Calculation of Fresnel equations:Reflection and Transmission Coefficients

Calculation of Fresnel equations:Reflection and Transmission Coefficients

1Incident angle:θi°-
2Refractive index:niRefractive index of incident medium
3Refractive index:ntRefractive index of transmitting medium
4GraphPlot Input Data: , Figure:
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Keyword・Reference・Remarks・History

LaTex


Markup:\\\theta _{t}=\sin^{-1}(\frac{n_{i}\sin\theta _{i}}{n_{t}}),\, \theta _{B}=\tan^{-1}\frac{n_{t}}{n_{i}}\\ r_{\parallel }=\frac{n_{i}\cos\theta _{t}-n_{t}\cos\theta _{i}}{n_{i}\cos\theta _{t}+n_{t}\cos\theta _{i}},\, r_{\perp }=\frac{n_{i}\cos\theta _{i}-n_{t}\cos\theta _{t}}{n_{i}\cos\theta _{i}+n_{t}\cos\theta _{t}}\\ t_{\parallel }=\frac{2n_{i}\cos\theta _{i}}{n_{i}\cos\theta _{t}+n_{t}\cos\theta _{i}},\, t_{\perp }=\frac{2n_{i}\cos\theta _{i}}{n_{i}\cos\theta _{i}+n_{t}\cos\theta _{t}}\\R_{\parallel }=r^{2}_{\parallel },\, R_{\perp}=r^{2}_{\perp},\, T_{\parallel}=\frac{n_{t}\cos\theta _{t}}{n_{i}\cos\theta _{i}}t^{2}_{\parallel},\,T_{\perp}=\frac{n_{t}\cos\theta _{t}}{n_{i}\cos\theta _{i}}t^{2}_{\perp}

Keyword

Fresnel's equation, Reflection and Transmission Coefficients, Incident angle, Reflected angle, Refracted angle, Refractive index of incident medium, Refractive index of transmitting medium, Snell's law.

Reference

[1]:Graham Woan著・堤正義訳:『ケンブリッジ物理公式ハンドブック』,共立出版,p.127,2007.
[2]:Georgia State University website. Fresnel's Equations
[3]:Raghuveer Parthasarathy:『5 REFLECTION AND TRANSMISSION(FRESNEL’S EQUATIONS)』.
[4]:Rick Trebino:『7. Fresnel's Equations for Reflection and Refraction』

Remarks

・Power reflectance:R
・Power transmittance:T
・Incident angle:θi
・Refractive index of incident medium:ni
・Refractive index of transmitting medium:nt
・Making Equation Image is powered by CODECOGS

History

・2010/08/19:Upload

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