Polarization of Light

Transcription

1 Purpose: To study the following aspects of polarization: Polarizer-analyzer Rotation of the plane of polarization by a solution Brewster s angle Equipment: Optical bench, component carriers, angular translator Optical accessory kit Light source LabPro Kit Light Sensor Glass polarization cells Fructose and sucrose solutions (5% sugar/ 20%sugar/ 35% sugar/ and 50% sugar/50% water by weight) Ring Stand Rods & Clamps Vernier calipers Red reading lights Theory: By now I m sure you all are aware that light (at least sometimes) behaves like a wave. If you remember back to the study of waves, you ll know that a wave consists of a displacement of a medium (water, string, air ) that propagates through that medium. Waves are a means of transferring energy from one place to another. The amount of energy determines the amplitude of the wave, or how much medium is displaced. The displacement may either be along the direction of wave velocity ( Longitudinal Waves ) or perpendicular to the direction of wave velocity ( Transverse Waves ). Sound is an example of a longitudinal wave. Water waves are an example of transverse. A Slinky or an earthquake can provide examples of either, or both at the same time. Light is a transverse wave. The displacement of the wave is perpendicular to the direction is which the wave is traveling. This brings us to the question of what is the medium that is being displaced, or What the heck is waving?!?. Years ago, it was postulated that there existed some sort of luminiferous ether the permeated the universe and was otherwise undetectable except by the transmission of light waves through it. Michelson and Morely disproved this theory in 1881 (though if you search for Michelson and Morely or ether on the internet, you ll find a number of people who disagree). It was Maxwell who described the nature of light. Previous experimenters (Foucalt, Michelson & Morely) had experimentally determined the wave speed of light: c = x 10 8 m/s. By applying his famous Maxwell s Equations to electromagnetic 1 of 13

2 waves (coupled electric and magnetic fields that are perpendicular to each other and to the direction of motion) he discovered that only one velocity would keep the waves propagating at the same amplitude for ever: v em = x 10 8 m/s! From this he deduced that what we d been calling light for millennia must be simply an electromagnetic wave. The medium that is waving is electric and magnetic fields. On to Polarization! What does an electromagnetic wave look like? Fig. A This is a snapshot of a plane-polarized light wave. The horizontal arrow shows the direction of wave velocity. Note how the E and B fields are perpendicular to each other and to the direction of wave velocity. They have the same frequency and are exactly in phase with each other. For clarity, the E and B fields have been drawn with equal amplitudes. In reality, however, the magnitude of the B-field is equal to c E. For simplicity in drawing, the B field is generally left out, and only the E field is represented. In unpolarized light, the electric fields (and B fields) point in all directions, much like this: z y x In this picture, the waves are depicted as propagating straight out of the page. Fig. B 2 of 13

3 This, of course, does not depict all of the E fields contained in a beam of light. That number is infinite. We simply attempt to show that unpolarized light is composed of many waves, all with a different E-direction and/or magnitude. Since E and B fields are represented by vectors, it is possible to define them as the sum of two orthogonal vectors. In the above picture, we would choose x and y. E 2 E 1 E 1y E 2y E 2x E 1x Only two of the vectors are shown being broken into components, though of course all the vectors shown have components in both the x and y directions. Because of this, we may simplify the above drawing representing unpolarized light into a drawing showing the sum of all of the E field components in two orthogonal directions: y E fields z x This is sufficient, because all components of the E and B fields (in this example) ultimately lay in either the x or y directions. A Polarizer is something that sorts out these randomly-distributed E fields into planes. In the above example, we could send the light through a polarizer and end up with perhaps this: Fig. C 3 of 13

4 or this: E-field vibrations in the y-direction as looking into the z-axis. Fig. D In the first case, the light is said to be polarized linearly and horizontally. In the second case, the light is polarized linearly and vertically. A polarizer chooses not just the one light wave that lies in its plane of polarization, but all components of all light waves that lie in its plane of polarization. These two choices are of course only two of an infinite number of options. You could choose to polarize your light at any angle. How does a polarizer work? One possible polarizer is an array of parallel wires. An electric field will exert a force on electric charges, like the ones existing in a wire. When an unpolarized electromagnetic wave passes through an array of wires, those parts of the E field which are parallel to the wires will cause a current to flow. Thus, the energy in the fields is transferred to the energy in the current; the energy in the fields is absorbed by the wires. This leaves only the component of the E field that is perpendicular to the wires to pass through unaltered. This type of polarizer is called dichroic referring to its ability to absorb one of the orthogonal components of light. In addition to the parallel wire array, there are a number of crystals and organic compounds which exhibit this property. Fig. E 4 of 13

5 While the wire array works, it is not practical. The separation of the wires must be on the order of one wavelength of light. This is very small. Today, people have come up with numerous ways of creating dichroic sheet polarizers, often using long chains of molecules or long crystals in place of wires. A simple polarizer may be made in this way by stretching Scotch Tape. The effect of polarized material on light. Fig. F Another process of polarization is not through transmission, but by reflection. It is useful at this point to define two types of polarization, Transverse Electric (TE) and Transverse Magnetic (TM). Fig. G Both TE and TM polarization are defined with respect to a Plane of Incidence. The plane of incidence is defined as the plane that contains the normal to the surface and the 5 of 13

6 incident ray of light. It is NOT the plane that contains the surface upon which the light is incident. In the examples above, the plane of incidence is the same as the plane of the paper. In figure (a), the electric field is drawn in the plane of incidence. Thus, the magnetic field is orthogonal (or transverse) to the plane of incidence, and this case is called TM polarization. In figure (b), the electric field is orthogonal to the plane of incidence so this is called TE polarization. If unpolarized light is incident upon a glass surface at some angle with respect to the normal, both the reflected and transmitted rays are found to be partially polarized. If the angle of incidence is increased to be equal or greater to the so-called Brewster Angle, the reflected light will be entirely TE polarized. The transmitted beam will contain some TE polarized light, but will be mainly TM polarized. Fig. H Brewster s angle may be found through the expression where and Fig. I n 2 is the index of refraction of the glass plate, n 1 is the index of refraction of the medium next to the glass plate The theory for this lab was written by Jennifer LK Whalen 2 Figures A-I from the LEOT by CORD International, Module 6-10, 6 of 13

7 Experiment and Analysis: Jordan O Bryant S99 Part A: Crossed Polarizers 1. Set an incandescent light source on the left end of the bench. Place three component carriers on the bench. On the one nearest the light source, place the aperture mask (9139). Place this close enough to the source so that the light beam is entirely blocked except for that passing through the rectangular aperture. 2. On the second carrier to the right, place a polarizer (9109) with the zero down and lined up with the index on the component carrier. Because it is the first in line to choose the axis of polarization for the light, it is called the polarizer. 3. On the third carrier to the right, place a second polarizer; because it is the second polarizer in line, this one is now called an analyzer. By rotating this second polarizer, we can analyze the light and determine the plane of polarization given by the first polarizer. Again place the zero down, lined up with the index. Observe the light intensity transmitted through the analyzer as you rotate it through Connect the AC adapter to the LabPro by inserting the round plug on the 6-volt power supply into the side of the interface. Shortly after plugging the power supply into the outlet, the interface will run through a self-test. You will hear a series of beeps and blinking lights (red, yellow, then green) indicating a successful startup. 5. Attach the LabPro to the computer using the USB cable that is Velcro-ed to the side of the computer box (do not unplug the USB cable from the computer!). The LabPro computer connection is located on the right side of the interface. Slide the door on the computer connection to the right and plug the square end of the USB cable into the LabPro USB connection. 7 of 13

8 6. Connect a light sensor to a digital port (DIG/SONIC1) on the LabPro. The digital ports, which accept British Telecom-style plugs with a left-hand connector, are located on the same side as the computer connections. If you are using an older light sensor, you will need to use the digital adapter labeled DIN-BTA. 7. Open the Experiments folder on the desktop and open the file polarize.xmbl (or.cmbl) This will start the program Logger Pro3.3 and bring up the appropriate data file. If you do not have an auto-id sensor (which is the likely case), a dialog box will pop up asking you to confirm the sensors being used. If you have the suggested sensor attached to the LabPro in the suggested port, click OK. If the OK button is not active, ask your instructor for help. 8. Construct a holder for the Light Sensor using a ring stand, rods and clamps. The end result should look something like this: to LabPro Light Sensor lab stand 9. We now need a way to shut out the ambient light of the room so that the sensor detects only the light that passes through the polarizers. Boxes seem to work fairly well. In fact, there may be a couple of boxes all ready for you to use, complete with notches cut in to fit around the optics bench, and a hole for the light sensor to poke through, otherwise you will have to construct your own. You may find that you need to adjust the height of your light sensor to match up with the hole. You will be lifting the box off the apparatus repeatedly, so make sure that your final set-up isn t too sensitive. Light Sensor analyzer polarizer aperture mask light source to LabPro lab stand 10. Place the cardboard box over the apparatus as shown above. Set the Range of the sensor to Lux. Keep the light source turned off, and click the ZERO button on the experiment screen to calibrate the sensor. 8 of 13

9 11. Now you should be ready to begin taking data. This particular experiment file will allow you to pick-and-choose data points. You will set the angle of the analyzer and replace the cardboard box. When the fluctuation of the sensor settles down, click KEEP and enter the angle into the dialog box that appears. The illuminance will be automatically recorded in the appropriate data column. 12. Repeat Step 11, each time increasing the angle of the analyzer by 10 o, until you have completed the full 360 o circle. 13. Now while looking at the light source through the polarizer and analyzer, rotate the analyzer until the filament appears purple (minimum intensity). The polarizers are now crossed. At what analyzer angle is minimum intensity attained? θ o = 14. Cut-and-Paste the angle vs. illuminance data into a spreadsheet program such as Excel or Graphical Analysis, and make a plot of the data. 15. Perform a line-fit to the data and record the equation returned by the fit. 16. If you don t already know, look up in your book or ask your instructor (in that order!) to find what equation describes the ideal relationship between the analyzer angle and the illuminance. Is it the same equation as returned by the line fit? Plot the ideal equation on top of the data, using your experimental values for the maximum intensity (use an average, if you need to). 17. Make a statement about how well your data fits the theoretical curve. If the data and theory are not described by the same trigonometric function, is there a relation between the two functions you have? Part B: Rotation of the Plane of Polarization In this section, we will attempt to discover what effect different strength solutions of fructose and sucrose will have on the polarization plane of light. Begin with Sucrose: 1. Pour some of the 5% solution into a glass cell, nearly filling the cell. 2. Place the cell between the two polarizers and on the angular translator to raise it above the optical bench. Orient the cell transverse to the beam of light: i.e. so the light travels through the shorter path of solution. 3. Now rotate the analyzer until minimum intensity is reached. The angle through which the analyzer is rotated should be less than 90 o. Record this angle as angle θ. 4. Using the θ o obtained in Part A, subtract θ from θ o. This is the angle of the plane of polarization of the sugar solution. Record this angle in the data table. 9 of 13

10 5. Repeat Steps 1-4 with increasing strengths of sucrose solution. 6. Measure the width of the cell. 7. Choose another cell with a different width (another possibility is to rotate the cell by 90 o so that the light travels through the longer path of solution). 8. Fill this cell with the 50% solution of sucrose, and repeat Steps From the data obtained in Steps 6-9, calculate by what angle would the plane of polarization be rotated passing through 8cm of 50% sugar solution. 10. Repeat Steps 1-9 with the fructose solutions. Sucrose 5% 20% 35% 50% (a) 50% (b) Fructose 5% 20% 35% 50% (a) 50% (b) Sucrose Width of cell A Width of Cell B θ 0 θ through Cell A θ 0 θ through Cell B θ 0 θ through 8cm of solution 10 of 13

11 Fructose Width of cell A Width of Cell B θ 0 θ through Cell A θ 0 θ through Cell B θ 0 θ through 8cm of solution C. Brewster's angle Component Carrier with Aperture Mask Angular Translator with Polarizer (Analyzer) Acrylic Plate (Polarizer) 1. Place the "angular translator" on the optical bench with 0 o o line parallel to the bench with the zero toward the light source. Rotate the table of the angular translator so that the arrow points to 0 o. 2. Place the acrylic plate (9129) on the special carrier and mount it centrally on the table. 3. Place the polarizer (used as an analyzer) on the viewing arm of the angular translator. To observe the polarization upon reflection, place the 90 o of the analyzer downward, lined up with the index on the viewing arm. 4. Now rotate both the table with the acrylic plate and the viewing arm, keeping the reflection of the light source in view. Make sure the 0 o o line of the circular scale remains parallel to the bench. Continue watching the reflection of the light source until it reaches a minimum intensity. Calculate Brewster's angle and the index of refraction for acrylic. (tanθ = n) Note: Since n > 1, θ must be greater than 45 o. Record results and make calculations below. θ p = n = 11 of 13

12 Results: Write at least one paragraph describing the following: what you expected to learn about the lab (i.e. what was the reason for conducting the experiment?) your results, and what you learned from them Think of at least one other experiment might you perform to verify these results Think of at least one new question or problem that could be answered with the physics you have learned in this laboratory, or be extrapolated from the ideas in this laboratory. 12 of 13

13 Clean-Up: Before you can leave the classroom, you must clean up your equipment, and have your instructor sign below. How you divide clean-up duties between lab members is up to you. Clean-up involves: Completely dismantling the experimental setup Removing tape from anything you put tape on Drying-off any wet equipment Putting away equipment in proper boxes (if applicable) Returning equipment to proper cabinets, or to the cart at the front of the room Throwing away pieces of string, paper, and other detritus (i.e. your water bottles) Shutting down the computer Anything else that needs to be done to return the room to its pristine, pre lab form. I certify that the equipment used by has been cleaned up. (student s name),. (instructor s name) (date) 13 of 13