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EX-5543 Polarization of Light.docx.pdf

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University of Toronto Mississauga
Wagih Ghobriel

Polarization EX-5543 Page 1 of 10 Polarization Equipment INCLUDED: 1 Polarization Analyzer OS-8533A 1 Basic Optics Bench (60 cm) OS-8541 1 Red Diode Laser OS-8525A 1 High Sensitivity Light Sensor PS-2176 1 Rotary Motion Sensor PS-2120 NOT INCLUDED, BUT REQUIRED: 1 850 Universal Interface UI-5000 1 PASCO Capstone UI-5400 Introduction Laser light (peak wavelength = 650 nm) is passed through two polarizers. As the second polarizer (the analyzer) is rotated by hand, the relative light intensity is recorded as a function of the angle between the axes of polarization of the two polarizers. The angle is obtained using a Rotary Motion Sensor that is coupled to the polarizer with a drive belt. The plot of light intensity versus angle can be fitted to the square of the cosine of the angle allowing us to verify the Law of Malus. As part of the two polarizer experiment, we demonstrate that the diode laser is 100% polarized. We use this to simulate a three polarizer system. The non-rotating polarizer is set perpendicular to the laser polarization so transmission is minimized. The analyzer is then placed between the laser and the fixed polarizer and the student finds that some of the beam is now transmitted. This allows a striking verification of the vector nature of the electric field. This experiment can be performed with the room lights on. Written by Chuck Hunt Polarization EX-5543 Page 2 of 10 Theory A polarizer only allows light which 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 of the light intensity will be transmitted through the polarizer. Figure 1: Light Transmitted through Two Polarizers Written by Chuck Hunt Polarization EX-5543 Page 3 of 10 The transmitted light is polarized in one plane. If this polarized light is incident upon a second polarizer, the axis of which is oriented such that it is perpendicular to the plane of polarization of the incident light, no light will be transmitted through the second polarizer. See Fig.1. However, if the second polarizer is oriented at an angle not perpendicular to the axis of 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, and thus some light will be transmitted through the second polarizer. Figure 2: Component of the Electric Field If the polarized electric field is called E a1ter it passes through the first polarizer, the component, E 2 after the field passes through the second polarizer which is at an angle φ with respect to the first polarizer is E cos φ (see Fig.2). Since the intensity of the light varies as the square of the 1 electric field, the light intensity transmitted through the second filter is given by I = I cos φ2 Eq. (1) 2 1 Written by Chuck Hunt Polarization EX-5543 Page 4 of 10 Theory for Three Polarizers Figure 3: Electric Field Transmitted through Three Polarizers Unpolarized light passes through 3 polarizers (see Fig.3). The first and last polarizers are o oriented at 90 with respect each other. The second polarizer has its polarization axis rotated an angle φ from the first polarizer. Therefore, the third polarizer is rotated an angle (π/2 - φ) from the second polarizer. The intensity after passing through the first polarizer is I and th1 intensity after passing through the second polarizer, I , is2given by 2 2 = I1cos φ The intensity after the third polarizer, I , is given by 3 3 = I2cos (π/2 - φ) = I cos1φ cos (π/2 - φ) = I cos φ sin1φ 2 2 Eq. (2) since cos (π/2 - φ) = sin φ. Using the trigonometric identity, sin 2φ = 2cosφ sinφ, gives: 2 3 = (I1/4)sin 2φ Eq. (3) So we predict that the maximum intensity will be four times smaller than the max intensity for the two polarizer case and that intensity will run through its full cycle in π/2 radians rather than π radians as was the case with two polarizers. This does assume that the polarizers are ideal and transmit 100% of the light aligned with their optical axis and 0% of the light perpendicular to their optical axis. This is not true for real polarizers and we expect that the intensity will not quite go to zero. It also means that the max intensity decreases when more polarizers are inserted in the beam even though all the optical axes are aligned with the beam. This does not affect our results since both the two and three polarizer experiments insert two polarizers in the beam. Written by Chuck Hunt Polarization EX-5543 Page 5 of 10 Setup SetupS Figure 4: Equipment Separated to Show Components 1. Mount the aperture disk on the aperture bracket holder. 2. Mount the Light Sensor on the Aperture Bracket with the attachment thumbscrew (not the 6 cm rod) and plug the Light Sensor into a PASPORT input on the 850 Universal Interface. Click the low sensitivity (0-10,000) button on the side of the Light Sensor. 3. Rotate the aperture disk so the open aperture is in front of the light sensor (see Fig. 5). Figure 5: The Aperture Disk 4. Remove the black rod attachment adaptor from the Rotary Motion Sensor (RMS) using the attached tool. Make sure the pulley on the RMS is mounted so the large pulley is toward the body of the RMS. Using the two mounting screws stored on the Polarization Analyzer bracket, mount the Rotary Motion Sensor on the polarizer bracket so the pulley is toward the bracket. Connect the large pulley on the Rotary Motion Sensor to the polarizer pulley with the plastic belt stored on the polarization bracket (see Fig.6). 5. Plug the Rotary Motion Sensor into a PASPORT input on the 850 Universal Interface. Written by Chuck Hunt Polarization EX-5543 Page 6 of 10 Figure 6: Rotary Motion Sensor Connected to Polarizer with Belt 6. Push all the components on the Optics Track as close together as possible. See
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