Physics 313: Laboratory 8 - Polarization of Light Electric Fields Introduction: The electric fields that compose light have a magnitude, phase, and direction. The oscillating phase of the field and the scalar wave properties of light have been verified in the previous experiments. In many examples, the vector nature of the field is overlooked since natural light is rarely highly-polarized. complete description of light, however, must include the direction of the electric field in addition to its magnitude and wavelength. fter completing these experiments you should be able to answer the following questions: How can natural light, with random polarization, be transformed into linearly polarized light, with a fixed polarization? How do polarized sunglasses reduce glare? Method/Experiments: Complete your understanding of light by studying the vector nature of its vibrating fields. Become familiar with methods of detecting and creating polarized light by using a linear polarizer to investigate the degree of polarization of common light sources. Create polarized light by reflecting natural light off a surface. Interact light with optically active compounds to explore the vector component, e.g. electric field direction, of light. The following equipment is required to collect the data: optical table polarizing film injection molded plastic lenses rotation stage l/2 and l/4 retarding film light bulb calcite crystals in petri dish microscope slide HeNe laser 1
Experiment 1: Polarization of various light sources and reflected light Light with an isotropic electric field direction is considered unpolarized, while light that is 100% polarized has a single, well-defined direction to the electric field. Polaroid film attenuates the electric field component parallel to the direction of the aligned polymers, thus the transmitted light is polarized perpendicular to them. Use Polaroid film to inspect various light sources including: room light, laser light, sunlight, skylight, scattered light, and reflected light (try light reflected off of the hallway floor). Record your observations and estimate the degree to which everyday light is polarized (Figure 2). Using a second Polaroid film, verify that once light has been resolved in one direction, the directionality of the electric field persists and can be detected. Unpolarized light incident on a surface can be described by two electric field components, an s-wave [electric field polarized perpendicular to the plane of incidence, also known as TE transverse electric wave] or a p-wave [polarized parallel to the plane of incidence, TM transverse magnetic wave]. These two different electric field orientations give rise to very different interactions with the surface. Hence, the amount of light reflected from and transmitted through the surface depends upon the polarization as shown in the Fig. 1. The p-wave has been shown (section 4.6) to reflect less strongly than the s-wave, so that what results is a partially polarized reflected beam. However, at a certain angle, the reflected beam is completely polarized with its electric field parallel to the surface and perpendicular to the plane of incidence. Reflectance (percent) 100 80 60 40 20 0 p-wave s-wave θ p 0 10 20 30 40 50 60 70 ngle of Incidence (deg) Figure 1: Reflectance vs. angle of incidence for an air-sapphire interface. V I Imax I I + I I + I p = = p n max Figure 2: Degree of polarization of partially polarized, linear, quasi-monochromatic light as determined from the maximum and minimum intensities measured when an analyzer polarizer is rotated (Equations 8.29, 8.30) min min 2 R R!
The angle of incidence in which the reflectance of the p-wave vanishes is called Brewster s angle, θ p. t this angle, the reflected wave is a completely polarized s- wave. You can determine Brewster s angle for an air-glass interface using a microscope slide and a linear polarizer. Tape the slide to the center of a rotation stage and illuminate it with collimated light from a light bulb. Set the slide at normal incidence, then rotate the stage until the p-wave reflection is a minimum. Describe the observed s-wave and p- wave reflectance as a function of incidence angle from 70 to 90 degrees. Experiment 2: Polarizers Illuminate optically active compounds with linearly-polarized white light and describe the results (see Fig. 3). With each of the five samples listed below, describe the effects as a function of the light s polarization angle (i.e. the electric field direction). unpolarized light polarizer sample analyzer Figure 3: Basic set-up for exploring the polarization effects of materials. Chiral compound (C 12 H 22 O 11 - Sucrose) in solution ligned molecules in plastic sheet to introduce ¼-wave retardation ligned molecules in plastic sheet to introduce ½-wave retardation Calcite crystals (CaCO 3 ) Stressed plastic (injection molded or pulled) 3
What effect does the sucrose solution have on the plane of polarization? For the plastic sheets, determine which of the 2 by 2 squares is ¼-wave plate and which is ½-wave plate. One of the two will have a notch in the edge. It is known that anisotropy in a medium s molecular structure can result in birefringence. In the case of calcite, describe the double refraction as fully as possible by analyzing the polarization of the transmitted light from the crystal. B C void touching the crystals and handle them in a glass petri dish. Observe the stressed plastic objects with polarized light as shown in Fig. 4. Then observe them with a second polarizer and describe what you see as in Fig. 5. Rotate the analyzer and note that the colors shift. Figure 4: Various objects as seen when illuminated by linearly polarized white light: -stressed plastic, B-Polaroid film, C- tissue paper. What causes the emergence of the many colors and how do they relate to the angle of the analyzer? From the figures, can you deduce which of the two sandwiched polarizers (Fig. 4 B) is on top of the other? Why are two layers of tissue darker in Fig. 4 and brighter in Fig. 5 when compared to only one layer? Figure 5: Various objects as seen when illuminated by white light and placed between two crossed polarizers. 4
Experiment 3: Quantitative analysis of stress in glass Residual stress in plastic is introduced by the manufacturing process. This includes injection molding, machining, vacuum forming and extrusion. Stress also occurs in glass as a result of a cooling or polishing process. Sometimes these stresses have an important purpose, but more often, high levels of stress can compromise a product s performance. In these cases, for example, impact strength is lowered, the surface may develop chemical susceptibility, and extreme temperature performance is diminished. Therefore, careful evaluation of stress in transparent materials is very important at all levels of the production process. When a transparent material is stressed, it becomes birefringent. s in the case with all polarization effects, this is due to a stress induced alignment (anisotropy) of the molecules that compose the material. n extreme case of this is the pulling of a plastic to form a Polaroid polarizing film. The birefringence means that the propagation of the light in the material depends upon the field direction relative to the molecules aligned by the stress. Naturally, birefringent materials have two refractive indices. s polarized light passes through stressed plastic, the light waves separate as a result of the birefringence and their polarization. fter crossing the material s thickness (t), the retardation between the two light polarizations, due to their different velocities, is proportional to the amount of birefringence, i.e. the stress on the material. The stress can be evaluated using the angle of retardation, the thickness, and the stress optical constant (C) of the sample. Retardation is measured using an instrument called a polarimeter or polariscope. 5
polariscope consists of a polarizer, an analyzer, and an incandescent light source arranged as shown in figure 2. The polarizer and analyzer should be crossed at 90 degrees. fter the polarized light passes through the sample, the analyzer selects the light that has been rotated by 90, 270, 450, etc... degrees relative to the initial light. Just as in an interferometer, the fringes represent different path lengths. However, the different path lengths are in this case analyzed by a polarizer to determine the phase differences accumulated by passing through more or less birefringent material. Examine several pieces of injection molded plastic and explain why different colors represent different stress levels. To gain a quantitative understanding of stress in glass, take a 1 inch optic and mount it in a mirror mount. Tighten the screw holding the lens in place until a definite fringe pattern is viewed using your polariscope. Be very careful when tightening the screw, as these are thin lenses and they will crack. Leaving the polarizer and analyzer stationary, rotate the mount and count how many fringes you observe. Two observed fringes will give you an angle of retardation equal to 360 º since distance between fringes is equal to 360 º. Calculate the stress in the lens using the following formula: Stress (pounds per square inch) = ngle of retardation in degrees / (0.1786 x C x Sample thickness in inches) where C=3.8 for glass. Next, make an analysis of stress by drawing a contour map of the stress in the lens. Figure 5: Monochromatic fringes induced by stress. 6