# Mutilple beam reflection question in Fabry-Perot cavity

1. Sep 29, 2016

### anthony27149

1. The problem statement, all variables and given/known data
Just having some trouble with a question about Fabry-Perot intereferometers. Here's the question:

a) Consider a beam of light undergoing multiple reflections in a Fabry-Perot cavity between two surfaces, both with reflectance R, and with no absorption.

2. Relevant equations

3. The attempt at a solution

So my problem is incorporating N into my final answer. I've derived a general equation of the electric amplitude of the reflected waves inside the cavity (as shown in this diagram), which I found to be:

EN = A·τ·ρ'N·ei(ωt-Nδ),

where ρ is the Fresnel reflection coefficient and τ is the transmission coefficient [Not sure if the equation is entirely correct]

And by geometric series:

Ec = A·τ·ei·ω·t/(1-sqrt(R)·e-iδ)

Using a power density function for both inside the cavity Sc and the original beam S:

Sc = 1/2·nf·c·ε(Ec*·Ec),

where E* is a complex conjugate

S = 1/2·n·c·ε·A2

I get: Sc/S = (nf·τ2 )/(n·(1-sqrt(R))2 ·(1+C·sin2 (δ/2))),

where C is 4·sqrt(R)/(1-sqrt(R))2

So, as you can see, this ratio doesn't have the number of reflections N, and I'm not sure where to go from here.

2. Sep 29, 2016