S-108-2110 OPTICS 1/6 REFLECTION AND REFRACTION Student Labwork
S-108-2110 OPTICS 2/6 Table of contents 1. Theory...3 2. Performing the measurements...4 2.1. Total internal reflection...4 2.2. Brewster angle...5 3. Measurement report...6
S-108-2110 OPTICS 3/6 1 Theory In this work we study the total internal reflection and Brwester angle using polarized light. A laser source, polarizer, rotation stage and D shaped acrylic plate will be used to carry out the measurements and determine the index of refraction of the acrylic plate. The measurement setup for total internal reflection is depicted in Figure 1. Due to the D-shaped form of the plate, the beam path from air to acrylic will not change. n 2 Acrylic plate n 1 Figure1. Measuring the total internal reflection. First we determine the angle θ c where the total internal reflection occurs. This presupposes, that n 1 >n 2. Snell s law (also known as law of refraction) tells that n 1 sin θ 1 = n 2 sin θ 2. The angle of total internal reflection can be calculated when taking θ 2 = 90 θ 1 = θ c. The relative index of refraction for the acrylic plate becomes then The Brewster angle will be determined using similar setup but the measurements will be carried out using both propagation directions, i.e. beam going from air to acrylic (n 1 < n 2 ) and from acrylic to air (n 1 > n 2 ). First the incident light has to be polarized in the plane of incidence. In this case the intensity of the reflected beam will be zero if the angle of incidence satisfies the condition or using markings in the lecture notes. Angle θ P is called the polarization angle or Brewster angle. When light is incident under Brewster angle the following relation is valid θ 1 + θ 2 = 90.
S-108-2110 OPTICS 4/6 In the following we ll use two different setups regarding beam propagation direction: n 1 < n 2 (n 1 = air, n 2 = acrylic) and n 1 > n 2 (n 1 = acrylic, n 2 = air) 1) n 1 =air, n 2 =acrylic: The experimental setup is shown in figure 2. In this case we ll get tan θ p =n Acrylic plate Figure 2. Brewster angle in case of n 1 < n 2. 2) n 1 =acrylic, n 2 =air: The experimental setup is shown in figure 3. Accordingly we ll get Acrylic plate 2. Performing the measurements 2.1 Total internal reflection Figure 3. Brewster angle in case of n 1 > n 2. First set the acrylic plate with the round surface facing the light source. Then set the angle of incidence from the plane surface to be zero (θ 1 = 0). This is easiest to achieve observing the back-reflected beam from the plane surface of the plate. If the beam reflects back to the source then the plane surface is perpendicular with the incoming beam. Mark the corresponding angle on the rotation stage as α 0. Thereafter find the two angles α 1 and α 2 at which the total internal reflection occurs. This holds true when the reflected beam propagates along the plane surface. Experimental setup is shown in figure 4.
S-108-2110 OPTICS 5/6 Figure 4. Measuring the total internal reflection. The angle of total internal reflection can be determined from the following relation. To calculate θ c one does not need actually find α 0. This is only used to verify the measurement correctness. In the measurement report find the quantities α 1 α 0 and α 0 α 2. If measurement is correctly performed these quantities have to be equal within the measurement uncertainty. 2.2 Brewster angle In the case of n 1 < n 2 (n 1 = air, n 2 = acrylic) align the back-reflected beam from plane surface to coincide with the incoming beam. The angle of incidence is then zero. Mark the corresponding angle β 0 in the rotation stage. Using the polarizer set the light to be linearly polarized in the plane of incidence. Polarizing plane is marked on the polarizer. Then find the two angles β 1 and β 2 at which the back-reflected beam disappears. Polarization angle θ P can be found as In the case of n 1 > n 2 (n 1 = acrylic, n 2 = air) carry on similar way but mark the angles as γ 0, γ 1 and γ 2.
S-108-2110 OPTICS 6/6 Measurement report Name and student number: c = angle of total internal reflection P = polarization angle, also known as Brewster angle n = index of refraction Total internal reflection: angle of total internal reflection 0 1 2 c n Correctness check: 1 0 2 0 Brewster angle: Propagation direction: air acrylic glass Brewster angle 0 1 2 P n Correctness check: 1 0 2 0 Propagation direction: acrylic glass air Brewster angle 0 1 2 P n Correctness check: 1 0 2 0