A student wants to record the first seven bright fringes (m=1 through m=7) of a double-slit interference pattern while ensuring that the small-angle approximation remains within 5% error for every recorded fringe. Three experimental setups using light of wavelength λ=560nm are proposed:
Setup A: d=0.12mm, L=1.0m
Setup B: d=0.25mm, L=1.5m
Setup C: d=0.08mm, L=0.75m
(a) For each setup, calculate the angle θ7 corresponding to the seventh bright fringe and determine the percent error between tanθ7 and θ7. Present your results in a comparative table.
(b) Identify which setup(s), if any, satisfy the 5% error requirement for all fringes m=1 through m=7. Justify quantitatively.
(c) Discuss two experimental trade-offs (such as fringe spacing or pattern visibility) that arise from choosing the setup that best meets the small-angle criterion.