<jupyter_start><jupyter_text>Show that the oblique incidence case can be handled by the Lorentz boost method. Proof: ![](./img/ObliqueIncidence.jpg)We can apply the Lorentz transform formula. After boost by $c\sin \theta$ in $y$  direction, the speed of light in the new reference frame is$$\begin{aligned}v_y=&\frac{c\sin\theta-c\sin\theta}{1-\beta\sin\theta}=0\\v_x=&\frac{\gamma c\cos\theta}{1-\beta\sin\theta}\end{aligned}$$where $\beta=\cfrac{c\sin\theta}{c}=\sin\theta$, then we can simplify the formulas (2) into$$\begin{aligned}\gamma&=\sqrt{1-\beta^2}=\cos \theta\\v_x&=c\end{aligned}$$In other words, in the view of the observer in the new frame, the incidence EM wave is parallel to the $x'$ axis, and the speed of EM wave is still $c$.Which is apparent since there's a basic principle that the speed of light should be conserved. Note that now the plasma are in motion, with velocity $v_y'=-c\sin\theta$.![](./img/Boosted.jpg)  Use the JPIC1d program to simulate the relativistic Doppler effect. Plot how the reflected wave frequency depends on the flying mirror's $\gamma$ factor, and compare the result with theoretical predictions.<jupyter_code>with open("./jpic1d_comp/data/input.inp","+") as f:<jupyter_output>驱动器 D 中的卷是 Data
 卷的序列号是 84CA-CF99

 D:\Shaw Haines\OneDrive - zju.edu.cn\Curriculum\Physics\Computational Physics\Homework 的目录

2021/01/16  11:05    <DIR>          .
2021/01/16  11:05    <DIR>          ..
2020/12/18  16:20               428 .gitattributes
2020/12/28  22:33                88 .gitignore
2021/01/16  10:35    <DIR>          .ipynb_checkpoints
2020/12/18  16:07           345,915 08_PDE.html
2020/12/03  12:21            95,134 1.pdf
2020/12/18  16:18             1,541 1_Nondimensionalization.md
2021/01/16  11:05             3,047 10_JPIC.ipynb
2021/01/16  09:42           605,488 11_MonteCarlo.ipynb
2020/12/06  15:49           134,022 2.pdf
2020/12/18  16:18             2,868 2_ErrorAnalysis.md
2020/12/18  16:18             7,184 2_SubtractiveCancelation.ipynb
2020/12/09  22:30         1,734,295 3_Interpolation.pdf
2020/12/18  16:18             2,982 4_Differential.ipynb
2020/12/18  16:18            57,123 5_Integral.ipynb
2020/12/20  16:18           309,802 6_ODE.ipynb
2020[...]
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