Polarized Light. Nikki Truss. Abstract:

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1 Polarized Light Nikki Truss Abstract: In this experiment, the properties of linearly polarised light were examined. Malus Law was verified using the apparatus shown in Fig. 1. Reflectance of s-polarised and p-polarised light was investigated over a range of angles of incidence. Brewster s angle for glass was found to be 56 ±1.This was then used to calculate the refractive index of glass, which was found to be approximately equal to Aims: Our aims in this experiment were; To measure the intensity of light transmitted by a polariser To measure the intensity of light reflected from a glass surface for different angles of incidence and different polarization directions To determine Brewster s angle and from this estimate a value for the refractive index of glass Introduction and Theory: Light is a transverse wave comprised of an electric field component and a magnetic field component, each oscillating perpendicular to each other and the direction of motion. Natural light is made up of many of these waves each oscillating in a different plane. A polarizer is a device which prevents this from happening, it only allows through light which is oscillating along one particular axis. There are various types of mechanisms by which polarisers achieve this, one example being a material where all the dipoles are aligned parallel to each other, meaning one component of the wave will be absorbed along this axis. By rotating the polaroid we can polarize the light in whichever direction we choose. Malus Law relates the intensity of light transmitted through a polarizer to the relative angle θ between the axis of polarization of the polarizer and the plane of incident light, by the following formula: Where is transmitted intensity, is the incident intensity and θ is the relative angle. This is derived from the fact that only the only the component of the parallel to the axis of the polarizer,, gets through. vector Since We get and hence our relationship.

2 Brewster s Angle is the angle of incidence at which light polarized parallel to the plane of incidence (p-polarized) is completely transmitted, (i.e. not reflected, so reflectance=). As such, any unpolarized light reflected at this angle becomes polarized in a plane perpendicular to the plane of incidence (s-polarized). This angle is the angle at which the reflected ray id perpendicular to the transmitted ray, ie From the Law of Reflection we know And from Snell s Law we know So we get And finally we get Where are the indices of refraction for media 1 and 2, and is the angle of incidence. Experimental Method: Fig 1. The laser used was a Helium-Neon laser, and the detector used was a silicon photodiode mounted on a rotatable arm. Part 1: Malus Law: This part of the experiment was carried out without the prism or the half wave plate. The apparetus was arranged as shown above (Fig. 1), with the laser shining directly onto the polaroid, the beam passing through and landing on the detector. Maximum transmission intensity was found by rotating the polaroid until the largest value of voltage across the photodiode was found. Using this as a relative angle of degrees, the polaroid was rotated in 1 increments up to 18, and the intensity readings noted. Two graphs were then plotted to verify Malus Law, the first being the intensity (I) vs the angle of the polarizer (θ), the second being a plot of the intensity (I) vs the cosine squared of the angle of the polarizer.

3 Intensity Part 2: Reflectance and Brewster s Angle: 2(a): Making sure the plane of polarization was perpendicular to the plane of incidence, the maximum intensity was once again determined. The glass prism was placed on its stand such that the beam from the laser was normal to its surface. The detector was rotated to find the intensity of reflected beam. The prism was then rotated in 1 increments and the corresponding intensities recorded. 2(b): A half wave plate was placed between the laser and the polaroid in order to rotate the polarization of light. Once again maximum transmission was determined without the prism in place. The prism was then replaced and once again rotated in 1 increments and the corresponding intensities recorded, as far as the geometry of the system would allow, which for this particular case was 7. Brewster s angle was then determined by observing which angle corresponded to the minimum transmitted intensity. A graph was then plotted containing the data from part (a) and part (b), of the reflectance vs the angle of incidence. From the graph Brewster s angle was observed. Results and Analysis: Part 1: Malus Law: Intensity vs Polarizer Angle Angle (degrees) R² =.999 Fig. 2 From the above graph it can be seen that the intensity is at a minimum at approximately 9, which is to be expected as at this angle the axis of the polaroid is perpendicular to the axis of the polarisation of the light. The intensity is at a maximum at and 18.

4 Reflectance (unitless) Cos^2 of Angle Intensity vs Cos ^2 of Polarizer Angle R² = Intensity Fig. 3 This graph Fig.3 verifies the relationship given by Malus Law as we obtained a straight line through the origin. An error appears to have been made while measuring the 3 rd point from the right as it does not sit on this straight line Part 2: Reflectance:.12 Reflectance vs Angle Angle of Incidence (degrees) Fig. 4

5 In Fig. 4 the blue line corresponds to light polarised perpendicular to the plane of incidence, while the red line corresponds to the light polarised parallel to the plane of incidence. For p-polarised light, (blue) we see an increase in reflectance as the angle of incidence increases. For s-polarized light we see a minimum at approximately 56 ± 1, which corresponds to Brewster s angle. At angles of incidence greater than this angle we see a very sharp increase in the reflectance. Using Brewster s angle and the formula derived earlier, ( ) we calculated the value of the refractive index for glass, which is approximately. Discussions and Conclusions: o Malus Law was verified experimentally o For p-polarized light, it was found that reflectance increases with angle of incidence o For s-polarized light it was found that reflectance is at a minimum at an angle approximately 56 ± 1, and at angles greater than that the reflectance increases dramatically o Brewster s angle was found to be 56 ± 1 o The refractive index of glass was calculated from Brewster s angle to be o Part 2, on reflectance had many difficulties. There was often a second beam out of the prism due to reflection inside the prism as well as outside. Also the voltage readings fluctuated, creating more uncertainty in recording the values.