# 光学代写 optics代考2023

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## 光学代写optics

### 量子光学Quantum optics代写

• 反射（物理学）Reflection (physics)
• 折射Refraction

## 光学的历史

The history of optics is a part of the history of science. The term optics comes from the ancient Greek τα ὀπτικά. It is originally the science of everything related to the eye. The Greeks distinguish optics from dioptrics and catoptrics. We would probably call the first science of vision, the second science of lenses and the third science of mirrors. The great names of Greek optics are Euclid, Heron of Alexandria and Ptolemy.

Since antiquity, optics has undergone many developments. The very meaning of the word has varied and from the study of vision, it has passed in several stages to the study of light, before being incorporated recently into a broader body of physics.

## 光学相关课后作业代写

A glass plate is sprayed with uniform opaque particles. When a distant point source of light is observed looking through the plate, a diffuse halo is seen whose angular width is about $2^{\circ}$. Estimate the size of the particles. (Hint: consider Fraunhoffer diffraction through random gratings, and use Babinet’s principle)

The diffraction pattern of an opaque circular particle is complementary to that due to circular apertures of the same size in an otherwise opaque screen.
Under the Fraunhofer condition $\left(\frac{k\left(x^{\prime 2}+y^{\prime 2}\right)}{2 z} \ll 1, \frac{k\left(x^2+y^2\right)}{2 z} \ll 1\right)$
\begin{aligned} & E\left(x^{\prime}, y^{\prime}\right) \approx \frac{1}{z} \iint \exp \left(-i k\left(\theta_{x^{\prime}} x+\theta_{y^{\prime}} y\right)\right) t(x, y) E(x, y) d x d y \ & \text { Where } \theta_{x^{\prime}} \approx \frac{x \prime}{z}, \theta_{y^{\prime}} \approx \frac{y \prime}{z} \ & \end{aligned}
For the given problem, we may further assume $\mathrm{E}(\mathrm{x}, \mathrm{y})$ is a plane wave at normal incidence, and the transmission function $t(x, y)$ for a single can be expressed as:
$$t(x, y)=1-\operatorname{circ}\left(\frac{\sqrt{x^2+y^2}}{R}\right)$$
Where $R$ is the radius of the opaque particles.
$$\begin{gathered} E\left(x^{\prime}, y^{\prime}\right) \approx \frac{1}{z} \iint \exp \left(-i k\left(\theta_{x^{\prime}} x+\theta_{y^{\prime}} y\right)\right)\left[1-\operatorname{circ}\left(\frac{\sqrt{x^2+y^2}}{R}\right)\right] d x d y \ E\left(x^{\prime}, y^{\prime}\right) \approx \frac{1}{z} \mathcal{F}\left[1-\operatorname{circ}\left(\frac{\sqrt{x^2+y^2}}{R}\right)\right] \ \text { With } x^{\prime}=\frac{z}{k} k_x, y^{\prime}=\frac{z}{k} k_y \ E\left(k_x, k_y\right) \approx \frac{1}{z}\left[\delta\left(\sqrt{k_x{ }^2+k_y{ }^2}\right)-|R|^2 \frac{2 \pi J_1\left(R \sqrt{k_x^2+k_y{ }^2}\right)}{R \sqrt{k_x{ }^2+k_y{ }^2}}\right] \end{gathered}$$

Where $\gamma=R \sqrt{k_x^2+k_y^2}=\frac{2 \pi}{\lambda} R \theta$
From the above table,
$$\frac{2 \pi}{\lambda} R \Delta \theta=7.106-3.832=3.274$$
Taking central wavelength at visible frequency, $\lambda=500 \mathrm{~nm}$ and given $\Delta \theta=2^{\circ}$, we find the radius of the particle:
$$R=\lambda \frac{3.274}{(2 \pi)^2\left(\frac{\Delta \theta}{360}\right)}=500 \mathrm{~nm} \times\left(\frac{3.274}{(2 \pi)^2 \frac{2}{360}}\right)=7463 \mathrm{~nm}=7.4 \mu \mathrm{m}$$