## 物理代写|力学代写mechanics代考|The Ellipsoid Mirror

Consider an axisymmetric ellipsoid mirror with semiaxes $a$ and $b$ along the $z$ and $r$ axes, respectively, illuminated by a point light source $S$ placed along its axis of symmetry $z$ at a distance $A$ from the $r$-axis (Fig. 6.2). A reference screen is placed at a distance $z_0$ from the $r$-axis. The equation of the surface $z=f(x, y)$ of the mirror referred to the system $\operatorname{Orz}$ is
$$z=f(x, y)=\frac{a}{b}\left(b^2-r^2\right)^{1 / 2}$$
The equation of the caustic on the screen is given by Eq. (6.11) with
$$\tan \alpha=\frac{\mathrm{d} z}{\mathrm{~d} r}, \quad \tan \varphi=\frac{r}{A+z}$$
Using Eq. (6.13) we obtain the following equation for the initial curve of the caustic

$$\frac{z_0}{b}=\frac{B_1\left[1-\left(\frac{r}{b}\right)^2\right]^{1 / 2}+B_2}{\Delta_1\left[1-\left(\frac{r}{b}\right)^2\right]^{1 / 2}+\Delta_2}$$
with
\begin{aligned} B_1=& 2\left(\frac{a}{b}\right)^2\left{1+\left[\left(\frac{a}{b}\right)^2-1\right]\left(\frac{r}{b}\right)^2-\left(\frac{a}{b}\right)^2\right} \ &+\left{1-\left[\left(\frac{a}{b}\right)^2+1\right]\left(\frac{r}{b}\right)^2-2\left(\frac{a}{b}\right)^2\right}\left(\frac{\mathrm{A}}{b}\right)^2 \ B_2=\left(\frac{A}{b}\right)\left(\frac{a}{b}\right)\left(3\left{1+\left[\left(\frac{a}{b}\right)^2-1\right]\left(\frac{r}{b}\right)^2\right}-4\left(\frac{a}{b}\right)^2\right) \ \Delta_1 &=\left(\frac{A}{b}\right)\left{1+\left[\left(\frac{a}{b}\right)^2-1\right]\left(\frac{r}{b}\right)^2-4\left(\frac{a}{b}\right)^2\right} \ \Delta_2=&\left(\frac{a}{b}\right)\left(\left{1+\left[\left(\frac{a}{b}\right)^2-1\right]\left(\frac{r}{b}\right)^2\right}\right.\ &\left.-2\left{\left(\frac{a}{b}\right)^2-\left[\left(\frac{a}{b}\right)^2-1\right]\left(\frac{r}{b}\right)^2\right}-2\left(\frac{A}{b}\right)^2\right) \end{aligned}

## 物理代写|力学代写mechanics代考|Intensity Distribution of Light Rays Reflected

The intensity of light reflected from the front or the rear face of the specimen is the same at each reflection; let $\beta$ be the reduction ratio of the intensity of reflected rays relative to the incident rays $(\beta<1)$. The reduction ratio for the rays that refract at the two faces differs for the rays that enter or emerge from the specimen. Let $\alpha$ and $\alpha^{\prime}$ be the corresponding reduction ratios.

If $I$ is the intensity of the incident light ray, the intensity of the first reflected ray is $\beta I$ and the intensity of the first refracted ray is $\alpha I$. This last ray emerges from the rear face of the specimen with intensity $\alpha \alpha^{\prime}$ I. At reflection from rear face, the ray passes through the thickness of the specimen with intensity $\alpha \beta 1$. The intensity of light for the first three rays that emerge from the front face and the first two rays that emerge from the rear face of the specimen is shown in Fig. 6.5. According to the law of conservation of energy and assuming that the specimen does not absorb light energy we have
$$I=I_f+I_r$$
where $I_f$ and $I_r$ are the total intensity of light that emerges from the front and rear faces of the specimen, respectively.
We obtain for the intensities $I_f$ and $I_r$
$$\begin{gathered} I_f=\beta I+\alpha \alpha^{\prime} \beta\left(1+\beta^2+\beta^4+\beta^6+\cdots\right) I=\beta\left(1+\frac{\alpha \alpha^{\prime}}{1-\beta^2}\right) I, \quad \beta<1 \ I_r=\alpha \alpha^{\prime}\left(1+\beta^2+\cdots\right) I=\frac{\alpha \alpha^{\prime} I}{1-\beta^2} \end{gathered}$$
Introducing the values of $I_f$ and $I_r$ into Eq. (6.23) we obtain
$$I=\beta\left(1+\frac{\alpha \alpha^{\prime}}{1-\beta^2}\right) I+\frac{\alpha \alpha^{\prime} I}{1-\beta^2}$$
from which it follows that
$$\alpha \alpha^{\prime}=(1-\beta)^2$$

## 物理代写|力学代写mechanics代考|The Ellipsoid Mirror

$$z=f(x, y)=\frac{a}{b}\left(b^2-r^2\right)^{1 / 2}$$

$$\tan \alpha=\frac{\mathrm{d} z}{\mathrm{~d} r}, \quad \tan \varphi=\frac{r}{A+z}$$

$$\frac{z_0}{b}=\frac{B_1\left[1-\left(\frac{r}{b}\right)^2\right]^{1 / 2}+B_2}{\Delta_1\left[1-\left(\frac{r}{b}\right)^2\right]^{1 / 2}+\Delta_2}$$

## 物理代写|力学代写mechanics代考|Intensity Distribution of Light Rays Reflected

$$I=I_f+I_r$$

$$I_f=\beta I+\alpha \alpha^{\prime} \beta\left(1+\beta^2+\beta^4+\beta^6+\cdots\right) I=\beta\left(1+\frac{\alpha \alpha^{\prime}}{1-\beta^2}\right) I, \quad \beta<1 I_r=\alpha \alpha^{\prime}\left(1+\beta^2+\cdots\right) I$$

$$I=\beta\left(1+\frac{\alpha \alpha^{\prime}}{1-\beta^2}\right) I+\frac{\alpha \alpha^{\prime} I}{1-\beta^2}$$

$$\alpha \alpha^{\prime}=(1-\beta)^2$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: