Error analysis of acousto-optic effect

[jaykob_hxc]

Homework Statement

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.

Homework Equations

v = fλ1
λ1 = m*λ2/2sinθ

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.

 

[jbsteele]

I don't think I'm taking into account the error in θ properly. Any help would be greatly appreciated!