Finding the Fresnel coefficients from interface conditions

[Cathr]

I'm studying for an exam (so this is existential) and I never really got how to write the limit conditions for an interface.

In my problem, there is an incident electric field, and there are two cases:
1) the field is polasised perpendicularly to the incidence plane (TE)
2) polarised in the plane (TM)

Here I must be able to correctly apply the limit conditions, to find the Fresnel formulas that give the amplitudes of the electric fields Er (reflected), Et (refracted) as a function of: Ei (incident field amplitude), ai (I meant so say alpha i, the angle of incidence) and ar (angle of refraction) and the constants that caracterise the environment for the two polarisations TE and TM.

The conditions are like E2-E1=0 or D2-D1=sigma (surface charge between media - how do we know there's any??) etc. I would like to know where they come from and how to be sure I'm writing them correctly and what they imply. Many many thanks in advance!

Sorry if my english doesn't quite fit your expectations. Eagerly waiting for your responses, if something's not clear please ask.

 

[BPHH85]

Hi

I think it might be helpful if you post the full problem with all possible pictures of the scenario you are talking about.

 

[Cathr]

Hi

I think it might be helpful if you post the full problem with all possible pictures of the scenario you are talking about.

I already found a solution, thank you! I might as well delete the thread. But, if you don't mind, please look at my other post on thermodynamics. I have an exam tomorrow and I would be really grateful if someone could help!