Fresnel Equations | Refractive Index Interface

[xiaoipower]

Hi guys!

Was wondering if anyone was confident with Fresnel equations for a refractive index interface. From what I understand:

Assume incoming normal plane wave traveling in z-direction and polarised in x plane.

Assume z=0 is the plane that separates two materials: n_1 and n_2 (refractive index)

I think the Fresnel solution for the wave should go:

Ex = (for z>0) exp(-i*k0*n_1*z)+r*exp(i*k0*n_1*z)

(for z<0) t*exp(-i*k0*n_2*z)

the RED term representing the normal incident component and the GREEN term represents the reflected component which only exist in the n_1 half

and the BLUE term representing the transmitted component which only exists in the n_2 half.

I am uncertain about if I should be adding both the incident and reflected term (for z>0) as long as they are traveling in different directions or if I need to subtract them. i.e. should it be RED+GREEN or RED-GREEN? As I already have defined them to travel in opposite directions.

Any thoughts?

Many thanks!

 

[vanhees71]

You find the coefficients by solving for the boundary conditions at the surface between the two media. This can be found in any textbook on electrodynamics or optics.