Answer to Question #284481 in Optics for luna

Question

Reflection of a plane wave at the interface between two dielectrics.

Answer 1

We know that

Incidence wave $E=E_0e^{j(k.r-wt)}$

$Reflected wave \\E_1=E_{01}e^{j(k_1.r-w_1t)}$

Refracted wave

$E_2=E_{02}e^{j{(k_2.r-w_2t)}}$

$k_1$ = Reflected wave propagation constant

$k_2$ =Refracted wave propagation constant

$k=$ Incidence wave propagation constant

$k_{1x}=k_{2x}=k_x$

$k_{1r}=k_{2r}=k_r$

For reflection

$k_{1x}=k_{x}$

$k_1sin\theta_1=ksin\theta$

$k_1=k$

$sin\theta_1=sin\theta$

$\theta_1=\theta$

This is reflection law