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Error analysis of acousto-optic effect

  1. Oct 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Hey guys,

    I have recently done an experiment in regards to the acousto-optic effect (which in itself is freaking amazing!!). And i need to do an error analysis for my value of the phase velocity.
    I believe i have made a mistake but i can't find it anywhere.

    Firstly i have an equation relating tanθ = H/L

    so Δθ = Δ(tanθ)/sec^2(θ)
    where Δ(tanθ)^2 = tanθ[(Δh/h)^2 + (Δl/l)^2]

    then i have the equation of snells law n1sinθ1 = n2sinθ2

    so Δsinθ1 = cosθΔθ

    we can then say that Δsinθ1 = Δsinθ2 since snell's law dosen't introduce anymore error.

    now here comes the fun part. let λ1 be the wavelength of the soundwave and λ2 be the wavelength of the laser and m is an integer so:

    λ1 = m*λ2/2sinθ

    no i'm trying to determine the error in λ1 so that i can determine the error in v = fλ1.


    2. Relevant equations

    v = fλ1
    λ1 = m*λ2/2sinθ


    3. The attempt at a solution

    so far i've got:

    (σλ1)^2 = (σλ2)^2(∂λ1/∂λ2)^2 + (σm)^2(∂λ1/∂m)^2 + (σθ)^2(∂λ1/∂θ)^2

    since m is an integer:

    (σλ1)^2 = (σλ2)^2(∂λ1/∂λ2)^2 + (σθ)^2(∂λ1/∂θ)^2

    however i don't think this is correct.
     
  2. jcsd
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