Propagation of Error for Focal Length

[Browntown]

Homework Statement: Propagation of Error for Focal Length
Homework Equations: f = (s'*s) / (s' + s)

In my lab, we had to calculate the focal length of a lens based on object distances (s) and image distances (s') that we measured. The object distances were measured with an uncertainty of Delta s = +/- 1mm and image distances were measured with an uncertainty of Delta s' = +/- 2.5 mm.

Since we had to add, multiply and divide values, I'm not quite sure what to do to propagate the error from those two values into the one for focal length.

Any help would be much appreciated.

Thank you.

[Moderator's note: Moved here as it is of general interest and not a specific homework exercise.]

 

[haruspex]

Homework Statement: Propagation of Error for Focal Length
Homework Equations: f = (s'*s) / (s' + s)

In my lab, we had to calculate the focal length of a lens based on object distances (s) and image distances (s') that we measured. The object distances were measured with an uncertainty of Delta s = +/- 1mm and image distances were measured with an uncertainty of Delta s' = +/- 2.5 mm.

Since we had to add, multiply and divide values, I'm not quite sure what to do to propagate the error from those two values into the one for focal length.

Any help would be much appreciated.

Thank you.

There are two approaches to this.
In engineering, where tolerance limits may be crucial, you simply plug in combinations of extreme values and look at the results that come out.
In science, it is standard to use a statistical approach. See http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm for the formulae that apply to products and sums. However, the formulae there assume the measurements are independent. If you treat the s' in the numerator as independent of the s' in the denominator you will get a greater error than is correct. So to use these formulas you need to put the equation into the form $f=\frac 1{\frac 1s+\frac 1{s'}}$.

 

[Browntown]

Oh ok, thank you, I'll give that a try