﻿ Calculation of Fresnel equations：Reflection and Transmission Coefficients

# Calculation of Fresnel equations：Reflection and Transmission Coefficients

 1 Incident angle：θi ° - 2 Refractive index：ni Refractive index of incident medium 3 Refractive index：nt Refractive index of transmitting medium 4 Graph x-axis：θi(°),y-axis：r：Reflection Coefficient x-axis：θi(°),y-axis：t：Transmission Coefficient x-axis：θi(°),y-axis：R,T：Parallel x-axis：θi(°),y-axis：R,T：Perpendicular Plot Input Data： YesNo , Figure： OnOff
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## 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