# Data-analysis (Uncertainty and errors)

This is just a data anlysis question but I thought you might need an introduction.

In order to calibrate de Michelson interferometer one needs to find $\eta$ in the relation: $d = \eta D_\mu$ where $d$ is the displacement of the mobile mirror with respect to the light source and $D_\mu$ is the micrometric change done with the screw that moves the mirror.

We registered how many micrometers (from the screw) $D_\mu$ were needed to repeat $n$-times the position of the interference pattern of light. Then knowing that each time the pattern repeated itself the mirror moved $d=\frac{\lambda}{2}$ we have $\eta D_\mu=n\frac{\lambda}{2}$.

Here are my questions:

We have four sets of measurements for $D_\mu$ ($n=5,10,15,20$) each with five values. To find $\eta$ we've made a linear fit ($d = a D_\mu + b$) using the average $D_\mu$'s. I want to know what is the correct error related to each $\overline{D_\mu}$ so I can use propagation of errors and get the error for $\eta$. Is it $\frac{\sigma}{\sqrt{N}}$ or the propagation of each measurement's uncertainty which would result in 2.2$\mu$m (using $\delta\overline{D_\mu}² = [\frac{\partial D_\mu}{\partial D_{\mu1}}\delta D_{\mu1}]²+...+$ , given that the uncertainty of each measurement is 5$\mu$m

Is it maybe the sum of both errors?

Also, what am I supposed to do with the second coefficient of my fit $b$, should I just ignore it??