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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Thin Lenses

Lenses are very important optical devices employed in optical methods of experimental mechanics. In this section, we will study lenses using the concept of light rays within the frame of geometric optics. Lenses as Fourier transform analyzers will be examined later on in this chapter in the section of diffraction.

A lens is a simple transmissive optical devise that focuses or disperses light. It is made of glass or transparent plastic, so its index of refraction is higher than that of the surrounding air. Its principle of operation is based on refraction (Snell’s law). It usually consists of two spherical surfaces, even though cylindrical surfaces are possible. A thin lens is defined by a small diameter compared to the radii of curvature of the two lens surfaces. The two surfaces of a thin lens can be concave, convex, or flat (Fig. 2.8). The axis of the lens is a straight line that is perpendicular to the two surfaces of the lens and passes through its center. The lenses are divided into converging and diverging. A converging lens is thicker at the center than at the edges. A diverging lens is thinner at the center than at the edges (Fig. 2.8). When a beam of light parallel to the axis strikes a converging lens the refracted rays after passing the lens are focused to a point called the focal point $\mathbf{F}$ of the lens (Fig. 2.9a). If parallel rays fall at a lens at an angle they focus at a different point $\mathbf{F}{\mathrm{a}}$ at the same distance from the lens (Fig. 2.9). The plane of all points $F$ and $F{a}$ are called the focal plane of the lens (Fig. 2.9b). When the bean strikes a diverging lens the refracted rays appear to diverge at the focal point (Fig. 2.10). A lens has two focal points, symmetrical with respect to the lens. The distance of the focal point $F$ from the lens is called the focal length, $f$. It is the most important property of a lens.

## 物理代写|力学代写mechanics代考|The Wave Nature of Light—Huygens’ Principle

Geometric optics which is based on the concept of the light ray was successfully used in the previous sections to explain the phenomena of reflection and refraction and the formation of images by mirrors and lenses. However, geometric optics does not account for the explanation of the phenomena of interference and diffraction of light. For such phenomena, the wave or the electromagnetic theory of light is most appropriate. Optical phenomena that can be explained by these theories of light are dealt with by the so-called physical optics.

Huygens proposed a technique within the frame of the wave theory of light for finding the shape of a wave front at a later time from the wave front at a present time. This technique, known as Huygens’ principle may be stated as: each point on a wave front may be regarded as a source of secondary tiny wavelets that propagate in all directions at a speed equal to the speed of propagation of the wave. The position of the new wave front is the envelope of these secondary wavelets.

We apply Huygens’ principle to explain the propagation of light from a point light source and the phenomena of reflection and refraction. Later, we will use this principle for the explanation of the diffraction of light.

Propagation of light from a point source: It is well established that light from a point source propagates in a homogeneous isotropic medium along spherical wave fronts. Consider a point light source at $S$ and the spherical wave front $A B$ of light traveling at a speed $v$ and find the new wave front after time $t$ (Fig. 2.12). From each point of $A B$ we construct circles of radius $r=v t$ centered at that point. The envelope of these circles (wavelets) in the direction of propagation of the wave is the new wave front $A^{\prime} B^{\prime}$. It is a spherical surface as the wavefront $A B$.

# 力学代考

## 有限元方法代写

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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。

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