1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mutilple beam reflection question in Fabry-Perot cavity

  1. Sep 29, 2016 #1
    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. jcsd
  3. Sep 29, 2016 #2

    Charles Link

    User Avatar
    Homework Helper
    Gold Member

    The (sum of the ) geometric series that you (correctly) used assumes an infinite number of reflections, of which the E amplitude for the Nth reflection contributing to the sum gets smaller and smaller. The derivation for this can also be found in the Optics Textbook by Hecht and Zajac if you wish to check your algebra.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted