Chi-Square in Fraunhofer Approximation Lab Report

[tedkopel]

Hello there if anyone could help me out with this question I would very much appreciate it. (Note this is my first post)

For my optics lab Fraunhofer(single slit) diffraction patterns were observed(measured distance to screen(x) and had readings for intensity in the y direction.) I converted the y distances into degrees by taking inverse tangent (y/x). So for horizontal values I have my theta and vertical values my intensity. The experiment looks like this

http://physics.wpi.edu/wiki/images/...ffraction.GIF/180px-SingleSlitDiffraction.GIF
<br><img src="http://physics.wpi.edu/wiki/images/thumb/5/5e/SingleSlitDiffraction.GIF/180px-SingleSlitDiffraction.GIF" /><br>


Anyway for my data, when plotted, I had the standard gaussian looking bell curve(i know it isn't a gaussian curve, but right now i can't think of better words to describe this). It looks like this

http://cnx.org/content/m12915/latest/SingleSlitDiffraction__3.png
<br><img src="http://cnx.org/content/m12915/latest/SingleSlitDiffraction__3.png" /> <br>

I was wondering how I calculate the uncertainty for these results. My professor mention a Chi-Square was possible. I don't see how I could calculate the theoretical value, even when I used the value for my experiment maximum intensity at I(0), for this experiment. This is the formula I am using for Fraunhofer approximation

I(ϴ)=I(0) {sin(∏D(sin(ϴ)/λ) / (∏D(sin(ϴ)/λ) )}^2

Where I(0) is the intensity for Ө=0(maximum intensity), λ is the wavelength, and D is the slit width.

 

[Nate810]

Any help/suggestions would be great. To calculate the uncertainty in your measurement results, you will need to use a statistical technique, such as a Chi-Squared test. The Chi-Squared test is used to compare your measured values with the theoretical model that you are using (in this case the Fraunhofer approximation). The Chi-Squared test provides a measure of how well the observed data fits the model, and the resulting value can be used to determine the uncertainty in your measurements. You can find more information about the Chi-Squared test here: https://en.wikipedia.org/wiki/Chi-squared_test