Error Propagation Question - Estimating a value based on straight fit lines

[JesseCoffey]

I have already turned this lab report in, but I am sure this will come up in the future. I just want to insure that I am doing it correctly.

Homework Statement

We did an experiment on the photoelectric effect. We found the negative voltage plateau and took readings of the photocurrent for small changes in the voltage being applied.

Homework Equations

Method of Least Squares
Error Propagation

The Attempt at a Solution

The instructor told me that even though the data will show a curve, that we should estimate where the peak is by extending the linear portions of the curve.

What I did was I separated the data into two different groups. Each one of the linear relations. I disregarded the data points on the curve portion that was between the two linear groups.

From these two groups I used the method of least squares to approximate a straight fit line to both relation ships. Once I had my linear equation ( y=m[tex]\pm[/tex][tex]\sigma[/tex]_mX + c[tex]\pm[/tex][tex]\sigma[/tex]_c )
I used the weighted method using the error I got from my readings (watched the voltmeter for 15 seconds and recorded the high and low)

I subtracted the two equations to find the value of X that satisfied both equations. This is the value i used to Estimate the stopping potential of the specific wavelength.

I repeated this for 7 different wavelengths.

Now that I had a data comparing frequency and stopping potentials, I graphed them together and formed another straight fit line, again using method of least squares.

I used the slope of this line to estimate the value of Planck's constant and to find the work function.

So, my question is, how exactly do I propagate the error through multiple equations?

I did it just as I did the mathematics. When I did the combination of the two line equations: when i subtracted the equations, I just did normal error propagation for the addition of two errors for both m and c. When I did the division to find the final value of x, I again did the normal propagation. This gave me an error of my estimated value.

I used these errors in the least squares error equations for the stopping potential vs frequency. And my final value had one more propagation to go (by substituting zero in for X).

Did I do this correctly? The part that worries me is that the difference in magnitude on the voltage compared to the photocurrent is quite large. so even though my answers were quite nice (linear relationship) the errors were tiny.

Thanks for any clarification.

 

[AvroArrow]

Yes, you did the error propagation correctly. Error propagation is a mathematical method of calculating the uncertainty of a measurement based on the individual uncertainties of each component used in the calculation. In this case, you used the errors from the two linear equations to calculate the uncertainty of the combined equation, then used that uncertainty to calculate the stopping potential and work function. The magnitude of the voltage compared to the photocurrent does not affect the error propagation, as long as the errors are properly accounted for.