Predicting the actual points of total constructive interference requires us to forgo using the small angle approximation. The path length difference for constructive interference is mλ = d sin θm and the distance of the maxima to the central peak are ym = L tan θm.
eq 9: ym, approx = mλL d
(a) Using Eq. 9 and your favorite spreadsheet application, calculate the distances ym, approx to the maxima for a double-slit diffraction pattern generated by a laser with λ = 750nm shining on a double slit with slit width of d = 0.1mm, with distance to the screen of L = 2m and m = 1 to m = 22.
(b) Using the above equations, find an expression for ym, corrected as a function of m, λ, d and L without using the small angle approximation. Please show any work separate from your spreadsheet.
(c) Using your expression from step 2b and the numbers in step 2a, calculate ym, corrected for m = 1 to m = 22. Hint: the function for the arcsin in both Excel and Google Spreadsheet is "=ASIN()".
(d) Calculate the percent error between ym, approx and ym, corrected using ym, corrected as the accepted value. At what value of m does the error exceed 1%?
(e) Does the error depend on the distance to the screen, L? How did you deduce this OR what is your reasoning?