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# 物理代写|光学代考Optics代写|PHYS202 Doppler effect

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## 物理代写|光学代考Optics代写|Doppler effect

A red shift by $\Delta \lambda=0.0001 \mu \mathrm{m}$ of the hydrogen spectral line at $\lambda_0=0.6565 \mu \mathrm{m}$ in the radiation spectrum of a star is measured using a spectrograph located on Earth. Determine the velocity $v$ of the star moving away from Earth.
A light source $S$ moves with velocity $|\vec{v}|=30 \mathrm{~km} / \mathrm{s}$ in a direction, forming an angle $\theta=45 \mathrm{deg}$ with the direction pointing at the photodetector PD. Determine the shift of the wavelength $\Delta \lambda$ of light received by the light detector with respect to the wavelength $\lambda_0=0.6 \mu \mathrm{m}$ of the light from motionless source S.

The light source $\mathrm{S}$ moves with velocity $\vec{v}_s$ in a direction forming angle $\alpha_s$ with the direction pointing at photodetector PD, which moves at angle $\alpha_p$ with respect to the same direction and has velocity $\vec{v}_p$. Determine frequency $v$ and wavelength $\lambda$ of the light received by photodetector PD if the wavelength of light emitted by the motionless source (in its own reference frame) is $\lambda_0$. The velocities of the source and the detector are small compared to the velocity of light.

## 物理代写|光学代考Optics代写|Sagnac interferometer

In a Sagnac interferometer placed on a rotating platform, the light beam from source $\mathrm{S}$ with wavelength $\lambda_0$ is split by beam splitter BS into two beams that, by means of three mirrors $\left(\mathrm{M}_1, \mathrm{M}_2\right.$, and $\left.\mathrm{M}_3\right)$, are made to propagate in the opposite directions along the perimeter of the square with length of side $L$. Determine the phase shift $\Delta \phi$ arising between the interfering waves at the output of the interferometer, owing to the rotation of the platform with angular velocity $\Omega$.

A fiber optic gyroscope (fiber optic Sagnac interferometer) is mounted on a rotating platform. Light with wavelength $\lambda_0$ from source $S$ is introduced into an optical fiber with refractive index $n$, split by coupler $\mathrm{BS}$ into two waves that propagate in opposite directions along a fiber with length $L$ laid in $N$ rings, returned to the coupler BS, and is superposed in the output fiber branch and then on the photodetector $\mathrm{PD}$ used to detect the signal $u_P(t)$ of interference of these two waves. Determine the period of interference signal $T$ when the platform is rotating with uniformly variable angular velocity $\Omega(t)$, with constant angular acceleration $\eta=d \Omega / d t=$ const.

# 光学代写

## 物理代写|光学代考Optics代写|Sagnac interferometer

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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。