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Homework Statement
How can I calculate the relative error of a laser beam waist and angle of divergence using this experimental data:
I have measured the increase in laser beam diameter as the distance from the laser increases. With this data I plotted a graph of distance from the laser beam2 vs. laser beam diameter2.
Homework Equations
half angle of divergence = 2*λ / π*s0
s2=s02+Φ2z2
s0: beam waist
z: distance of beam from source
Φ: angle of divergence
The Attempt at a Solution
I fitted a LINEST trendline in excel to the graph of laser beam2 vs. laser beam diameter2, which equals y = 4.7E-7x + 3.4E-1. I also got absolute uncertainties in both of these values, being 5.5E-9 for the 4.7E-7, and 6.24E-3 for the 3.4E-1.
I know that from the trendline 3.4E-1 = beam waist2. Taking the √3.4E-1 gives me the beam waist = 5.8E-1. Converting this beam waist to 1/e2 gives a beam waist = 8.2E-1 mm
If I use the equation: half angle of divergence = 2*λ / π*beam waist = 4.8E-4. Multiplying by 2 and the full angle of divergence = 9.6E-4 rad.
beam waist = 8.2E-1 mm and angle of divergence = 9.6E-4 rad are consistent with the manufacturers specs, but I'm not sure how to calculate the relative uncertainties of each.
Any guidance would be much appreciated.