Polarisation of Light Investigation

Polarisation of Light InvestigationValentin HaemmerliAbstract. An ocular system consisting of a laser, a polariser, a quarter- curve family, a optical prism, and a light detector affiliated to a multi-meter was used to find the infection axes of the polariser and the quarter-wave scale leaf, find the travel of polarization of the laser relative to the optical axis and investigate the quality of the polariser and quarter-wave racing shell by comparing the hypothetic and experimental values of tier of polarization for linear, orbitual and elliptic polarizations. These were found to be 0.980.03 female genitalsvasd to 1 for linear, 0.180.03 comp ared to 0 for poster and 0.590.03 compared to 0.65 for a particular ellipse.IntroductionPolarisation of electromagnetic radiation is a fundamental phenomenon arising directly from the wave properties of light. Polarisation of light in the opthalmic spectrum has many commercial applications such as stress analysis of birefringent materials1, 2, sugar content analysis in the brewing industry and in food chemistry1, liquid crystal displays 2 and in sunglasses. In addition to these applications, polarisation of light has a number of important scientific uses, including determining the refractive indices, absorption constants and reflecting power of highly absorbing materials 1.There are iii antithetical cases for polarised light linear, bank none and elliptical. The aim of this investigation was to calibrate the optical system and subsequently use it to analyse transmittal intensities for distributively of these types, and compare the respective marks of polarisation to theoretical values.TheoryPolarisation TypesElectromagnetic waves stool electric and magnetic sphere of influence elements propagating as sinusoidal waves where the directions of the electric theme sender is perpendicular to two the direction of the magnetic field sender and to the direction of propagation at all times. Due to this constant copulation surrounded by electric and magnetic field transmitters, we can describe polarisation in terms of electric field only for simplicity.Linear polarisation is the case where the x and y components of electric field for a wave traveling in the z-direction are varying in stagecoach with each other, so they are twain at their maxima at the homogeneous time, and both at their minima at the same time, and the electric component of the wave is ceaselessly in the same plane. This is shown in aim 1a).Circular polarisation, shown in embodiment 1b), occurs when the x and y components of the electric field vector have the same amplitudes and have a phase remainder of /2, or /2 gain an integer multiple of . The end point of the resulting electric field vector traces out a circle in the x-y plane, which translates to a helix one time time is taken into account.Elliptical polarisation, of which circular polarisation is merely the spare case when the amplitudes are equ al and the phase difference is where . Elliptical polarisation is whence any case for which the end point of the electric field vector traces out an ellipse in the x-y plane. This is shown in fancy 1c).Brewsters LawBrewsters Law states that for a communicate ensuant on a flat horizontal glass sur formulation of a prism at the Brewster shift, sendn by,(1)where is the refractive index of the prism, only the component of the beam with polarisation parallel to the incident plane is reflected. This fact can be used to determine the polarisation of the incident beam afterward it has passed through with(predicate) the analyzer. By rotating the analyzer until there is no reflected component the beam is polarised vertically and hence has not component in the horizontal direction.Quarter-wave coatA quarter-wave plate is an optical device which is made of two materials with different refractive indices which has the effect of introducing a phase difference of /2 surrounded by th e perpendicular x and y component of the electric field vector for light of a particular wavelength. The quarter-wave plate has two perpendicular transmission axes. A quarter-wave plate can therefore be used to stir the polarisation of the incident light from linear to elliptical and in the artless case of the ellipse, circular.Degree of polarisationThe equation used to find the degree of linear polarisation of light for transmitted intensities measured for tips of analyzer is,(2)where I is specialty.Experimental Method We first found the transmission axis of the Polaroid analyzer using Brewsters Law of horizontal polarisation using the rear up in ascertain 2.We started at an approximate value of Brewsters Angle using n=1.6 for the refractive index of the prism. We set the incident angle to this, and then rotated the analyser until no light was reflected from the face of the prism, but light was still transmitted through the analyser. By supple commutes of the incident ang le on the face of the prism and the angle of the analyser to minimise the transmission, we found the transmission axis of the Polaroid analyser. We found the degree of polarisation of linearly polarised light using the set up in Figure 3, by rotating the analyser through 360 and noting the transmitted intensity detected by the light detector and multi-meter in volts. Plotting the intensity as a fail of angle and comparing it to a theoretical game of transmission from genus Malus Law, we also found the angle at which the laser beam was polarised. using the set up shown in Figure 4 we found the transmission axes of the quarter-wave plate. With the analyser set to an angle perpendicular to the angle of polarisation of the laser beam (i.e. a minimum intensity), transmitted intensity was measured for angles surrounded by 0 and 360 of the quarter-wave plate. The minima of this dependance correspond to the transmission angles of the quarter-wave plate.Once the transmission axes were f ound, the quarter-wave plate was set to an angle of one of the transmission axes cocksure 45 to give circularly polarised light. The intensity was measured as a function of the angle of the analyser. This was used to find the degree of polarisation of circularly polarised light by rotating the analyser through angles from 0 to 360.Finally we tested for a theoretical value of elliptical degree of polarisation of 0.65 by turning the quarter-wave plate 22.7 past one of the transmission axes and once again rotating the analyser through 360 and measuring intensities to give an experimental degree of polarisation.The error in the analyser angle and quarter-wave plate angle was dogged by observing the affirm of angles over which the intensity did not change. This was 2 in both cases, and when both the analyser and quarter-wave plate were on the optical bench this gave a have error of 4. The ambient light reading was taken to take place a systematic error in intensity readings. This wa s found to be 0.00 V.Experimental ResultsThe degree of polarisation of the analyser is 0.980.03 from the maximum and minimum intensities in Figure 5 and equation (2). The error comes from the uncertainty in the touchstone of the intensity. The angle of polarisation of laser beam is 102. This was determined from the angle difference between the experimental data and the theoretical plot of Malus law. The error is given by the error in analyser angle.The transmission axis of the analyser runs from 170 to 350 2, this is given by the maxima of the experimental data in Figure 5.The transmission axes of the quarter-wave plate are 204 to 2004 and 1104 to 2904 from the minima in Figure 6, corrected for the angle of polarisation of the laser beam.The degree of polarisation of circularly polarised light is 0.180.03 from the maximum and minimum intensities in Figure 7. Theoretically the quarter-wave plate should be at one of its transmission axes plus 232 for a degree of polarisation of 0.65. At this angle the experimental degree of polarisation was 0.590.03 from the maximum and minimum intensities in Figure 8.DiscussionThe error in the sensitivity of the polariser and quarter-wave plate are some(prenominal) greater than the accuracy of the scales on the polariser and quarter-wave plate. The errors are found to be 2 for each, slice the accuracy of the scale is 0.5. This is farther too small because intensity did not change over such a small change in angle.One possible reason for such a prominent difference between theory and experimental values for degree of polarisation for the case of elliptical polarisation, 9.2%, is that the quarter-wave plate was knowing to give a phase difference of /2 for a specific wavelength of light due to the dependence of refractive index on wavelength. The wavelength of our laser was not the same as this design. The difference could be reduced by using a more than suitable laser or quarter-wave plate.The theoretical degree of polaris ation for circular polarisation settings of the quarter-wave plate and analsyer is 0, compared to the 0.180.03 found experimentally. Similarly, the analyser was not desirel, imperfectly auction block components perpendicular to the transmission axis. The theoretical degree of polarisation for the analyser is 1, while experimentally we found it to be 0.980.03. The contribution to the error from the quarter-wave plate is therefore larger than that from the analsyer.There are two possible reasons for imperfect circular polarisation. The first of these is that the quarter-wave plate was set to the wrong angle, not at 45 to a transmission axis. This would lead to an error in the degree of polarisation of approximately twice the error in the angle, or approximately 4. This is far too large for our degree of polarisation and therefore unlikely, since the difference between theory and experiment is only 0.18. The other reason is that the quarter-wave plate did not shift the phase of one c omponent of polarisation by /2. thence the difference is approximately the difference between the theoretical phase difference and the actual phase difference. This is the more likely case, as discussed above, the quarter-wave plate is designed for a specific wavelength of light.ConclusionsWe investigated three types of polarisation of light using an analyser and a quarter-wave plate. We found degrees of polarisation for each type, and compared them to their theoretical values. This gave us an idea about the quality and suitability of the analyser and quarter-wave plate for our laser, with the quarter-wave plate contribute the largest amount to the difference between the theoretical and experimental polarisations. In the movement of finding these values we also determined the transmission axes of the analyser and the of the quarter-wave plate. addendumDerivation of the angel of the quarter-wave plate for degree of polarisation 0.65From equation (2) , (3), (4)From (3) and (4),, ( 5)where is the angle offset from the transmission axes of the quarter-wave plate and is the component of the electric field vector.This gives us, from equations (1) and (5),. (6)References1C. A. Skinner, The polariscope and its practical applications, Journal of the Franklin Institute, vol. 196, pp. 721-750, 1923.2P. A. Tipler and G. Mosca, Physics for scientists and engineers with modern physics, 2008.1