Answer to Question #180859 in Electricity and Magnetism for passout

Question

Assume that the wave is propagating from free space and striking to a dielectric medium normally. Give the derivation for reflection and transmission coefficient.

Answer 1

Solution:-

To be asked in question

Reflection coefficient (R)=?

Transmission cofficient (T)=?

We know that fregenel equation

Reflection coefficient

$E_{or}=\frac{n_{1}-n_{2}}{n_{1}-n_{2}}E_{i}$

Transmission cofficient

$E_{oT}=\frac{n_{1}}{n_{1}+n_{2}}E_{i}$

Relation between c and v and n

$v=\frac{c}{n}$

Intensity

$I=\frac{1}{2}\epsilon vE^2$

We know that

R=$\frac{I_{R}}{I_{I}}$

$R=[\frac{E_{OR}}{E_{oi}}]^2$

$R=(\frac {n_{1}-n_{2}}{{n_{1}+n_{2}}})^2$

Transmission cofficient

$T=\frac{I_{T}}{I_{R}}$

$T=\frac{\epsilon_{2}v_{2}}{\epsilon_{1}v_{1}}(\frac{E_0T}{E_0i})^2$

$T=\frac{4n_{1}n_{2}}{(n_{1}+n_{2})^2}$

$R+T=1$