# Homework Help: Calculating Experimental Error of Braggs Equation

1. Oct 5, 2014

### Lemenks

1. The problem statement, all variables and given/known data

I am writing a lab report for an X-ray diffraction. I have been attempting to come up with an equation for the error using formulas some people from college gave me and also some I found on wikipedia but I am quite sure I am doing it wrong. The only variable is the angle where the maximum intensities are found. I am using Bragg's law to calculate the spacing between the atoms.

2. Relevant equations

D = (N*wavelength)/(2*sin(x))

As there is no error in N, wavelength, or "2", we can let that equal A.

D = A/sin(x)

Some equations I was given:

Z = aX
dZ = adX

Z = X^a
dZ/z = |a|dx/x

Z = SinX
dZ = dX CosX

3. The attempt at a solution

D = Z = A/sin(x) = A (sin(x))^-1 = A f(y)^-1

I have tried loads of ways of calculating this but I keep getting silly answers. Any help, ideas or links would be really appreciated.

2. Oct 5, 2014

### BvU

Hello Lemenks, and welcome to PF :)

I don't see an attempt at solution under 3, only a repeat of D=A/sin(x).

From your account, I think what you are asking is: What is the error in D = A/sin(x), given the error in x. Correct ?

Your relevant equations are some examples of error propagation in functions of a single variable. Generally: $df = {df\over dx} dx$, which in error analysis is extended to finite differences: $\Delta f = {df\over dx} \Delta x$.
Do you know how to find the derivative of 1/sin(x) ?

And I am interested in the way you determine $\Delta x$ too. Is it really just a simple reading off of a single angle ?

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