If we take d to be the central point of every millimeter marking then we can see that the path length difference between two beams incident at nearby millimeter marks and then continuing to the wall will be as shown in equation \ref{eq:1}. Some hesitation may come from the knowledge that the end of the ruler is not necessarily cut so that there is only 1 millimeter left after the final measurement mark but in general the laser should incident with enough millimeter markings, given the small angle, that this final discrepancy does not affect our ability to measure an appropriate bright spot.
Data
Data was evaluated by two methods. First by rearranging equation \ref{eq:1} into its linear form and then by treating \(\cos\left(\beta_n\right)\) as our y variable, \(n\) as our x variable, and \(\lambda\) as our slope and parameter to be fit too. A best fit was then made using the scipy.optimize package of python and the standard deviation of our best estimate was taken by the square root of the covariance also generated by the scipy.optimize package. Error in our measurements of \(\cos\left(\beta_n\right)\) were included so that a visual estimate of the accuracy of the best fit could be made. These errors were created via equation \ref{eq:3}.