Solving for d in Bragg's Law | Quick Question

[cahill8]

Homework Statement

I am inquiring about Braggs Law $$2 d\sin\theta = n\lambda$$.
The question I'm working on gives me the first four Bragg angles ($$\theta$$ values) and I have also calculated the wavelength of the light. I want to solve for d but I am unsure what value to use.

Homework Equations

Rearranging for d: $$d = \frac{n\lambda}{2\sin\theta}$$

The Attempt at a Solution

I seem to have multiple options. Using the different $$\theta$$ values with the corresponding n value (n=1,2,3,4) gives a different answer for d each time. I'm not sure whether to use just the first value ($$\theta_1$$ and n=1) or whether I should sum them all and divide by 4 to get an average? This site http://www.bruker-axs.de/fileadmin/user_upload/xrfintro/sec1_8.html (1/4 of the way down) suggests that each $$\theta$$ and corresponding n value account for different reflection orders. To me this sounds like the best value would be getting the average but I just want to make sure.

i.e. $$d = \frac{1}{4}\left(\frac{\lambda}{2\sin\theta_1}+...+\frac{4\lambda}{2\sin\theta_4}\right)$$

What do you think?

 

[fzero]

It would be better to use all 4 data points to establish a linear relationship which is such that you can obtain d as the slope. You could either do this graphically or by using the formulas for a linear regression http://en.wikipedia.org/wiki/Simple_linear_regression#Fitting_the_regression_line

 

[sungod]

Plot sin(theta) against n. This is a linear equation with a slope of lambda/2d. If you know lambda, you can get d.