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# 物理代写|光学代考Optics代写|EGR558 Polarization prisms

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## 物理代写|光学代考Optics代写|Polarization prisms

A Wollaston prism is made of Iceland spar $\left(n_o=1.658, n_e=\right.$ 1.486) with angle $\alpha=20$ deg between the leg and hypotenuse faces of the prism. Determine angle $\beta$ between the linearly polarized rays output from the prism if a ray of natural light is normally incident on the prism.

A linearly polarized ray of light is incident on a Wollaston prism; the direction of oscillations form the angle $\theta=30 \mathrm{deg}$ with the optical axis of the first half of the prism. Determine intensity ratio $I_o / I_e$ for the rays emerging from the prism. Ignore the reflection of light by the prism faces.
A circularly polarized ray of light is incident on a Wollaston prism. Determine the intensity ratio $I_o / I_e$ for the ray emerging from the prism.
Determine angle $\beta$ between the orthogonally polarized rays emerging from a Rochon prism made of Iceland spar $\left(n_o=\right.$ $\left.1.658, n_e=1.486\right)$ with angle $\alpha=20$ deg between the leg and hypotenuse faces of the prism. Determine the ratio of intensities of these rays $I_o / I_e$, ignoring the losses in the course of reflection from the faces of the prism for the following incident rays: (a) natural (randomly polarized); (b) circularly polarized; (c) linearly polarized with the azimuth of polarization $\theta=60$ deg with respect to the optical axis of the second half of the prism; and (d) elliptically polarized with the ratio of the semiaxes $E_o / E_e=0.5$, with the major semiaxis parallel to the optical axis of the second half of the prism. The prism is immersed in air.

## 物理代写|光学代考Optics代写|Induced optical anisotropy

A glass plate with thickness $d=4 \mathrm{~mm}$ is subjected to homogeneous mechanical stress $\sigma_y=50 \mathrm{MPa}$ along the $y$ direction. The plate is placed between two crossed linear polarizers, $\mathrm{P}1$ and $\mathrm{P}_2$, so that the $y$ axis forms angle $\alpha=$ 45 deg with the transmission axes of the linear polarizers. An interference minimum is observed in the visible range of the white light at wavelength $\lambda_m$. Using the Brewster photoelasticity law, determine the optical path difference $\Delta{o e}$ between the ordinary and extraordinary waves in the plate and wavelength $\lambda_m$. The Brewster constant for the plate glass is $C_B=2.5 \times 10^{-12} \mathrm{~Pa}^{-1}$ Solve the previous problem for such orientation of the linear polarizers $\mathrm{P}_1$ and $\mathrm{P}_2$ that their transmission axes are parallel and form angle $\alpha=45$ deg with direction $y$ of the mechanical stress in the plate.
Electric voltage $U$ is applied to a Kerr cell with nitrobenzene placed between crossed polarizers $\mathrm{P}_1$ and $\mathrm{P}_2$. The distance between the capacitor plates of the cell is $d=1 \mathrm{~mm}$, the length $l$ of the capacitor is $6.4 \mathrm{~cm}$, and the Kerr constant is $K=2.2 \cdot 10^{-12} \mathrm{~m} / \mathrm{V}^2$. The transmission axes of the polarizers form angle $\alpha=45 \mathrm{deg}$ with the plates of the condenser. Determine the voltage $U$ at which a beam of light leaving the cell becomes circularly polarized. Determine intensity $I_2$ of light output from the system in this case if the beam of natural light with intensity $I_i=0.06 \mathrm{~mW} / \mathrm{mm}^2$ is passed through the first linear polarizer $\mathrm{P}_1$.

# 光学代写

## 物理代写|光学代考Optics代写|Induced optical anisotropy

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。