A physics team measures the angles of the first four diffraction minima produced by a single slit illuminated with light of known wavelength 550nm. Their measurements are listed below.
Measurement table (each angle has an uncertainty of ±0.2∘):
m 1 2 3 4
θ (°) 3.2 6.4 9.7 13.1
a. Part 1: Convert each measured angle to its sine value and tabulate the results, including the uncertainty in sinθ that arises from the angular uncertainty.
b. Part 2: Using the tabulated data, determine the best-fit straight line for sinθ versus the order number m. Report the slope of this line along with its uncertainty. (You may use two-point or averaged-slope methods provided the procedure is clearly shown.)
c. Part 3: From the slope obtained in part (b), calculate the slit width and its percent uncertainty.
d. Part 4: Evaluate whether the small-angle approximation is appropriate for the highest-order measurement in the data set, and discuss the impact this has on the reliability of the width you obtained.