Measurement of Faraday Rotation in SF57 glass at 670 nm **Third and Final Draft**

We performed an experiment to measure the Faraday rotation of polarized light passing through a magnetic field, as well as measuring the Verdet constant of an SF57 glass tube with a length of \(0.1\) m. Our results are consistent with the general idea of Faraday rotation, which suggests that linearly polarized light experiences rotation when applying a magnetic field. We used three different methods to find Verdet constants, which are Direct Fit, Slope Fit and Lock-in Method. The values we found are \(21\pm 5 \frac{radians}{T \cdot m}\), \(21.095\pm0.003 \frac{radians}{T \cdot m}\) and \(20.43\pm0.06 \frac{radians}{T \cdot m}\) respectively, and those values are consistent with each other within uncertainty.

1. To observe Faraday effect in this lab, which says that the rotation of plane of polarization of light changes when applying a magnetic field, which can be described using Equation \ref{1} \[\label{1} I=I_{0}cos^{2}(\theta_1−\theta_0-\phi(B))\] Equation \ref{2} descries the transmission of polarized light through a second polarizer: \[\label{2} I=I_{0}cos^{2}(\theta_1−\theta_0)\] where \(I_{0}\) is the intensity of the light after passing through the first polarizer and \(I\) is the light intensity passing through both polarizers at angles \(\theta_{1}\) and \(\theta_{0}\).

The Faraday effect was first observed by Michael Faraday in 1845, before light and matter interaction was understood. Light waves contain both a magnetic field and electric field. The electric and magnetic fields are transversely polarized with respect to the direction of propagation. Linearly polarized light refers to light that is polarized in one plane, the most simple examples being vertical polarization and horizontal polarization. Vertically polarized light refers to light whose \(E\) field vector oscillates in the vertical direction, and horizontally polarized light refers to lights whose \(E\) field vector oscillates in the horizontal direction. Circular polarization occurs when light has two different polarizations orthogonal to each other, but with a phase difference of 90 degrees. The resulting polarization vector oscillates circularly and can be right- or left-handed, depending on whether the phase difference is +90 degrees or -90 degrees. When light passes through a magnetic field in certain media, propagating in the same direction as the field, the magnetic field can cause different refractive indices for right- and left-circularly polarized light. This causes the right and left polarized light to have different phases. Linearly polarized light can also be thought of as a superposition of right- and left-circularly polarized light, so when linearly polarized light passes through a magnetic field, the polarization of the light will have rotated by some angle \[\varphi=\frac{\pi v}{c}L(n_{R}-n_{L})\] Where c is the speed of light, \(\nu\) is the frequency of the light, \(n_{R}\) is the refractive index of the material for right polarized light, \(n_{L}\) is the refractive index of the material for left polarized light, and L is the length of the material. The angle of rotation is also proportional to the magnetic field B, so it can also be described by Equation \ref{3}.

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