Bending of light Snell's law Equation Formula Latex Code and Summary

Bending of light Snell's law

Tags: #physics #optics #Snell's law

Equation

$$n_i\sin(\theta_i)=n_t\sin(\theta_t) \\ \frac{n_2}{n_1}=\frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2} \\ n^2=1+\frac{n_{\rm e}e^2}{\varepsilon_0m}\sum_j\frac{f_j}{\omega_{0,j}^2-\omega^2-i\delta\omega} \\ v_{\rm g}=c/(1+(n_{\rm e}e^2/2\varepsilon_0m\omega^2)) $$

Latex Code

                                 n_i\sin(\theta_i)=n_t\sin(\theta_t) \\
            \frac{n_2}{n_1}=\frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2} \\
            n^2=1+\frac{n_{\rm e}e^2}{\varepsilon_0m}\sum_j\frac{f_j}{\omega_{0,j}^2-\omega^2-i\delta\omega} \\
            v_{\rm g}=c/(1+(n_{\rm e}e^2/2\varepsilon_0m\omega^2))

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Introduction

$\Psi(t)=\hat{\Psi}(t)e^{i(\omega t \pm \phi)}=\hat{\Psi}(t)\cos (\omega t \pm \phi) \\ \sum_{i} \hat{\Psi_{i}}\cos(\alpha_{i} \pm \omega t) =\hat{\Phi}\cos (\beta \pm \omega t) \\ \tan (\beta)=\frac{\sum_{i} \hat{\Psi_{i}} \sin (\alpha_{i})}{\sum_{i} \hat{\Psi_{i}} \cos (\alpha_{i})} \\ \hat{\Phi}^{2} = \sum_{i} \hat{\Psi_{i}^{2}} + 2 \sum_{j > i} \sum_{i} \hat{\Psi_{i}} \hat{\Psi_{j}} \cos (\alpha_{i} - \alpha_{j}) \\ \int x(t) dt=\frac{x(t)}{i \omega} \\ \frac{d^{n}(x(t))}{d t^{n}}=(i \omega)^{n} x(t)$

Latex Code

            n_i\sin(\theta_i)=n_t\sin(\theta_t) \\
            \frac{n_2}{n_1}=\frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2} \\
            n^2=1+\frac{n_{\rm e}e^2}{\varepsilon_0m}\sum_j\frac{f_j}{\omega_{0,j}^2-\omega^2-i\delta\omega} \\
            v_{\rm g}=c/(1+(n_{\rm e}e^2/2\varepsilon_0m\omega^2))

Explanation

Latex code for the Bending of light, Snell's law. I will briefly introduce the notations in this formulation.

$n$ : refractive index of the material
$n_{\rm e}$ : electron density
$f_j$ : oscillator strength

Discussion

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Richard Miller

I'm aiming for a successful outcome on this exam.

2023-04-09 00:00
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Walter Kelley reply to Richard Miller

Gooood Luck, Man!

2023-04-09 00:00
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Lawrence Howard

Really hoping for a pass on this exam.

2023-01-12 00:00
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Amanda Harris reply to Lawrence Howard

Gooood Luck, Man!

2023-01-12 00:00
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Jacob Wright

A pass in this test is all I need to move forward.

2023-08-07 00:00
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Nathan Cooper reply to Jacob Wright

Nice~

2023-08-24 00:00
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