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Polarization by Reflection at a Dielectric and verifying Fresnel’s                                   EquationsPrinciplePla...
| |     |     |                 (the law of reflection)and                                               (the law of refra...
i.  Components parallel to the plane of incidence Ep, Rp, . These amplitude       components are called the p – components...
fluxes over a period of time in the reflected and refracted waves to the averageenergy flux in the incident wave are calle...
In such a case, the difference between the components s and p disappears, sincethe concept of plane of incidence loses mea...
2. Make the transmission axis of the polarizer in the horizontal orientation,        i.e., the transmitted laser beam will...
transmitted laser beam will have vertical polarization: the electric field          component vibrating perpendicularly to...
170                 85            160                 80             .                   .             .                  ...
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Polarization by reflection at a dielectric and verifying fresnel’s equations

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Optics Experiment No. 10 for 3rd Class Physics

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Polarization by reflection at a dielectric and verifying fresnel’s equations

  1. 1. Polarization by Reflection at a Dielectric and verifying Fresnel’s EquationsPrinciplePlane-polarized light is reflected at a glass surface. Both the rotation of the planeof polarization and the intensity of the reflected light are to be determined andcompared with Fresnels formulae for reflection.Tasks i. The reflection coefficients for light polarized perpendicular and parallel to the plane of incidence are to be determined as a function of the angle of incidence and plotted graphically. ii. The refractive index of the flint glass prism is to be found. iii. The reflection coefficients are to be calculated using Fresnels formulae and compared with the measured curves. iv. The reflection factor for the flint glass prism is to be calculated. v. The rotation of the polarization plane for plane polarized light when reflected is to be determined as a function of the angle of incidence and presented graphically. It is then to be compared with values calculated using Fresnels formulas.What you can learn about▪ Electromagnetic theory of light▪ Reflection coefficient, Reflection factor▪ Brewsters law▪ Law of refraction▪ Polarization, Polarization levelTheory:When unpolarized light is incident on a dielectric medium such as a glass, thereflected rays are partially plane – polarized, i.e., it is a mixture of a planepolarized and unpolarized (ordinary) light.Let a plane light wave strike a boundary between two media having refractiveindexes n1 and n2. The angles , , and are the angles of incidence, reflection,and refraction, respectively. In this case:Optics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 1
  2. 2. | | | | (the law of reflection)and (the law of refraction)The fraction of light reflected or refracted depends on: i. The refractive indices of the media ii. The angles of incidence iii. The state of polarization of the incident lightAt a certain angle of incidence , the reflected light is totally plane – polarized,(Figure 1). This angle is called the “Brewster’s Angle” or “Polarizing Angle”, and itis related to the refractive index of the Normal Reflected raymedium by: Incident ray (polarized, 𝐸 ) ⊥ (Unpolarized) 𝜑 𝜑This relation is called “Brewster’s law”. 𝑛 𝐵 𝐵Also, for this angle the reflected electric 90 𝑛vector E is normal to the plane of 𝜑incidence, i.e., the plane containing theincident ray and the normal at the point Refracted ray (polarized)of incidence.Let the plane of vibration makes an angle with the normal to the plane ofincidence (figure 2). This angle is called Figure 1: Unpolarized light incident at the polarizing anglethe orientation angle whether it refers tolight vibration in the incident, reflected or refracted light. The vector E in theincident, reflected or refracted light can be resolved into two amplitudecomponents: Normal 𝐸𝑝 𝐸 𝑅𝑠 𝜓 𝐸𝑠 𝜑 𝑅 𝑅𝑝 𝜑 80 Figure 2: Plane - polarized light externally reflected from a glass surface at 80 degrees angle of incidence.Optics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 2
  3. 3. i. Components parallel to the plane of incidence Ep, Rp, . These amplitude components are called the p – components. ii. Components normal to the plane of incidence Es, Rs, . They are called the s – components.For unpolarized light, Ep=Es.According to the electromagnetic theory, the amplitudes, phase, and state ofpolarization of the reflected and refracted waves for the p – vibrations and s –vibrations are related to the corresponding characteristics of the incident wave byFresnel’s equations:for the reflected amplitudes.for the refracted amplitudes.It follows from equations (2 - 5) that for any value of the angles thesigns of and and the signs of and coincide. This means that thephases also coincide; that is, in all cases the refracted wave retains the phase ofthe incident wave. For the components of the reflected wave (Rp and Rs), thephase relations depend on , n1, and n2. For example, if = 0, then when n2 > n1the phase of the reflected wave will be shifted by π.From 2 and 3, one gets:This is the tangent of the angle , i.e.,In experiments, rather than measuring the amplitude, scientists usually measurethe intensity of a light wave, that is, the energy flux carried by it, which isproportional to the square of the amplitude. The ratios of the average energyOptics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 3
  4. 4. fluxes over a period of time in the reflected and refracted waves to the averageenergy flux in the incident wave are called the reflection coefficient r and thetransmission coefficient t. We obtain from equations (2 - 5) the Fresnel equationsthat define the reflection and transmission coefficients for the s- and p-components of the incident wave: ( )In the absence of light absorption, rs + ts = 1 and rp + tp = 1, in accordance with thelaw of the conservation of energy. If natural light is incident on the boundary,that is, if all directions of oscillations of the electric vector are equally probable,then, one half of the wave’s energy is accounted for by p – oscillations and theother half by s – oscillations. In this case, the total reflection coefficient is: ( ) [ ]If 90 and , then rp = 0; that is, light that is polarizedsuch that its electric vector lies in the plane of incidence under these conditionswill not be reflected at all from the boundary. The reflected light, when naturallight is incident at this angle, will be completely polarized.For normal incidence of light on the boundary between two media ( = 0), theFresnel equations for the amplitudes of reflected and refracted waves can bereduced to the form: ( ) ( ) ( ) ( )Optics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 4
  5. 5. In such a case, the difference between the components s and p disappears, sincethe concept of plane of incidence loses meaning. In this case, we obtain, inparticular, ( )It follows from the above two equations that the reflection of light at theboundary is greater the larger the absolute value of the difference n2 – n1; thecoefficients r and t do not depend on which side of the boundary the incidentlight wave arrives from.A condition for applicability of the Fresnel equations is that the refractive index ofthe medium be independent of the amplitude of the electric field strength of thelight wave. This condition, which is trivial in classical (linear) optics, is not satisfiedfor high – power radiant fluxes, such as those radiated by lasers. In these cases,the Fresnel equations do not provide a satisfactory description of the observedphenomena, and consequently the methods and concepts of nonlinear opticsmust be used.Procedure  Brewster’s angle and the index of refraction n. 1. Arrange all the optical components on the optical bench as in figure 3. 0 360 - graduated rotatable stage Polarizer Prism or glass plate Laser Analyzer Intensity meter Figure 3 – Experimental setup for reflectance measurements as a function of angle of incidence.Optics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 5
  6. 6. 2. Make the transmission axis of the polarizer in the horizontal orientation, i.e., the transmitted laser beam will have horizontal polarization with the vibration of the electric field vector component E parallel to the plane of incidence ( ). Remove the analyzer from the optical bench. 3. Align the incident laser beam spot with the 0 mark on the graduated rotating stage. 4. Align the photocell with the incident polarized laser spot and read the initial intensity (I0) as registered by the attached multimeter. 5. Put the prism on the rotating stage which must be level and make the laser beam incident normally on the prism. This is done whenever the reflected and incident laser spots coincide with each other. If not, simply rotate the prism (not the stage!) clockwise or anticlockwise direction around the vertical axis until the reflected laser spot precisely becomes aligned with the incident beam. 6. Slowly turn the graduated rotatable stage clockwise in 10 – degree steps. At each orientation, rotate the Photocell arm slightly to get into the beam. Read the intensity (I) as registered by the attached multimeter. Record the measured data in a table 1 below. I0= mV at =0 degree Ip Is rp=Ip/I0. rs=Is/I0 degrees mV mV 10 20 30 40 . . 90 7. Repeat step 3 by rotating the stage of the prism in 10 – degree angle increments until reaching the value 80 0 (or even 90 0, if possible). 8. Using the same procedure as before, take measurements with the transmission axis of the polarizer in the vertical orientation, i.e., theOptics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 6
  7. 7. transmitted laser beam will have vertical polarization: the electric field component vibrating perpendicularly to the plane of incidence ( ⊥ ).Analysis 1. Take the ratio Ip/Io, graph it versus angle . Determine the Brewster’s angle. 2. Use Brewsters angle to calculate the index of refraction of glass prism using equation 1. Use n1 = 1.000308 3. Calculate the parallel and perpendicular reflectances using Fresnel equations.  Verification of Fresnel’s equations 1. Record the value of the analyzer scale at which the laser beam has totally been extinct. Notice that there are always two analyzer positions to give the extinction. Use the one closest to the zero reading of the analyzer. 2. Rotate the analyzer exactly 450 from its initial reading Remove the 0 prism and return the analyzer arm to 180 . Insert the polarizer between the laser and the prism (on the optical bench) and rotate it until the light is extinguished. The transmission axis of the polarizer is now 45 0 to the horizontal and vertical directions. Hence, Ep=Es. Don’t change this polarizer setting during the remaining part of the experiment. 3. Turn the analyzer arm to position 170 0 ( 8 . Place the prism on the stage. Rotate this stage until the laser beam falls on the analyzer. 4. Rotate the transmission axis of the analyzer until the light is extinguished. The difference between the current analyzer reading and the zeroth reading recorded previously at the Brewster’s angle gives the angle . Be sure that is closest to the zeroth reading of the analyzer scale. 5. Repeat steps 6 and 7 for rotating stage angles of 160, 150, 140, 130, 120, 110, and 100. Tabulate your readings as in table 2 below.Optics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 7
  8. 8. 170 85 160 80 . . . . 100 50 Analysis 1. Use Snell’s law and the evaluated refractive index n to calculate the angle of refraction for each angle of incidence 2. Calculate the value of using equation 7. 3. Plot a graph of vs. Compare it with that of Jenkins and White. Questions 1. Would Brewsters angle be more or less for light in air reflecting off water? 2. How would data look like for an arrangement with vertical square polarizer? 3. How do polarized sunglasses reduce glare? Which direction is the axis of polarization in a pair of polarized sunglasses? How could you check this?Optics Lab – Department of Physics – Baghdad University 2012 – Exp. No. 10 8

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