# Solution to Exercise 5.1-1: Derivation of Snellius Law

| Show that you obtain Itr = Iin – Iref and Snellius law (sina/sinb = n) from energy and momentum conservation
| Solution:
|  | The intensity I of the beams is given by their power (energy /t) which is given by the nunber of photons/s in the beams: Ein, Ere, Etr. Everythin always per cm2 but that is not important for what follows.
|  | Energy conservation demands
Ein | = | Ere + Etr
--- | --- | ---
Etr = | = | Ein – Ere
Itr = |  | Iin – Ire
| Looking at the x-component of the momentum p and considering that the wavelength in the material is l/n we have
|pz, in| | = | Iinkin · sina | = | Iin · 2p · sina l
--- | --- | --- | --- | ---
|pz, re| | = | Irekre · sina | = | Ire · 2p · sina l
|pz, tr| |  | Itrktr · sinb | = | Itr · 2p · sinb · n l
|  | Momentum conservation demands that pz, in + pz, tr – pz, re = 0, or
Iin sina + Itr sinb · n – Ire sina | = | 0
--- | --- | ---
|  | Substituting Ire = Iin – Itr leads straight ot
n | = | sina sinb
--- | --- | ---

With frame

Exercise 5.1.1 Derivation of Snellius Law

Exercise 5.2.4 Fresnel Equations and Polarization

© H. Föll (Advanced Materials B, part 1 - script)