). 9. Turn on the power supply and set the voltage to about 4.0 volts (if the voltage does not go up, turn up the current limiting knob). 10. We will use distances of 0.100, 0.125, etc., up to 1.00 m. As you move the light source away, make sure that it stays on the axis of the sensor the sensor and light need to always be in a straight line down the meter stick. 11. Dim the room lights!! Figure 9. Measuring Intensity vs. Distance. Polarization and Light Measurements 13

12. With the light source set at the 0.1 m distance, click on Preview and adjust the power supply voltage so that the measured light sensor output intensity is about 90-92% (exceeding 98% will saturate the sensor). Taking Data 1. Click on Keep Sample to lock in the current value of the light sensor intensity. 2. Move the light source to 0.125 m, and click on Keep Sample. 3. Continue to record the intensity at the remaining distances listed in the table. Always make sure that the Distance value corresponds to the actual position of the light source. You may need to use your flashlight to read the meter stick. Note that the distance value interval changes at 0.400 m. 4. When you have kept the intensity for 1.0 m, click on Stop. Fit the Experimental Data 1. Click anywhere on the Graph to make it active. 2. From the drop down Curve Fits menu select Inverse Power: A(x-x 0) n +B. Click on the Inverse Power box that has appeared in the graph to make it active (it may be behind the menu). Look at the value of n, the power. This should look odd to you, not at all what the inverse square law says! Now click on the Curve Fit Editor button at the left edge of the screen. Here you will find that Capstone has decided to lock the initial value of n at 3 for its initial curve fit. Remove the checkmark from the n parameter and click on Update Fit. Analysis 1. To print the graph, select File Print Page Setup, and then select Landscape. Click on <OK>. Now select File Print and click on <Print> Include this graph with your report. 14 Polarization and Light Measurements

2. What is the value for the exponent n for the curve fit of inverse n th power. 3. Explain any observed differences between the theoretical curve and your experimental data points. 4. For a real light bulb, where would you expect the inverse square law to fail, at short distances or at long distances? Why? Polarization and Light Measurements 15