# Error Propagation Question

1. May 13, 2014

### UncertaintyMan

My goal is to find the uncertainty $δd$ in the following equation.

$d=C_1 \frac{1}{\sqrt{V}} \frac{1}{D}$

• $C_1$ is the collection of constants $\frac{2Lhc}{\sqrt{2m_e c^2 }}$
• $D$ is a value measured in meters with an uncertainty $δD = 0.001 m$
• and $V$ is a value measured in volts with an uncertainty $δV = 100 V$

My best guess on how to calculate $δd$ is

$\frac{δd}{d}=|C_1| \sqrt{(\frac{δV}{V})^2+(\frac{δD}{D})^2 }$
... then plug in all the known values and solve for $δd$

...Unfortunately I have no resources to tell me if I'm doing this right. I appreciate any helpful pointers any of you may have, I'm a big time noob when it comes to error analysis.

For those of you who are curious, this is from a Bragg Scattering lab and $d$ represents the distance between atoms in a polycrystalline graphite crystal.

Last edited: May 13, 2014
2. May 13, 2014

### SammyS

Staff Emeritus
d is inversely prop. to √(V) , not V itself.

You should have something like:
$\displaystyle \frac{δd}{d}=|C_1| \sqrt{\left(\frac{δ(\sqrt{V})}{\sqrt{V}}\right)^2+\left(\frac{δD}{D} \right)^2 }$​

3. May 13, 2014

### UncertaintyMan

Awesome, thank you!

Quick side question: is it true that both of these equations have the same δd formula?

Equation 1. $d = \sqrt{V}D$
Equation 2. $d = \frac{1}{\sqrt{V}D}$

Error for either equation:
$\frac{δd}{d} = \sqrt{(\frac{δ(\sqrt{V})}{\sqrt{V}})^2 + (\frac{δD}{D})^2}$

4. May 13, 2014

### SammyS

Staff Emeritus
Yes, for reasonably small relative error.